Stability-Level Evaluation of the Construction Site above the Goaf Based on Combination Weighting and Cloud Model

Abstract

Mineral resource-based cities have formed a large number of goafs due to the long-term mining of coal. It is of great significance to make full use of the abandoned land resources above the goaf to promote the transformation and development of resource-based cities. In order to avoid the threat of surface residual deformation to the proposed construction project, it is an urgent problem to obtain the stability results of the construction site accurately. First of all, based on the principles of relevance, hierarchy, representativeness and feasibility of index selection, 10 indexes are selected to construct the stability evaluation index system. Then the subjective weight and objective weight of evaluation indexes are determined based on improved AHP, rough set and CRITIC methods, which improves the accuracy of the determination of the index weights. In addition, the membership degree of each index is determined using the cloud model. Finally, the stability grade can be obtained according to the maximum membership degree theory. The above researches are applied to evaluate the stability of the Mianluan expressway construction site, and the results show that the stability level of the study area is not uniform and that there are two states: stable and basically stable. Finally, a sensitivity analysis of the subjective weight of each index is carried out, the index stopping time has the highest sensitivity to weight (12.44%), which is far lower than the corresponding weight change rate of 100%, indicating that the determination of weight is scientific and reasonable. These things considered, the reliability of the evaluation result is indirectly verified according to the field leveling. This research can provide a reference for the effective utilization of land resources above an old goaf.

1. Introduction

As the supplying place of basic energy, mineral-resource-based cities have made great contributions to China’s economic and social development [1,2]. The goafs formed by the long-term mining of coal occupy a number of land resources and restrict the development of cities [3,4]. If the land resources above a goaf can be reasonably developed and utilized, it can not only reduce the waste of resources and turn waste into treasure but also help to promote the transformation and development of resource-based cities [5,6]. For example, the InterContinental Shimao Wonderland Hotel in Shanghai is the first natural ecological hotel built on an abandoned goaf site in China [7], the Dawang Mountain Mine Pit in Changsha has been turned into an ice and snow theme park and a water park according to its geological conditions and regional development characteristics [8], and the Jiaozuo Seam Mountain National Mine Park is a comprehensive mine park that focuses on displaying the landscape of coal mining relics [9]. When a building is built over a goaf, the internal rock strata will produce secondary deformation under the action of building load stress, which will lead to residual deformation on the surface and damage to the building [10,11], including road damage and house cracking, as shown in Figure 1. Therefore, the study on the stability of the construction site above a goaf is the basis for the reuse of land resources above abandoned goafs [12,13].

Many scholars have carried out research around this topic using to different theories. By analyzing the overburden failure and structure formation conditions, Bai et al. (2022) proposed a regional division method and concluded that the residual surface deformation of a goaf was closely related to the mining time [14]. Xu et al. (2023) evaluated the stability of a goaf through numerical simulations, and then classified the suitability of the site based on the simulation results and proposed different ecological restoration schemes [15]. Kalantari et al. (2023) combined a finite element method with a geostatistical method and evaluated the influence of borehole location on the stability of a sloped construction site by selecting effective soil parameters with significant influence [16]. Jia et al. (2022) combined field monitoring data with numerical simulation to achieve deformation and failure of a goaf over time and made a comprehensive evaluation of its stability [17]. Tao et al. (2022) selected 15 indexes to analyze the site selection for the development and utilization of abandoned goafs, obtained the weight of the indexes by using a triangular intuitionistic fuzzy number and then determined the optimal site-selection decision-making framework by using the multi-criteria decision theory [18]. Dai et al. (2022) established an evaluation system for the stability of a goaf based on AHP and conducted a case study by obtaining evaluation cloud maps through cloud models. The evaluation results were consistent with reality, which could provide reference for the subsequent management work [19].

The above methods have achieved good evaluation results, but the numerical simulation is too complex, the workload is large, and the evaluation results rely too much on the reliability of the parameters. The mathematical methods are easily affected by subjective factors in the process of evaluation, ignoring the randomness of the system. Considering that the stability evaluation of a construction site is a complex nonlinear problem, nonlinear scientific theory can scientifically assess the risk of complex fuzzy system engineering.

It should be noted that when solving problems with nonlinear science, the weights and memberships are important parameters to determine the correctness of the evaluation results; however, the existing index weight determination method is singular, and only comprehensive weight can more comprehensively express the importance of the indexes. The memberships are determined by expert experience in the past, and it is highly subjective. At the same time, how to determine the level of stability scientifically and reasonably also needs to be solved at present. The normal cloud model can unify the randomness of the evaluation index and improve the accuracy and reliability of the results.

In view of this, this paper will firstly build a construction site stability evaluation index system combined with the existing research and use improved AHP, rough set and CRITIC to weigh the evaluation index subjectively and objectively, and finally, it will be based on the normal connection cloud theory, which will establish a set of stability evaluation models. The model will conduct a case study for the Mianluan Expressway construction site to better illustrate the superiority of the proposed method.

2. Study Area

The Mianluan Expressway is one of the 10 routes in the planning and adjustment scheme of the expressway network in Henan Province. The route adopts the technical standard of a four-lane highway. The section K4 + 800~K8 + 150 from Mianchi to Luoning passes through 14 working faces of the Qianqiu coal mine, and the length of the route above the mine field is 3.35 km in total (Figure 2).

The terrain of Qianqiu is relatively undulating and the thickness of the stratum is 31.89 to 76.66 m. The surface is mostly covered by Quaternary brown-red clayey, there are near north-south trending valleys being developed, and the dip angle of the coal seam is 11~13°. In addition, it is a high gas mine with simple structure and is a medium hydrogeological type; the main coal seam is relatively stable.

3. Methodology

In this paper, an evaluation index system is constructed firstly, and the comprehensive weight is obtained based on the improved AHP, rough set and CRITIC methods. Then, the cloud model is applied to determine the stability level of study area, and finally, the evaluation results are verified. The research framework is shown in Figure 3.

3.1. Construction of Index System

There are many indexes related to the stability of a construction site [20]. According to the site conditions of the research area and through combing the relevant literature, the evaluation indexes are selected based on relevance, hierarchy, representativeness and feasibility [21,22,23,24]. Therefore, 10 indexes such as structural complexity, mining method and relative position are selected, as shown in Figure 4. In order to better evaluate the construction site, the stability level is divided into grades I, II, III and IV, representing stable, basically stable, under stable and unstable, respectively [25]. According to the relevant literature combined with the actual situation of the study area, the corresponding grade standard of each evaluation index is determined, as shown in

Table 1. Grading standard of evaluation index.

Group	Index	Stable (I)	Basically Stable (II)	Under Stable (III)	Unstable (IV)
Qualitative indexes	Score	0–0.25	0.25–0.5	0.5–0.75	0.75–1
	C1	Simple structure	Simple, slightly structured	Complex structure	Extremely complex structure
	C2	Weak-weak	Hard-weak	Weak-hard	Hard-hard
	C3	No water seepage	Little water seepage	Stagnant water area	Large stagnant water area
	C4	Longwall mining	Shortwall mining	Extra-thick top caving mining	Horizontal seam mining
	C5	Slow compressive creep	Strength decay creep	Strength attenuation structural instability	Structural instability disturbed by external forces
	C6	No load disturbance	Not affected by the water-conducting fracture zone	Tangential to the height of the water-conducting fracture zone	Spread to the interior of the water-conducting fracture zone
Quantitative indexes	C7 (°)	0–8	8–25	25–45	45–65
	C8	400–600	200–400	50–200	0–50
	C9 (y)	8.5–40.5	5.5–8.5	3.5–5.5	0.5–3.5
	C10	0–0.25	0.25–0.5	0.5–0.75	0.75–1

.

3.2. Index Weight Determination

After constructing the evaluation index system, due to the different degrees of influence of any index on the results and in order to fully reflect the importance of a single indicator in the evaluation model, corresponding weights to each index according to its importance degree need to be assigned. The weights of indexes are directly related to the overall evaluation results. Therefore, how to obtain the index weight reasonably and scientifically is another problem that needs to be solved in this paper.

3.2.1. Improved AHP

AHP determines the subjective weight by constructing the judgment matrix. If the matrix does not satisfy the consistency test, it needs to reconstruct the judgment matrix, which greatly increases the workload [26]. Therefore, this paper improves the AHP based on the weight coefficient, establishes the judgment matrix through the optimal transfer matrix, removes the consistency-check process, and avoids the possible inconsistency problem [27].

1. Judgment matrix. The improved AHP makes pairwise comparisons of the importance of evaluation indexes and uses a 1–9 scale (

Table 2. 1–9 Scale table.

Scale	Meaning
1	Equally important
3	Slightly more important
5	Obviously more important
7	A lot more important
9	Substantially more important
2, 4, 6, 8	Intermediate values of the scales

) to quantify the relative importance [28]. Then, matrix A is constructed by Equation (1).

$$A={(A_{ij})}_{n\times n}=\left[\begin{array}{cccc}{A}_{11}& A_{12}& \cdots & A_{1n}\\ A_{21}& A_{22}& \cdots & A_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ A_{n1}& A_{n2}& \cdots & A_{nn}\end{array}\right]$$

(1)

where A_ij is the relative importance between index A_i and index A_j and n is the number of indexes.

2. Antisymmetric matrix. The judgment matrix A is transformed into an antisymmetric matrix G by Equation (2).

$$G={(g_{ij})}_{n\times n}=\log A_{ij}$$

(2)

3. Quasi-optimal transitive matrix. The optimal transfer matrix F_ij is solved by Equation (3), and then the quasi-optimal transfer matrix E_ij is obtained by Equation (4).

$$F_{ij}=\frac{1}{n}{\displaystyle \sum _{k=1}^n(g_{ik}-g_{jk})}$$

(3)

$$E_{ij}={10}^{F_{ij}}$$

(4)

4. Weight coefficient. The weight coefficient b_i for the data in the matrix E_ij is obtained by Equation (5), and then the subjective weight B_i of the index is obtained by Equation (6).

$$b_i={\left({\displaystyle \prod _{j=1}^n{E}_i{}_j}\right)}^{\frac{1}{n}}$$

(5)

$$B_i=b_i/{\displaystyle \sum _{i=1}^n{b}_i}$$

(6)

3.2.2. Improved Rough Set

A rough set can deal with the expression and induction of incomplete and uncertain data. The results obtained are objective and reliable and can effectively avoid the influence of subjective factors [29]. In this theory, data information is expressed in the form of a decision table. In general, an information table belongs to an expression system, H, as shown in Equation (7) [30].

$$H=(U,C,D,V,f)$$

(7)

where U is the set of evaluation objects, C is the set of conditional attributes, D is the set of decision attributes, V is the set of attribute values, and f is the attribute value.

However, in the previous process of calculating attribute weight by using rough set theory, there will be the case that the index weight is 0. To solve this problem, conditional entropy is introduced to improve rough set theory [31].

In decision information table H, the conditional entropy D (U/D = {D₁, D₂, …, D_m}) relative to C (U/C = {C₁, C₂, …, C_n}) can be expressed by Equation (8).

$$I(D|C)={\displaystyle \sum _{i=1}^n\frac{|C_i{|}^2}{|U{|}^2}}{\displaystyle \sum _{j=1}^m\frac{|D_j\cap C_i|}{|C_i|}}\times \left[1-\frac{|D_j\cap C_i|}{|C_i|}\right]$$

(8)

where I(D|C) is the conditional entropy, and n and m represent the number of indexes and objects to be evaluated, respectively.

In the decision information table, the importance degree New Sig(C_i) of the conditional attribute C_i can be expressed by Equation (9).

$$New Sig(C_i)=I(D|C-C_i)-I(D|C)$$

(9)

where New Sig (C_i) is the change degree of the attribute set after removing conditional attribute C_i.

Then the weight P(C_i) of each condition attribute can be obtained by Equation (10).

$$P(C_i)=\frac{New Sig(C_i)+I(D|C_i)}{{\displaystyle \sum _{i=1}^m\{New Sig(C_i)+I(D|C_i)\}}}$$

(10)

where I(D|C_i) is the importance of the condition attribute C_i itself in the decision table.

3.2.3. Improved CRITIC

Criteria Importance Though Intercriteria Correlation (CRITIC) not only considers the amount of information between indexes but also considers the correlation between indexes [32]; however, the dimension and order of magnitude between different indexes are often different, and there are some shortcomings in using standard deviation to reflect the difference of indexes in the CRITIC method [33]. Therefore, the coefficient of variation is adopted to improve the CRITIC method to better realize the index weight assignment [34].

1. Matrix X is established with the original evaluation index value:

$$X={(x_{ij})}_{m\times n}$$

(11)

where x_ij is the ith evaluation object and the jth index value.

2. The elements in matrix X are standardized by Equation (12), and the standardized matrix X* = ($x_{ij}^{*}$) is obtained.

$$x_{ij}^{*}=\frac{x_{ij}-{\overline{x}}_j}{s_j}$$

(12)

where ${\overline{x}}_j=\frac{1}{m}{\displaystyle \sum _{i=1}^m{x}_{ij}}$ is the average value and $s_j=\sqrt{\frac{1}{m-1}{\displaystyle \sum _{i=1}^m\left(x_{ij}-{\overline{x}}_j\right)}}$ is the mean square error of index j.

3. v_j is the variation coefficient of the jth index, which can be calculated by Equation (13):

$$v_j=\frac{s_j}{{\overline{x}}_j}$$

(13)

4. Pearson correlation coefficient of each index in matrix X* can be calculated by SPSS software, and the correlation coefficient matrix R = (r_kj)_n×n can be constructed [35]. Then, the independence coefficient η_j is calculated by Equation (14).

$${\eta }_j={\displaystyle \sum _{k=1}^n(1-r_{kj})}$$

(14)

5. According to the results of Equations (13) and (14), the importance coefficient C_j is calculated by Equation (15).

$${\theta }_j=v_j{\eta }_j$$

(15)

From Equation (15), the larger the θ_j value, the stronger the reference value of the index j, and the higher its importance, which should be given greater weight. Therefore, the weight Q_j can be calculated by Equation (16).

$$Q_j={\theta }_j/{\displaystyle \sum _{j=1}^n{\theta }_j}$$

(16)

3.2.4. Game Theory

Based on game theory, the comprehensive weight can be obtained by combining the subjective weight and objective weight [36]. For multi-index evaluation systems, it is assumed that L methods are adopted to determine the weight, namely, the weight vector W, which is shown in Equation (17).

$$W=(w_{l1},w_{l2},\cdots ,w_{ln})(l=1,2,\cdots ,L)$$

(17)

Therefore, a weight set W can be obtained, and the linear combination of L weight vectors can be expressed by Equation (18).

$$W={\displaystyle \sum _{l=1}^L{\alpha }_l·w_l^T}({\alpha }_l>0)$$

(18)

where α_l is the linear combination coefficient.

In order to select the most appropriate weight vector W, the linear combination coefficient should be optimized to minimize the deviation between W and each w_l, and its objective function can be derived by Equation (19) [37].

$$\min ||{\displaystyle \sum _{l=1}^L{\alpha }_l·w_l^T}-w_l|{|}_2$$

(19)

Based on the differential properties, the optimal first-order derivative conditions equivalent to the above equation are shown in Equation (20).

$${\displaystyle \sum _{l=1}^L{\alpha }_l{w}_l{w}_l^T}=w_l{w}_l^T$$

(20)

The available coefficient vectors (α₁, α₂, …, α_L) are obtained by solving the Equation (21). Then, the comprehensive weight W* can be obtained by Equation (22):

$${\alpha }_l^{*}={\alpha }_l/{\displaystyle \sum _{l=1}^L{\alpha }_l}$$

(21)

$$W^{*}={\displaystyle \sum _{l=1}^L{\alpha }_l{w}_l^T}$$

(22)

3.3. Cloud Model

3.3.1. Basic Concepts

The cloud model was first proposed in 1995 to solve the uncertainty transition between qualitative concepts and quantitative descriptions [38], which can be used to obtain the membership degree of evaluation indexes, mainly using the forward Gaussian cloud generator as the medium [39]. Three cloud digital features (expectation Ex, entropy En and hyper entropy He) are input so as to output the membership degree of cloud droplets [40]. The specific algorithms are as follows:

1. Three digital features can be calculated by Equation (23).

$$\{\begin{array}{c}Ex=(H_{min}+H_{max})/2\\ En=(H_{max}-H_{min})/6\\ He=\lambda \end{array}$$

(23)

where H_min and H_max are the upper and lower boundary values of the index range, respectively. λ is a constant, and it can be changed with randomness and the actual situation of the index. In this paper, λ = 0.02 [41].

2. The normal numbers En′, with En as the expectation and He² as the variance, are generated randomly by Equation (24) [42]:

$$E{n}^{\prime }=norm(En,H{e}^2)$$

(24)

3. Normal numbers x_i, with Ex as the expectation and En′² as the variance, are generated randomly by Equation (25):

$$x_i=norm(Ex,E{n^{\prime }}^2)$$

(25)

4. Membership μ is calculated by Equation (26):

$$\mu =\exp \frac{-{(x_i-Ex)}^2}{2E{n^{\prime }}^2}$$

(26)

3.3.2. Determination of Stability Grade

Before calculating the membership degree of the indexes, three cloud digital features need to be calculated, as shown in

Table 3. Digital characteristics of cloud models.

Level	Ci	C7	C8	C9
I	(0.125, 0.042, 0.02)	(4, 1.333, 0.02)	(500, 33.333, 0.02)	(24.5, 5.333, 0.02)
II	(0.375, 0.042, 0.02)	(16.5, 2.833, 0.02)	(300, 33.333, 0.02)	(7, 0.5, 0.02)
III	(0.625, 0.042, 0.02)	(35, 3.333, 0.02)	(125, 25, 0.02)	(4.5, 0.333, 0.02)
IV	(0.875, 0.042, 0.02)	(55, 3.333, 0.02)	(25, 8.333, 0.02)	(2, 0.5, 0.02)

. The cloud model of each evaluation index is shown in Figure 5. The digital characteristics of the indexes are the same where i = 1, 2, 3, 4, 5, 6, 10 in order to reduce the space and do not repeat the expression.

By compiling the program of the normal cloud generator, the membership degree can be obtained, and the fuzzy operator is used to multiply it with the corresponding index weight by Equation (27). Finally, the value of each working face construction site belonging to each stability grade can be obtained [43].

$${\phi }_j={\displaystyle \sum _{i=1}^n{W}_i^{*}\times {\mu }_{ij}}$$

(27)

where φ_j is the membership degree of the jth level, and μ_ij is the membership degree of the ith index at the corresponding level j.

4. Results

In order to verify the feasibility and reliability of the established model, 14 working faces traversed by the Mianluan Expressway are taken as the stability objects, and the stability of the sites are evaluated. The specific index values of each working face are in

Table 4. Index value of each working face.

Working Face	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
Irregular goaf	0.30	0.60	0.60	0.20	0.80	0.80	12.00	11.28	40.00	0.43
Unnamed region	0.28	0.60	0.40	0.50	0.20	0.25	12.00	35.57	36.00	0.09
18081	0.30	0.60	0.35	0.60	0.20	0.15	12.00	51.26	33.00	0.27
18101	0.35	0.20	0.30	0.55	0.10	0.10	13.00	149.73	25.00	0.33
18121	0.38	0.60	0.28	0.65	0.15	0.10	13.00	57.55	30.00	0.29
18141	0.35	0.60	0.35	0.70	0.20	0.20	13.00	64.15	32.00	0.40
18021	0.30	0.60	0.30	0.65	0.28	0.15	12.00	53.65	28.00	0.10
18041	0.40	0.60	0.40	0.60	0.15	0.20	12.00	153.33	30.00	0.42
18061	0.45	0.40	0.40	0.55	0.20	0.15	12.00	48.90	19.00	0.30
21101	0.30	0.40	0.35	0.60	0.18	0.15	12.00	54.55	24.00	0.34
21121	0.35	0.40	0.28	0.50	0.25	0.20	12.00	56.82	13.00	0.41
21141	0.40	0.40	0.30	0.70	0.20	0.20	12.00	61.82	8.00	0.44
21181	0.35	0.60	0.40	0.60	0.25	0.10	11.00	240.00	15.00	0.73
21201	0.42	0.60	0.42	0.65	0.20	0.10	11.00	250.00	11.00	0.26

.

4.1. Stability Evaluation Results

Firstly, according to the improved AHP theory, matrix A is constructed by pairwise comparison of 10 evaluation indexes, as shown in Equation (28). Then the subjective weight W₁ is calculated according to Equation (1) to Equation (6)

$$A=\left[\begin{array}{cccccccccc}1& 1/4& 3& 2& 1/2& 1& 1/3& 1/6& 1/7& 1/5\\ 4& 1& 6& 5& 3& 4& 2& 1/3& 1/4& 1/2\\ 1/3& 1/6& 1& 1/2& 1/4& 1/3& 1/5& 1/8& 1/9& 1/7\\ 1/2& 1/5& 2& 1& 1/3& 1/2& 1/4& 1/7& 1/8& 1/6\\ 2& 1/3& 4& 3& 1& 2& 1/2& 1/5& 1/6& 1/4\\ 1& 1/4& 3& 2& 1/2& 1& 1/3& 1/6& 1/7& 1/5\\ 3& 1/2& 5& 4& 2& 3& 1& 1/4& 1/5& 1/3\\ 6& 3& 8& 7& 5& 6& 4& 1& 1/2& 2\\ 7& 4& 9& 8& 6& 7& 5& 2& 1& 3\\ 5& 2& 7& 6& 4& 5& 3& 1/2& 1/3& 1\end{array}\right]$$

(28)

Then, according to the improved rough set theory and the grading standards in Table 1, attribute reduction is carried out on the index values in Table 4 to construct the decision table, as shown in

Table 5. Evaluation index decision table.

Working Face	Conditional Attributes (C)										Decision Attributes
	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
Irregular goaf	2	3	3	1	4	4	2	4	1	2	II
Unnamed region	2	3	2	3	1	2	2	4	1	1	I
18081	2	3	2	3	1	1	2	3	1	2	II
18101	2	1	2	3	1	1	2	3	1	2	I
18121	2	3	2	3	1	1	2	3	1	2	I
18141	2	3	2	3	1	1	2	3	1	2	II
18021	2	3	2	3	2	1	2	3	1	1	I
18041	2	3	2	3	1	1	2	3	1	2	II
18061	2	2	2	3	1	1	2	3	1	2	I
21101	2	2	2	3	1	1	2	3	1	2	II
21121	2	2	2	3	2	1	2	3	1	2	II
21141	2	2	2	3	1	1	2	3	2	2	II
21181	2	3	2	3	2	1	2	2	1	3	II
21201	2	3	2	3	1	1	2	2	1	2	II

. The calculation results of conditional entropy, importance and index weight W₂ are in

Table 6. Weight determined by improved rough set.

Index	I(D/Ci)	I(D/C−Ci)	New Sig(Ci)	W2
C1	0.4592	0.0408	0.0000	0.1360
C2	0.1837	0.0510	0.0102	0.0574
C3	0.4082	0.0408	0.0000	0.1208
C4	0.4082	0.0408	0.0000	0.1208
C5	0.2653	0.0510	0.0102	0.0816
C6	0.2449	0.0408	0.0000	0.0725
C7	0.4592	0.0408	0.0000	0.1360
C8	0.2551	0.0510	0.0102	0.0785
C9	0.4082	0.0510	0.0102	0.1239
C10	0.2449	0.0408	0.0000	0.0725

.

The correlation coefficients of the indexes are calculated according to the improved CRITIC method, and the heat map of the correlation coefficient is shown in Figure 6. Then, according to Equation (14) to Equation (16), the weight W3 can be obtained, as shown in

Table 7. Combination weights of evaluation indexes.

Weight	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
W1	0.0340	0.1076	0.0166	0.0231	0.0508	0.0340	0.0744	0.2148	0.2912	0.1535
W2	0.1360	0.0574	0.1208	0.1208	0.0816	0.0725	0.1360	0.0785	0.1239	0.0725
W3	0.0396	0.0570	0.0484	0.0670	0.1560	0.1955	0.0143	0.2157	0.0978	0.1087
W*	0.0399	0.0892	0.0310	0.0412	0.0861	0.0879	0.0573	0.2097	0.2219	0.1358

.

In addition, according to the combination principle of game theory, the normalized linear combination coefficient was obtained as α₁ = 0.6430, α₂ = 0.0343, α₃ = 0.3227, so the comprehensive weight W* can be obtained, which can reflect that the comprehensive weight not only considers the judgment of experts’ subjective factors but also takes into account the characteristics of the index itself, as shown in Table 7.

According to the cloud model theory, the membership degree of each evaluation index is calculated, and then the certainty degree of each working face construction site belonging to each stability level is calculated by Equation (27). The results are shown in Figure 7 and in columns 3 to 6 in

Table 8. Membership degree of each working face site.

Number	Working Face	Membership Degree				Result
		Stable	Basically Stable	Under Stable	Unstable
1	Irregular goaf	0.0112	0.1223	0.0940	0.0032	Basically stable
2	Unnamed region	0.1984	0.0652	0.0685	0.0394	Stable
3	18081	0.1713	0.0809	0.0968	0.0006	Stable
4	18101	0.3334	0.1875	0.0632	0.0000	Stable
5	18121	0.2878	0.1243	0.0984	0.0001	Stable
6	18141	0.1010	0.2544	0.0800	0.0005	Basically stable
7	18021	0.3104	0.0698	0.0968	0.0004	Stable
8	18041	0.2212	0.1906	0.1432	0.0000	Stable
9	18061	0.1848	0.1802	0.0112	0.0014	Stable
10	21101	0.2393	0.2600	0.0320	0.0002	Basically stable
11	21121	0.0514	0.2715	0.0051	0.0001	Basically stable
12	21141	0.0807	0.2055	0.0153	0.0005	Basically stable
13	21181	0.1265	0.0949	0.1186	0.0065	Stable
14	21201	0.1629	0.0978	0.0967	0.0001	Stable

. From Table 8, the membership degree of the stability level of the irregular goaf is φ = (0.0112, 0.1223, 0.0940, 0.0032) based on the principle of maximum membership degree, concluding that the state of the irregular goaf is basically stable. Similarly, stability levels of other sites can be obtained, as shown in column 7 of Table 8.

It can be seen intuitively from Figure 7 that the stability levels of the construction site of the Mianluan Expressway are different and that there are two states: stable and basically stable. Considering that the stable site is also easily affected by the disturbance of mining hydrogeology and engineering geology, the subgrade should be paved with geotechnical materials to improve its safety when developing and utilizing the construction site.

4.2. Sensitivity Analysis of Subjective Weights

In this paper, the improved AHP is used to determine the subjective weight of an indexes, which can effectively improve the accuracy of the subjective weight; however, there will inevitably be human subjective factors that affect the credibility of the evaluation. Therefore, this paper uses the OAT (one at a time) method to test the sensitivity of the subjective weight, which can reflect the impact of the changes in the index weights on the evaluation results by changing the weight value of an evaluation index at a given time while keeping the weights of other indexes unchanged [44,45]. The steps of the OAT method are as follows:

1. Defining the RPC (range of percent change). The RPC is the variation range of the subjective weight of the evaluation index.

2. Defining the IPC (increment of percent change). The IPC represents each percentage change in the subjective weight within the RPC range.

3. An index C_m in the index system is selected as the target index. Under the premise of defined the RPC and IPC, its weight will generate different simulated weights after changing the percentage pc, as shown in Equation (29):

$$W\left(C_m,pc\right)=W\left(C_m,0\right)·\left(1+pc\right)$$

(29)

$$W\left(C_i,pc\right)=\left(1-W\left(C_m,pc\right)\right)·\frac{W\left(C_i,0\right)}{\left(1-W\left(C_m,0\right)\right)}$$

(30)

where pc is the percentage of weight change, W(C_m, 0) is the initial value of the weight of the index Cm, W(C_m, pc) is the simulated weight of the index C_m after changing the percentage pc, W(C_i, 0) is the initial value of the weight of the ith index C_i, and W(C_i, pc) is the changed weight of other indexes.

4. Calculating the evaluation score value after the weight change, as shown in Equation (31).

$$R\left(C_m,pc\right)=W\left(C_m,pc\right)·A_m+{\displaystyle \sum _{m\ne j}^{n}W\left(C_j,pc\right)}·A_j$$

(31)

where R(C_m, pc) is the evaluation score obtained as the weight of C_m changes, A_m is the weight ranking score of index C_m, W(C_j, pc) is the weight of other indexes, and A_j is the ranking score value of other indexes.

5. Calculating the rate of score change Rate(C_m, pc).

$$Rate\left(C_m,pc\right)=\frac{R\left(C_m,pc\right)-R\left(C_m,0\right)}{R\left(C_m,0\right)}\times 100\%$$

(32)

where Rate(C_m, pc) is the change rate of score after the weight of index C_m changes.

In this paper, the RPC and IPC are set to ±100% and ±5% respectively and applied to all indexes. A total of 410 sets of weight values are generated for the 10 indexes and the results of the corresponding rate of change of scores are shown in Figure 8.

From the Figure 8, the score change rate presents a centrosymmetric distribution at 0% and an approximate linear increase with the increase in the absolute value of the weight change rate. The higher the slope of the evaluation index, the higher its sensitivity. The sensitivity of index C₉ (stopping time) to weight changes is the highest, and when the weight changes by 100%, the corresponding rate value is 12.44%, which is much smaller than the degree of weight change, indicating that the subjective weights determined in this paper are reasonable and effective and can objectively reflect the stability of the construction site above the goaf.

4.3. Validation of Model Correctness

To verify the correctness of the model, settlement observation points are arranged in the study area, and the first settlement observation began on 6 May 2019. As of 15 November 2019, it had been monitored 6 times, with a cumulative observation duration of 6 months, as shown in Figure 9. The corresponding evaluation standard for each stability level is shown in

Table 9. Evaluation standard for stability level.

Stability Level	Surface Subsidence (mm)		Subsidence Velocity (mm/d)
	3 Months	6 Months
Stable	≤15	≤30	<1
Basically stable	15~30	30~60
Under stable	30~60	60~120	≥1
Unstable	≥60	≥120

[46,47].

It can be seen from Figure 9 that there is still residual settlement on the surface, but the maximum subsidence in 6 months is less than 3 mm, and the maximum subsidence velocity is less than 0.2 mm/d. According to Table 9, it is judged that the study area is stable as a whole, which further proves the reliability of the established model.

5. Discussion

In this study, improved AHP, rough set and CRITIC methods are used to determine the weights of evaluation indexes, which can effectively reduce the deviation caused by a single-weight determination method, and based on the game theory, the two weights are combined to increase the accuracy and rationality of the weight determination. In addition, so as to obtain the stability state of the study area, a cloud model is used as the medium to determine the membership degree of each index by calculating the cloud digital characteristics, which effectively solves the problem of uncertainty conversion between the qualitative concepts and quantitative values in the evaluation process. Furthermore, the stability level can be intuitively seen form Figure 7, and the degree of favoritism to the adjacent two levels can be clearly seen, which makes the evaluation level more intuitive.

Although the reliability of the evaluation results can be improved by this model, there are some disadvantages. In the process of constructing the evaluation index system, the correlation and redundancy between the indexes should be fully considered, and the results of the index system construction should be different for different research areas. Therefore, future research will focus on the establishment of a universally applicable stability evaluation index system. Moreover, it is also necessary to improve the quantitative standards of qualitative indexes.

6. Conclusions

In this study, the subjective and objective combination weighting method and the cloud model are combined to obtain the stability state of the construction site and it is applied to a specific case. Several main conclusions are discovered in this paper:

1. Based on the principles of relevance, hierarchy, representativeness and feasibility of index selecting, 10 indexes are selected to construct an evaluation index system, which not only avoids the repetition of information expressed by evaluation indexes, but also method ensures that the index system can fully reflect the data characteristics.

2. In view of the singleness of the weight determination method, an improved AHP method is used to determine the subjective weight, and improved rough set and CRITIC models are adopted to determine the objective weight, which not only reduces the unreasonable influence of the index weight caused by the objective weight being too sensitive to the data but also avoids the problem of excessive subjectivity caused by subjective weights. Then, the subjective and objective weights are combined based on game theory, which can increase the accuracy and rationality of the weight determination.

3. The qualitative concepts are quantified by the cloud model, and the cloud digital features are obtained according to the evaluation index grading standards. Then the stability grade of each working face is determined based on the principle of maximum membership degree, which improves the reliability of the evaluation results.

4. The evaluation results show that the stability level of the study area is not uniform and that there are two states: stable and basically stable. According to the high-resolution leveling results, the reliability of the results is further verified.