The Application of Variable Weight Theory on the Suitability Evaluation of Urban Underground Space Development and Utilization for Urban Resilience and Sustainability

Abstract

Urban underground space (UUS) is a significant natural resource to support many aspects of city development, but it is not sustainably developed and utilized during the urbanization process. This study considered 11 conditional and two sensitive factors and combined analytic hierarchy process (AHP) and variable weight theory (VWT) for the suitability evaluation of UUS development and utilization (SEUUSD&U) by taking the Jining city planning zone (JNPZ) as a case study. The results show that mining subsidence and groundwater-related factors are critical factors, which align with the real conditions. A significant increase in the weight of shallow groundwater can be observed after applying the VWT, rising from 0.1586 to 0.2544. This may result from significant extreme values, which WVT accurately identified and therefore increased the weights. From shallow to deep UUS, both the most suitable and least suitable areas increase, rising from 32.91% to 68.20% and from 0.57% to 3.01%, respectively. Based on two sensitive factors (key urban development and ecological protection), the study area was divided into four management zones. These sensitive factors often exhibit a “barrel effect”, showing the power to either definitively affirm or veto the outcomes. More importantly, this study proposes a generalized SEUUSD&U framework comprising six key steps, with particular emphasis on three aspects: “local conditions”, “barrel effect integration”, and “adaptive management strategies aligned with the United Nations sustainable development goals (SDGs)”. We strongly recommend that this framework be highly promoted in future research and strongly encourage future studies to place greater emphasis on the ultimate goal of achieving the SDGs by 2030 during updates to models, variable weight functions, factors, and frameworks.

1. Introduction

In recent years, rapid urbanization has resulted in urban development challenges such as land scarcity, increased water consumption, environmental pollution, ecological degradation, and reduced urban resilience, which significantly impact the progress of cities towards sustainability [1,2,3,4,5]. Urban underground space (UUS), as an extension of surface space, comprises the physical geological structures beneath urban areas, including rock, soil, water, gas, and other elements [6,7]. It is a significant natural resource to support various aspects of urban development, such as infrastructure [8], land policy [3], water management [9], energy storage [10] and emergency shelters [11], which further enhances urban resilience and sustainability [12,13,14]. However, improper development and utilization (D&U) may cause severe degradation of the rock and soil environment, disrupt hydrological cycles, and negatively impact geological conditions [15]. Therefore, the suitability evaluation of UUS development and utilization (SEUUSD&U), which comprehensively incorporates hydrological, geological, environmental, ecological and anthropogenic factors, enables the prioritization of the D&U areas for UUS and provides guidance for future sustainable urban development [16,17,18,19,20].

Research on SEUUSD&U began in the 1980s, mainly focusing on the aspects of geology, hydrology, and topography [21,22,23]. However, these studies primarily relied on detailed field surveys, which are time-consuming and costly. With advancements in GIS and remote sensing (RS) technology, numerous SEUUSD&U models have been developed, integrating a wide range of factors. For instance, Lu et al. [24] employed the fuzzy-AHP and TOPSIS method to develop an SEUUSD&U model from a geological perspective, providing a foundation for land space development, project selection, and urban planning. Zhang et al. [25] established a negative list of adverse factors that affect UUS development, including limiting, constraining, and influencing factors, and assessed SEUUSD&U in Xi’an, China. Xu et al. [20] utilized the Bayesian Network and analytic hierarchy process (AHP) models to evaluate UUS resources in Changsha, China, considering geological condition, socio-economic value, and construction status, and categorizing them into four suitability levels to support urban planning decisions. Liu et al. [26] used entropy theory and CRITIC methods to develop an SEUUSD&U model in Xiong’an, China, finding that deeper layers are more suitable and identifying critical factors for effective urban planning and disaster prevention. Zhang et al. [27] presented an intelligent planning model that integrates an improved artificial intervention genetic algorithm (GA) and multiple factors to optimize SEUUSD&U in Shenzhen’s Luohu District. Similar recent studies also include Peng and Peng [6], Deng et al. [28], Hao et al. [17], Dou et al. [29] and Zhang et al. [30]. Despite the significant contributions of these studies to SEUUSD&U, research gaps remain, primarily in three areas. Firstly, current models for SEUUSD&U are inadequate due to insufficient consideration of factors such as natural disasters, groundwater conditions, current urban development conditions, and ecological conservation aspects. Secondly, the models for SEUUSD&U primarily rely on subjective weighting systems based on experts’ opinions. However, from the perspective of geological safety in urban development, the absence of dynamic weight adjustment limits the ability to prioritize safety and adapt to the changing relative importance of sub-objectives. Finally, current studies primarily focus on obtaining distribution maps; the discussion on the relationships between the D&U of UUS, urban resilience, and sustainable development is limited. Therefore, it is necessary to develop new models and frameworks for SEUUSD&U to enhance urban resilience and sustainability.

The variable weight theory (VWT) was initially proposed by Wang [31], which enables us to addresses the problem of one-sidedness in practical decision-making by establishing a variable weight function [32]. In fields such as engineering, disaster management, safety, and risk assessment, the losses caused by extreme conditions are often unacceptable (e.g., property damage and loss of life) [33,34]. Hence, the relevant standards must be stricter than those under typical scenarios in extreme conditions. VWT, which adjusts weights based on the state of sub-objectives, can play a crucial role in ensuring more effective and adaptive decision-making in these extreme conditions. Building on these advantages, VWT has been widely used for many studies, including landslide susceptibility [35,36], groundwater vulnerability [37], pipeline risk assessment [38], stope stability prediction [39], coal and gas outburst risk [33], and mine water inrush risk [40]. These areas are highly suitable for applying VWT, as the consequences in extreme conditions can be severe, and conventional weighting methods are insufficient. Moreover, these studies have fully demonstrated the improvement of performance in models with VWT by different variable weight functions. Theoretically, SEUUSD&U is highly suitable for applying VWT, particularly the incentive–penalty type of VWT. This is because stricter standards should be proposed to restrict UUS development under extremely unsuitable conditions. On the contrary, UUS development should be encouraged to adapt to the context of urbanization under highly suitable conditions. However, in terms of UUS development, VWT remains underexplored. In the recent study, Peng et al. [16] applied 15 factors (including three socio-economic factors), the AHP model and VWT to SEUUSD&U. However, this study is constrained by its small scale of study area, insufficient consideration of the groundwater, disaster, and ecological impacts, as well as a lack of discussion on the U&D of mid-level and deep-level UUSs, and insufficient linkage to urban sustainability.

Based on the identified research gaps, this study aims to adopt a novel framework that integrates AHP and VWT with a new function to conduct SEUUSD&U, focusing on the urban area of Jining city planning zone (JNPZ), China. The evaluation factors include five major aspects: topography, engineering geological conditions, hydrogeological conditions, geological environmental issues and sensitive indicators (key urban development areas and ecological protection areas), while also taking into consideration the development of mid-level and deep-level UUSs. These sensitive factors often demonstrate a “barrel effect”, which has the capacity to either decisively affirm or veto the outcomes. Finally, the relationships between SEUUSD&U and urban resilience and sustainability are explored under the framework of the United Nations’ sustainable development goals (SDGs). Specifically, the innovations of this study include the following three aspects:

• Construct a new framework for SEUUSD&U for the JNPZ, involving new factors such as groundwater, natural disasters, and barrel effects (key urban development conditions and ecological protection).
• Display the application of VWT with a new variable weight function in SEUUSD&U and propose different levels of management strategies for D&U of UUS in JNPZ, and the application of VWT in SEUUSD&U is currently very limited.
• Provide a more general framework of SEUUSD&U and explore and discuss the relationship between SEUUSD&U, urban resilience and sustainable development under the framework of SDGs.

2. Study Area

The study area, known as “Jining city planning zone (JNPZ)”, is located in the southwestern part of Shandong Province, China. In the latest Jining City 2035 plan, the study area has been designated as a core region for key development initiatives. Geographically, it ranges from 115°54′ E to 117°06′ E longitude and 34°25′ N to 35°55′ N latitude, covering a total of approximately 3561.29 km². Figure 1 shows the geology and geomorphology of the study area. The geomorphologic type is primarily characterized by plains, with higher elevation in the eastern part. The JNPZ falls within the East Asian temperate monsoon climate zone. The average annual temperature ranges from 13.3 °C to 14.1 °C, while the average annual precipitation is approximately 597 mm to 820 mm. The JNPZ has two major river basins, namely the Yellow River and the Huai River, and it includes a total of 93 rivers with a basin area of over 50 km². The eastern part of the study area is characterized by bedrock mountains, while the central part consists of the alluvial plain of the Wenshi River, and the western part is the Yellow River alluvial plain. The loose rock deposits in the study area originate from diverse transportation and deposition environments, leading to variations in groundwater occurrence, migration conditions, and hydro-chemical environments. Based on the properties of the aquifer and geological era, the main aquifers can be classified into two categories: unconsolidated rock pore water of the Quaternary-Neogene and fractured karst water of the Cambrian-Ordovician [41]. Ground subsidence and mining subsidence are significant geological environmental issues in the study area, which leads to threats to the safety and normal operation of municipal pipelines, including water supply and gas pipelines [42]. At the same time, as part of the North China Plain (NCP), groundwater usage in the JNPZ has become increasingly significant over the past few decades, making it one of the critical factors for future urban planning [43,44]. Currently, geological-related research in Jining city focuses on fields such as water resources [41], mining subsidence [45], flooding management [46], and ecosystem services [47], with limited studies addressing SEUUSD&U under the urbanization context. Given the significant economic growth and urban expansion in the JNPZ in recent years, establishing a comprehensive framework of SEUUSD&U is crucial.

3. Materials and Methods

3.1. Methodology Framework

The methodology framework of SEUUSD&U in this study is shown in Figure 2. The main process includes data collection, conditional factor selection, assessment procedure, consideration of the barrel effect, and UUS development suggestions. It should be noted that the UUS in the study area is divided into shallow level (0~−15 m), mid-level (−15~−30 m) and deep-level (−30~−50 m) according to “UUS Planning Standard” in China (GB/T 51358-2019) [48].

3.1.1. Data Collection

Seven organizations participated in the data collection for this study, and the data collection information is shown in

Table 1. Data source and factors for UUS development suitability assessment.

Conditional Factors	Sources	Format	Period
Slope (C1)	China Geological Survey Geological Cloud Platform	Grid	2022
Crustal stability (C2)	Department of Natural Resources of Shandong Province, Jinan, China	Tiff	2014
Land homogeneity (C3)	Lunan Geological Engineering Survey Institute of Shandong Province (LGESI), Jining, China	Tiff	2019
Rock and soil compressibility (C4)	Lunan Geological Engineering Survey Institute of Shandong Province	Tiff	2019
PGA (C5)	No.801 Hydrogeology and Engineering Geological Brigade of Shandong Provincial Bureau of Geology and Mineral Resources, Guiyang, China	Tiff	2017
Shallow groundwater depth (C6)	Jining Urban and Rural Water Affairs Bureau, Jining, China	Tiff	2021
Aquifer thickness (C7)	Jining Survey Institute	Tiff	2022
Aquifer water abundance (C8)	LGESI, Jining, China	Tiff	2019
Groundwater corrosiveness (C9)	LGESI, Jining, China	Tiff	2022
Mining subsidence (C10)	LGESI, Jining, China	Tiff	2021
Ground subsidence (C11)	Jining Natural Resources and Planning Bureau, Jining, China; LGESI, Jining, China	Tiff	2021

. A total of 11 conditional factors were determined for SEUUSD&U. Also, sensitive factors (key urban development areas and ecological protection areas) were sourced from the Jining Bureau of Natural Resources and Planning (https://nrp.jining.gov.cn/ (assessed on 16 August 2024)).

3.1.2. Conditional Factor Determination and Classification

The selection of factors for SEUUSD&U originated from existing studies and consultations with experts specializing in urban geology. Initially, relevant factors were gathered from the current studies. These studies include Peng et al. [16], Hao et al. [17], Xu et al. [20], Liu et al. [26], Tong et al. [49] and Lai et al. [50]. Then, the experts selected appropriate factors from this list or proposed new factors based on the geological characteristics of the JNPZ. The consultations were conducted through discussion meetings to ensure the relevance and accuracy of the selected factors. Finally, 11 conditional factors and two sensitive factors were identified, including five specific aspects as follows:

• Topography (B₁), specifically considering slope (C₁) as a key factor.
• Engineering geology (B₂), including crustal stability (C₂), land homogeneity (C₃), rock and soil compressibility (C₄), and peak ground acceleration (PGA) (C₅).
• Hydrogeology (B₃), involving factors of shallow groundwater depth (C₆), aquifer thickness (C₇), aquifer water abundance (C₈), and groundwater corrosiveness (C₉).
• Natural disasters (B₄), which comprise mining subsidence (C₁₀) and ground subsidence (C₁₁).
• Sensitive factors, including key urban development areas and ecological protection areas.

For the scoring of factors, all the conditional factors were categorized into different sub-categories based on relevant standards, existing studies, the characteristics of the JNPZ, and expert opinions. The factor maps were generated using ArcGIS 10.8.

Topography

Slope plays a critical role in urban surface layout, groundwater flow direction, road alignment, and street distribution [51,52]. This influence is particularly marked in mountainous urban areas, impacting various aspects of UUS development such as alignment, engineering methods, construction difficulty, costs, and economic viability [6]. Areas with steeper slopes often face greater challenges for UUS development. In the JNPZ, slopes were categorized into three groups: <5°, 5–15° and >15° (Figure 3). This classification primarily references actual conditions and Tan et al. [53].

Engineering Geology

The size, type, activity level of faults, and the surrounding geological environment are key factors influencing crustal stability [54,55,56]. In this study, we combined the Chinese local standard DB41/T 2120-2021 (Technical Specification for Evaluation of Geological Environment Suitability for Urban Underground Space Development) [57] and adjusted it based on actual conditions in the JNPZ. Additionally, we referred to the study by Xu et al. [58], GB 50011-2010 (Code for Seismic Design of Buildings) [59] to design the fault classification criteria shown in

Table 2. Crustal stability classification standard in the JNPZ.

Exposed Faults			Concealed Faults (m)	Crustal Stability
Major Faults (m)	Other Faults (Near Unfavorable Areas) (m)	Other Faults (m)
0–500	0–300	0–200	/	High
500–1000	300–1000	200–1000	/	Relatively high
1000–2000	1000–2000	1000–2000	0–1000	Relatively low
>2000	>2000	>2000	>1000	Low

as standards for crustal stability evaluation factors. Major faults were derived from the study by Xu et al. [58] (1:4,000,000), while other faults were sourced from geological maps at a 1:200,000 scale. Unfavorable areas specifically include prominent headlands, isolated steep hills, steep slopes of non-rock or highly weathered rock, riverbanks, and slope edges, as these features may amplify the impact of faults on crustal stability.

Rock and soil compressibility reflects their load-bearing capacity, where lower compressibility indicates higher load-bearing capacity [60]. This results in simpler construction support measures, greater stability of underground structures, and lower construction costs. However, excessive rock strength can increase excavation difficulties, which is unfavorable for excavation methods and engineering costs [61]. In this study, the compressibility classification of rock and soil masses was determined and modified based on GB 50011-2010 (Code for Seismic Design of Buildings) [62] using shear wave velocity ($V_s$) and bearing capacity ($f_{ak}$), as shown in

Table 3. Rock and soil compressibility classification standard.

Shear Wave Velocity (m/s)	Soil Types	$\mathbf{Bearing} \mathbf{Capacity} {\mathit{f}}_{\mathit{a}\mathit{k}}$ (kPa)	Rock and Soil Characteristics	Compressibility Rating
$V_s$ ≤ 150	Soft soil	$f_{ak}$ ≤ 130	Silt and silty soils, newly deposited cohesive and silt soils, plastic loess	High
150 < $V_s$ ≤ 250	Medium-soft soil	130 < $f_{ak}$ ≤ 160	Loose fine, silt, plastic silt	Moderate
		160 < $f_{ak}$ ≤ 200	Slightly dense coarse and medium sand, fine and silty sand except loose, plastic loess	Low
$V_s$ > 250	Medium-hard soil (including bedrock)	$f_{ak}$ > 200	Bedrock, gravel soil, dense, medium-dense gravel, coarse, medium sand, cohesive soil and silt, hard loess	Extremely low

. The map of rock and soil compressibility (Figure 4b) is based on extensive engineering geological surveys and field investigations and was generated using Kriging interpolation in ArcGIS 10.8.

PGA refers to the highest level of ground acceleration experienced during an earthquake [63]. It serves as a critical factor in assessing building seismic resistance, as higher values imply greater risks of catastrophic incidents, making these areas unsuitable for UUS development [64]. The vector data for PGA were provided by the No. 801 Hydrogeology and Engineering Geological Brigade of the Shandong Provincial Bureau of Geology and Mineral Resources, primarily based on the seismic ground motion parameters zonation map of China (GB 18306-2015) [65] (https://www.gb18306.net/ (assessed on 16 August 2024)). Overall, the PGA in the Jining City Planning Zone (JNPZ) is relatively low. Following the standard of GB 50011-2010 and local experts’ opinions, areas with PGA values below 0.1 g are defined as stable zones, while those with values between 0.1 g and 0.15 g are classified as relatively stable zones. The symbol g represents gravitational acceleration, and the map of stability classified based on PGA is shown in Figure 4c.

Moreover, land homogeneity is an important factor: it affects engineering stability and facilitates construction in UUSs [66]. High land homogeneity enhances stability and simplifies construction processes. The map of land homogeneity classification is shown in Figure 4d, and high, moderate and low homogeneity correspond to single-layer, dual-layer, and multi-layer soil structures within 50 m, respectively. These classifications were based on borehole and geological survey data and interpolated using ArcGIS 10.8. The overall land homogeneity in the study area is relatively low. The subsurface soil within 50 m consists of multiple layers, largely due to the study area’s location in a plains region dominated by Quaternary strata.

Hydrology

Groundwater depth inversely affects D&U of UUS, with shallower depths causing greater impacts [15]. Groundwater influences underground construction, and may cause challenges during excavation, dewatering, and waterproofing processes [67]. It can also cause seepage damage, slope instability, and potential hazards like quicksand gushing [68]. The depth at which groundwater is encountered significantly affects the D&U of underground structures (e.g., stability, durability, and water leakage). In this study, groundwater depth was divided into four groups (>12 m, 9–12 m, 6–9 m and <6 m) based on borehole data and interpolated using ArcGIS 10.8 (Figure 5a).

Aquifer water abundance is a factor used to quantify the water richness of an aquifer, which is related to the risk of water inrush in the process of engineering D&U [69,70,71]. Based on hydrogeological maps and drilling data, the aquifer in the JNPZ consists of alternating fine sand and clay layers, with five to eight layers and a thickness of 30–50 m. Central areas have good water abundance (3000–5000 m³/day), while northern regions exhibit high water abundance (>5000 m³/day). In contrast, southwestern hilly and southeastern mountainous areas have lower water abundance (<1000 m³/day) (Figure 5b).

Greater aquifer thickness increases the likelihood of water inrush, which may result in safety hazards, and affect construction processes in UUS D&U [70]. In this study, aquifer thickness was categorized as follows: <20% of layer thickness as low thickness zones, 20–40% as medium thickness zones, 40–60% as high thickness zones, and >60% as extremely high thickness zones. By the depth of UUS, aquifer thickness can be divided into shallow aquifer thickness (0~−15 m) (Figure 5c), middle aquifer thickness (−15~−30 m) (Figure 5d) and deep aquifer thickness (−30~−50 m). The mapping process was based on hydrogeological borehole and geophysical borehole data, and interpolation was performed using ArcGIS 10.8 (Figure 5e).

Evaluating the corrosiveness of groundwater on construction materials in UUSs is crucial for ensuring their durability and integrity. This study follows the provisions of the revised Code for Investigation of Geotechnical Engineering in China (GB50021-2001, 2009 revision) to assess groundwater corrosiveness. The evaluation classifies groundwater corrosiveness into four levels: extremely low, low, moderate, and high. Specific evaluation criteria for concrete structures and reinforced concrete structures consider factors such as sulfate content, formation permeability, and the presence of soft water. The evaluation was conducted in the JNPZ using samples from 114 groundwater quality monitoring points, and the resulting corrosiveness evaluation is presented in Figure 5f.

Natural Disasters

Unregulated D&U of UUS during urban mining development has caused extensive subsidence areas, leading to significant safety hazards and severely constraining the stable development of the urban geological environment in Jining city [42,72,73]. By analyzing the mining conditions of 14 major coal mines in the study area, the developed areas of mineral resources are classified into four sub-classifications: high possibility (developed mining areas), moderate possibility (reserved development mining areas), low possibility (mining area boundary), and very low possibility (other areas) (Figure 6a).

Ground subsidence in urban areas significantly affects the D&U of UUS because of the compaction of soil due to water pressure generated by groundwater extraction, which leads to risks to the stability of underground structures [74,75]. In the study area, ground subsidence is observed, with most areas classified as slow subsidence zones, experiencing rates of 10–30 mm/year. Some regions are categorized as medium-speed subsidence zones, with subsidence rates of 30–50 mm/year, while no significant subsidence zones are identified (Figure 6b).

Sensitive Factors

Key urban development areas and ecological protection areas are identified as two sensitive factors in this study (Figure 7). Key urban development areas represent the current state of urban construction. As per the existing plan, UUS within these regions is designated for development. In contrast, ecological protection areas, which encompass geological relics, ecological protection red lines, and basic farmland, are strictly prohibited for development. These two sensitive factors are evaluated separately for their impact on the suitability of UUS D&U after the evaluation of the previous four categories of factors.

3.1.3. Score Determination of Different Levels of Conditional Factors

Scores are assigned to different levels of each factor based on prior analysis of the factors in Section 3.1.2. For the conditional factors with four levels, scores of 0.1, 0.4, 0.7, and 1 are assigned, while for the three levels, scores of 0.1, 0.55, and 1 are assigned (

Table 4. Classification criteria and scores for different conditional factors.

Conditional Factors	Classification Criteria
	Good		Poor
Crustal stability	High	Relatively high	Relatively low	Low
Rock and soil compressibility	Extremely low	Low	Moderate	High
Shallow groundwater depth	Deep	Moderate	Shallow	Extremely shallow
Aquifer thickness	Low	Moderate	High	Extremely high
Aquifer water abundance	<1000 m3/d	1000–3000 m3/d	3000–5000 m3/d	>5000 m3/d
Groundwater corrosiveness	Extremely low	Low	Moderate	High
Mining subsidence	Very low possibility	Low possibility	Moderate possibility	High possibility
Ground subsidence	Stable	Slow speed	Medium speed	High speed
Score (xi)	0.1	0.4	0.7	1
Slope	<5°	5–15°		>15°
PGA	<0.1 g	0.1–0.15 g		>0.15 g
Land homogeneity	High	Moderate		Low
Score (xi)	0.1	0.55		1

). A higher score indicates that classification contributes less to the suitability of UUS D&U.

3.2. Models

The modeling process in this study consists of three components: initial weight determination by the AHP model, the application of VWT, and weighted sum model (WSM) for the final comprehensive index calculation. Figure 8 shows the detailed process of using these models.

3.2.1. AHP Model

The AHP model, introduced by Saaty, is a multi-criteria decision analysis (MCDA) technique that incorporates both subjective expert opinions and objective comparative analysis into the decision-making process [76]. It employs a scale from 1 to 9 to assess the relative importance of comparison factors, enabling the determination of factor weights based on expert knowledge [77]. To ensure consistency in the weights obtained from the AHP model, the consistency ratio (CR) is calculated using Equations (1) and (2). A CR value below 0.1 indicates the reliability of the weights derived from the AHP model [78,79].

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

(1)

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

(2)

where $CI$ and $RI$ refer to consistency index and random index, respectively, ${\lambda }_{max}$ is the maximum eigenvalue, and $n$ is the total number of conditional factors. The calculation of $RI$ is shown in

Table 5. RI values calculation.

$\mathit{n}$	1	2	3	4	5	6	7	8	9	10
$RI$	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49

.

In this study, AHP scoring was conducted separately for the shallow UUS and unified for the middle and deep UUSs. To reduce the subjectivity of AHP model assessment, we invited six experts with relevant background in this process. We firstly invited Professor Chuanming Ma from China University of Geosciences (Wuhan) to establish the initial pair-wise comparison matrix through a questionnaire. Professor Ma has made significant contributions in the fields of hydrogeology, urban geology, environmental geology, UUS development and protection, as well as land planning, making him highly suitable as an expert for determining the AHP in this study. To ensure the rationality of the weights and their alignment with local conditions, we invited five local experts (Xia Hua, Henghua Zhu, Keyin Feng, Jiping Shou and Zhenrun Wei) to evaluate the matrix and weights via a Tencent Meeting, with Professor Ma also participating in the discussions. The five local experts have extensive backgrounds in the D&U of UUS, and participated in many projects related to hydrogeology, engineering surveys, urban planning, and geological disaster prevention. The finalized matrix was determined through this process, and the calculation process of the AHP weights is detailed in Appendix A.

3.2.2. Variable Weight Theory (VWT)

In the AHP method, the weights of factors are typically assumed to remain constant, regardless of changing circumstances. However, factors with extreme values can significantly influence the evaluation results [33,80,81]. This study introduces the VWT (incentive–penalty type) to adjust the weights of factors based on their values, aiming to better reflect the actual circumstances. We constructed the variable weight function in Equation (3) by referencing the study of Mao et al. [82]. Let the variable weight vectors, denoted as $S_i\left(x\right)$ in Equation (3), be $S_1\left(x\right)$ in the incentive interval, $S_2\left(x\right)$ in the constant interval, $S_3\left(x\right)$ in the penalty interval, and $S_4\left(x\right)$ in the strong penalty interval, with smooth and continuously differentiable connections at the connecting points (0, $d_1$), ($d_1$, $d_2$), ($d_2$, $d_3$), and ($d_3$, 1). The selection of these parameters depends on actual conditions and expert opinions. Under the constraint 0 < $d_1$ < $d_2$ < $d_3$ < 1, $d_1$ and $d_2$ determine where the incentive and penalty begin, and $d_3$ defines the point at which the penalty transitions to a different form. $a_1$, $a_2$, $a_3$ represent the evaluation strategies, which determine the extent of incentives and penalties. $c$ represents the adjustment coefficient and ensures the continuity of the function.

$$S_i(x_i)\left\{\begin{array}{c}{e}^{a_1(d_1-x_i)}+c-1,\hspace{1em} 0\le x_i\le d_1\\ c,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} d_1<x_i\le d_2\\ e^{a_2(x_i-d_2)}+c-1, d_2<x_i\le d_3\\ e^{a_3(x-d_3)}+e^{a_2(x-d_2)}+c-2, d_3<x_i\le 1\end{array}\right.$$

(3)

The calculation of the variable weight vector is shown in Equation (4).

$$w_i^{\prime }={\displaystyle \frac{w_i{s}_i}{{\sum }_{i=1}^n{w}_i{s}_i}}$$

(4)

where $x_i$ represents the value of the $i^{th}$ factor, $s_i$ denotes the state variable weight vector of the $i^{th}$ factor, $w_i$ represents the constant weight vector of the $i^{th}$ factor, and $w_i^{\prime }$ represent the variable weight vector of the $i^{th}$ factor.

Through the trial-and-error method, we compared the results with actual conditions and expert evaluations to select suitable parameters. While these results may not necessarily be optimal, they represent an improvement over the AHP approach. Finally, the following parameter assignments are obtained for the study area: $a_1$ = 4, $a_2$ = 2.6, $a_3$ = 0.34, $c$ = 1.4, $d_1$ = 0.25, $d_2$ = 0.5, $d_3$ = 0.75. Therefore, the equation of variable weight vector becomes Equation (5). Figure 9 partly shows the process we followed using the trial-and-error method.

$$S_i(x_i)\left\{\begin{array}{c}{e}^{4(0.25-x)}+0.4, 0\le x\le 0.25\\ 1.4, 0.25<x\le 0.5\\ e^{2.6(x-0.5)}+0.4, 0.5<x\le 0.75\\ e^{0.34(x-0.75)}+e^{2.6(x-0.5)}-0.6, 0.75<x\le 1\end{array}\right.$$

(5)

3.2.3. Weighed Sum Model

Based on the weights calculated by VWT and classification scores, shown in Table 3, a weighted sum model was used to calculate the comprehensive index for urban underground suitability in the study area (Equation (6)).

$$Comprehensive index={\sum }_{i=1}^n{w}_i^{\prime }{x}_i$$

(6)

where $n$ is the number of conditional factors, $w_i^{\prime }$ represent the variable weight vector of the $i^{th}$ factor, and $x_i$ represents the value of the $i^{th}$ factor.

3.2.4. Barrel Effects in SEUUSD&U

The SEUUSD&U may occasionally be influenced by the “barrel effect” under certain conditions. For instance, in areas of ecological environment protection, even if other conditions meet high suitability requirements, the development of UUS is still limited in these area, thereby affecting the overall suitability score of the region [83]. Therefore, it is necessary to combine these sensitive indicators into SEUUSD&U. In this study, key urban development areas and ecological protection areas are selected as the sensitive indicators with the consideration of “barrel effect”.

4. Results and Discussions

4.1. Weights Determined by AHP Model and AHP-VWT Model

Table 6. Weights determined by AHP and AHP-VWT models.

Conditional Factors	AHP Model		AHP-VWT Model
	Shallow UUS	Middle and Deep UUS	Shallow UUS	Middle UUS	Deep UUS
C1	0.0688	-	0.0691	-	-
C2	0.0991	0.1334	0.0990	0.0885	0.1426
C3	0.0495	-	0.0300	-	-
C4	0.0833	-	0.0895	-	-
C5	0.0589	0.0686	0.0477	0.0722	0.0543
C6	0.1013	-	0.2365	-	-
C7	0.0544	0.1603	0.0546	0.1686	0.1829
C8	0.1586	0.2544	0.1005	0.2676	0.1830
C9	0.1205	-	0.0763	-	-
C10	0.1542	0.2722	0.1451	0.2863	0.3105
C11	0.0514	0.1111	0.0516	0.1169	0.1267

shows the weights determined by the AHP and AHP-VWT models for shallow, middle, and deep UUS, respectively, while Figure 10 shows the comparison of weights between the two models. Several important findings have been identified. Firstly, both the AHP and AHP-WVT models identify mining subsidence as a critical conditional factor, aligning well with local conditions. Jining city, known for its rich mineral resources, has experienced frequent mining subsidence due to excessive extraction, making this factor particularly significant in the study area [42,73,84,85,86]. Secondly, the significant increase in the weight of shallow groundwater levels using the AHP-WVT model is an important observation. This suggests that the groundwater level factor has significant extreme values (particularly at very shallow depths), while the AHP-WVT model accurately identifies and assigns increased weights accordingly. By increasing the weights of shallow groundwater levels, issues such as groundwater seepage and structural instability caused by excessively high groundwater levels can be better addressed. In contrast, for land homogeneity, PGA and aquifer thickness, their weights remain relatively low even after applying WVT, which indicates that these factors are mainly distributed within moderately suitable areas, with fewer extreme values. Thirdly, compared to other types of indicators, hydrological factors, including shallow groundwater depth, aquifer thickness, aquifer water abundance, and groundwater corrosiveness, are crucial. This adequately reflects the impact of groundwater on UUS D&U. These impacts may include altering construction techniques, increasing operational costs, and requiring enhanced waterproofing measures, all of which necessitate more robust structural designs [87,88,89,90], which should be carefully considered in future SEUUSD&U studies. Finally, we observed that the weights of conditional factors for middle and deep levels are identical based on the AHP model. This indicates that subjective expert judgments fail to sufficiently differentiate the impacts of these indicators on UUS D&U at different depths. Finally, compared to the widely used AHP model in many studies [18,19,30,91,92], integrating WVT allows for effectively accounting for extreme values based on actual conditions and dynamically adjusted weights. In the context of UUS suitability evaluation, this approach ensures stricter standards of highly unsuitable areas while expanding the planning area for highly suitable areas. This is particularly well-suited for SEUUSD&U against a background of urbanization. However, studies applying the AHP-VWT model to UUS are still limited. A notable example is Peng et al. [16], who utilized this model for SEUUSD&U in Changjiang New Town, China. Building upon their work, this study improves the indicator system and variable weight function and incorporates considerations for mid-level and deep-level UUSs. We also strongly encourage future studies to explore the integration of VWT in UUS-related research.

4.2. Maps of SEUUSD&U with Conditional Factors and Sensitive Factors

Figure 11 shows the maps of SEUUSD&U for shallow, middle and deep UUS, respectively, by AHP-VWT. The equal interval method was used to divide the map into four classifications: very high suitability, high suitability, poor suitability and very poor suitability.

Table 7. Areas and proportion of UUS in different classifications.

UUS Suitability		Very High	High	Relatively Poor	Poor
Shallow	Area (km2)	1171.96	1825.36	543.54	20.43
	Proportion (%)	32.91	51.26	15.26	0.57
Middle	Area (km2)	2541.59	596.91	360.34	62.45
	Proportion (%)	71.37	16.76	10.12	1.75
Deep	Area (km2)	2428.54	685.84	339.56	107.35
	Proportion (%)	68.20	19.26	9.53	3.01

shows the area and proportion information of UUS. Generally, the UUS in the JNPZ has good suitability and great potential for development. The areas of high suitability and very high suitability in shallow, middle and deep UUS are much larger than poor and very poor suitability areas. However, the suitability of the shallow UUS is lower than that of the middle UUS, and the areas of very high suitability reached 1171.96 km². This may be attributed to the significant increase in the weight of the shallow groundwater level after applying VWT. Additionally, the areas of very poor suitability increased with increasing underground depth. For deep UUS, it reached 107.35 km². However, factors such as cost and development demands should also be considered in future UUS development planning.

When considering two sensitive factors with barrel effects (key urban development and ecological protection) in SEUUSD&U, the maps shown in Figure 12 are obtained. The study area is divided into four sections: key construction area, suitable construction area, conditional construction area, and restricted construction area. Based on these results, decision-makers can propose UUS development strategies for different levels. Here, we provide an example for each level, and the detailed development strategy examples are presented in Appendix C. The strategies developed here can serve as valuable references for similar zoning efforts in other study areas.

We compared this result with the current research [41] and Jining city development map (2014–2030), and it was evaluated by experts in a review meeting. The results align with the groundwater function zonation and future planning requirements of Jining city, which validates the model’s reliability. The Jining city development map (2014–2030) and groundwater function zonation is provided in Appendix D. These sensitive factors often exhibit a “barrel effect”, which shows the power to either definitively affirm or veto the outcomes. In fact, in urban construction planning, many factors may have a “barrel effect”, including but not limited to ecological protection areas, permanent basic farmland, flood-prone areas, active fault zones, natural heritage, and groundwater source protection zones. This study selects two typical sensitive factors as examples, and we encourage future research to effectively incorporate more “barrel effect” factors into SEUUSD&U studies.

4.3. The Modified Framework of SEUUSD&U and Correlation with SDGs from a Management Perspective

While extensive case studies on SEUUSD&U have been conducted, a standardized framework for its implementation is still lacking. Therefore, building on the case of JNPZ and incorporating the studies of Peng et al. [16], Hao et al. [17], Xu et al. [20], Liu et al. [26], Tong et al. [49], this study proposes a SEUUSD&U framework based on barrel effects, adaptable to various scenarios for managing UUS (Figure 13). This framework comprises six key steps, and compared to existing frameworks, this study emphasizes and improves upon three key aspects. Firstly, we emphasized “local conditions” in step 1. This study combined the factors from existing studies while incorporating the unique characteristics of Jining city during the evaluation, such as the impacts of groundwater and subsidence. Identifying the factors that precisely reflect the characteristics of the study area represents a fundamental and essential step in SEUUSD&U. In fact, this issue has also been highlighted in many spatial distribution evaluations [93,94]. The second point is the emphasis on barrel effects within this framework. As highlighted in the study of Zhang et al. [95] and Huang et al. [96] on geological disasters, as well as the various scenarios discussed in Section 4.2, it is a fact that some sensitive factors can definitively affirm or veto the assessment results. This study identified key urban development and ecological protection as examples, but such factors widely exist in the context of UUS development. Therefore, these sensitive factors should receive greater consideration in SEUUSD&U, with barrel effects established as a critical step in future evaluation frameworks. The third aspect is the “adaptive management strategies towards SDGs” highlighted in Step 5. Adaptive management emphasizes that management strategies should evolve in response to changes in indicators and real-time evaluation results [97,98,99,100,101]. Although numerous studies have emphasized the close relationship between UUS development and the SDGs [102,103,104], limited existing SEUUSD&U frameworks have incorporated the SDGs as a core consideration. While this study does not fully achieve this, we advocate for future frameworks and urban underground space management to better integrate the SDGs. For example, specific SDG targets can be incorporated as conditional factors into SEUUSD&U frameworks.

To support future research, we outline the relationship between D&U of UUS and the SDGs (

Table 8. The relationship between D&U of UUS and the SDGs.

No.	Goals	Interpretation
SDG 1	No Poverty	Contributes by enabling cost-effective underground infrastructure development, providing affordable housing and essential services, reducing urban inequality.
SDG 6	Clean Water and Sanitation	Proper evaluation ensures groundwater protection during the D&U of UUS, minimizing water contamination and enhancing access to clean water.
SDG 9	Industry, Innovation, and Infrastructure	Supports sustainable infrastructure projects, integrating innovative underground space solutions to enhance urban functionality and resilience.
SDG 11	Sustainable Cities and Communities	Links UUS development with sustainable urban planning, reducing surface space congestion, and fostering inclusive and resilient cities.
SDG 13	Climate Action	Encourages climate-resilient underground projects, mitigating heat islands, and protecting urban areas from extreme weather impacts.
SDG 15	Life on Land	Protects ecosystems by restricting UUS development in sensitive ecological zones, promoting harmony between urban growth and natural landscapes.

). Six key goals were highlighted, including SDG 1 (No poverty), SDG 6 (Clean water and sanitation), SDG 9 (Industry, innovation, and infrastructure), SDG 11 (Sustainable cities and communities), SDG 13 (Climate action), and SDG 15 (Life on land). Moving forward, management strategies should adopt a more holistic perspective, grounded in overarching sustainable development objectives. By analyzing the intrinsic linkages between SEUUSD&U and the SDGs and integrating these goals into evaluation frameworks and management strategies, future research and policy can provide a clearer pathway for leveraging UUS to address global sustainability challenges, ensuring that urban development aligns with long-term ecological, social, and economic goals.

4.4. Limitations and Future Research

This study has five primary limitations. Firstly, although the selection of factors considers current urban construction conditions and represents the degree of economic and social development to some extent, it does not incorporate more demand-driven factors such as GDP and population density, which might provide a more comprehensive economic and social perspective. Secondly, while employing a novel VWT combined with the AHP, a better approach would have been to compare the outcomes under different variable weight functions to validate and refine the model. Thirdly, although there is a parameter tuning process through a trial-and-error method in the variable weight model, it is unlikely that the most optimal parameters were achieved. In fact, determining the optimal parameters for the variable weight function has always been a significant challenge in the application of VWT. Fourthly, we primarily used interpolation methods to generate indicator maps in data processing, without accounting for spatial heterogeneity, which may introduce errors. Finally, during the classification of factors and AHP scoring, we placed greater emphasis on expert opinions, particularly regarding the use of uniform distance thresholds for crustal stability. The classification and scoring process may inherently involve some subjectivity. Despite these limitations, the innovative use of a new variable weight function with AHP to construct the WVT-AHP model, combined with the barrel effect and SDGs, introduces a significant new framework that makes a substantial contribution to the field of SEUUSD&U. Future directions are various, including developing more SEUUSD&U models for more study areas with complex conditions, comparing the effects of different variable weight functions on SEUUSD&U outcomes, promoting the proposed framework in this study, developing the framework with additional conditional (particularly in natural disasters and groundwater aspects) and sensitive factors, and expanding discussions on how SEUUSD&U can enhance urban resilience and achieve SDGs.

5. Conclusions

UUS supports many aspects of city development, and further enhances urban resilience and sustainability. SEUUSD&U is a crucial tool that enables us to prioritize the D&U areas for UUS and guide future sustainable urban development. This study introduces a new framework with 11 conditional and two sensitive factors, combining AHP and VWT for SEUUSD&U in JNPZ, and the key conclusions are as follows:

Firstly, mining subsidence and groundwater-related factors, identified as critical conditional factors, align with the local context of Jining city. In particular, the weight of shallow groundwater levels increased significantly after applying the WVT. This highlights the importance of fully considering local conditions in the evaluation framework. It also reflects the presence of extreme values in shallow groundwater levels, which the variable weight model effectively identified and adjusted by increasing the weight of this factor. Natural disaster and groundwater-related factors should receive greater attention in future SEUUSD&U. Additionally, further promotion and comparison of the application of VWT in UUS research are encouraged.

Secondly, the UUS in the JNPZ has good suitability and significant potential for development, with deeper levels showing higher suitability than shallow levels. However, factors such as cost and development demands should also be considered in future UUS development planning. By integrating two sensitive factors (key urban development conditions and ecological protection), we categorized the JNPZ into key construction areas, suitable construction areas, conditional construction areas, and restricted construction areas. These sensitive factors, demonstrating the barrel effect, should be individually considered in the construction of future SEUUSD&U systems. However, the examples provided in this study are not sufficient to include all factors having the barrel effect. Other potential factors include, but are not limited to, ecological protection areas, permanent basic farmland, flood-prone areas, active fault zones, natural heritage, and groundwater source protection zones. We encourage further exploration of additional sensitive factors beyond the two mentioned in this study.

Finally, we propose a more generalized SEUUSD&U framework comprising six key steps, with particular emphasis on three aspects: “local conditions”, “barrel effect integration”, and “adaptive management strategies towards SDGs”. Although numerous studies have emphasized the close relationship between UUS development and the SDGs, only limited existing SEUUSD&U frameworks have incorporated the SDGs as a core consideration. We encourage the broader application of this framework, and we also strongly encourage future studies to increasingly consider the ultimate goal (achieving SDGs by 2030) during the updates of models, factors, and frameworks in the field of SEUUSD&U.