Rock Mass Failure Classification Based on FAHP–Entropy Weight TOPSIS Method and Roadway Zoning Repair Design

Abstract

After the original support system in the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine failed, the extent of damage and deformation varied significantly across different sections of the drift. A single support method could not meet the engineering requirements. Therefore, this paper conducted research on the classification of roadway damage and zoning repair. The overall damage characteristics of the roadway are described by three indicators: roadway deformation, development of rock mass fractures, and water seepage conditions. These are further refined into nine secondary indicators. In summary, a rock mass damage combination weighting evaluation model based on the FAHP–entropy weight TOPSIS method is proposed. According to this model, the degree of damage to the roadway is divided into five grades. After analyzing the damage conditions and support requirements at each grade, corresponding zoning repair plans are formulated by adjusting the parameters of bolts, cables, channel steel beams, and grouting materials. At the same time, the reliability of partition repair is verified using FLAC3D 6.0 numerical simulation software. Field monitoring results demonstrated that this approach not only met the support requirements for the roadway but also improved the utilization rate of support materials. This provides valuable guidance for the design of support systems for roadways with similar heterogeneous damage.

1. Introduction

As coal mining goes deeper, the impact of geological factors on the roadway is also becoming more severe. Roadway deformations are increasing, and the impact on the supporting structure is more and more significant. At present, many roadways suffer from inadequate support strength and insufficiently targeted reinforcement, and still face the situation of failure again after repair [1,2,3]. Especially since, due to the occurrence of destructive deformation of soft rock roadways, achieving a more stable control is very difficult [4,5,6], which seriously affects production activities, the study of the destruction and deformation of the roadway peripheral rock law and targeted support and the safe production of coal mines is of great significance.

In recent years, many scholars at home and abroad have conducted research on the damage and deformation mechanism of roadway and repair technology. Shemyakin et al. investigated the mechanism of rock fragmentation [7,8], Wang Hui et al. investigated the deformation of cross roadway, and put forward a zonal anchored grouting reinforcing technology, and investigated the support effect through numerical simulation [9]. Liu Pengze et al. studied the control methods for rock masses on the goaf side of inclined coal seams, and put forward the CUSG support method and verified its effect [10]. Zhan Ping and others proposed using a combination of active and passive support techniques to address high stress damage to the surrounding rock [11]. Hao Jian et al. investigated the effects of active and passive support and proposed an active–passive coupled support scheme consisting of “bolts, steel bands, cables, beams, steel scaffolding” [12]. Zhang Yong et al. proposed the CRRFC support technology based on an analysis of the stability control of the surrounding rock [13]. Fang Wanwei et al. investigated the causes and patterns of asymmetric deformation in roadways and proposed corresponding support methods [14]. Wu Jingke et al. studied the properties of thick and soft surrounding rock in deep mines, and proposed the thick and soft surrounding rock control technology for hollow zone side retention under deep mines [15]. Ma Lu et al. designed a method for controlling side entry pipes in goaf areas by comprehensively utilizing numerical simulation and on-site monitoring techniques [16]. Peng Wenqing et al. proposed the support scheme of “U-beam + inverted arch + linkage beam + floor bolts”, which improved stability of broken rock [17]. Lv Jinguo et al. investigated the effectiveness of combining FRP and steel bolts and proposed combining FRP and steel bolts for support scheme for the outer perimeter of roadway [18]. Wang Xiangjun et al. proposed a multi-level reinforcement composite support technology centered on high-strength prestressed anchor bolts (cables) [19]. Wang Hui et al. established a three-dimensional finite element model of geological conditions and design plans, and proposed a support method combining U-shaped steel supports and anchoring [20]. Zuo Jianping et al. changed the active support effect by changing the preload, fully utilizing the support strength to achieve active–passive coupled support [21].

Nowadays, many scholars have proposed various methods and experiences for roadway support. However, during the roadway support process, some roadways, due to their excessive length, have developed significantly different rock mass failure conditions internally. If a single support method is used, ensuring the safety of the entire structure requires a support scheme designed for the most severe failure scenario. This far exceeds the support requirements in areas with minor damage, resulting in economic waste. Therefore, it is necessary to implement graded support for roadways. In terms of rock mass classification, Yang Yongjie et al. focused on the ground stress, combining fuzzy clustering to propose a SIM-based rock mass classification method [22]. Jin Changyu et al. used rock joints to describe rock characteristics and then completed the classification of surrounding rocks [23]. Liu Hai et al. studied the role of fractured rock zone thickness in comprehensive classification and proposed a method for designing bolts parameters for coal seam roadway based on fractured rock zone classification results [24]. Shi Shaoshuai et al. proposed a rock mass classification method based on fuzzy hierarchical analysis and roadway seismic prediction [25]. Sun Shunxian et al. evaluated the degree of crack development based on mainstream rock classification methods, and discussed a rock mass classification method based on three evaluation indicators [26]. In this regard, Zhao Bing et al. employed a game theory combination weighting–normal cloud model to assess the quality evaluation of surrounding rock [27]. Shi Longqing et al. proposed a water-richness predictive method based on game theory combinatorial weighting and a Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) [28]. Qin Xiantao et al. established a matrix according to an expert grading method and gray fuzzy theory to evaluate the risk level of bridges [29].

However, current research on the classification of roadway damage and targeted repair methods remains limited. Roadway requiring graded repairs lack the support of a scientific and effective classification system, leading to the use of a single support method, which results in significant waste of support costs. This paper takes the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine as the basis. Through laser ranging and borehole inspection, the roadway deformation and the fractures development of surrounding rock are measured. Combined with the water seepage conditions observed in the roadway, a classification method based on roadway damage characteristics is proposed. A combined weighting evaluation system using the FAHP–entropy weight TOPSIS method is established to process damage characteristic parameters and finish classification. Based on the comprehensive scores and rock mass damage characteristics, the selection of control methods and calculation of support parameters for each rock mass classification are determined. Ultimately, a zoning repair plan for the roadway is completed, ensuring the safety and reliability of the support while improving the effective utilization rate of support materials and reducing support costs.

2. Rock Mass Damage Grading Evaluation System

Under the existing rock mass control theory, roadway deformation is the most direct indicator of rock mass stability. However, relying solely on this indicator cannot fully reflect the extent of rock mass failure, so it is still needed to consider the internal conditions of the surrounding rock. Rock mass is influenced by mining-induced stress, leading to relaxation and fracturing of rock within a certain surrounding area, forming a fractured rock zone. The distribution of internal fractures also reflects the extent of mass failure and is included in the evaluation system. Considering the water seepage conditions present in this roadway, the following evaluation indicators are defined in this paper, as shown in Table 1.

Table 1. Evaluation index table.

Indicator Name	Indicator Symbols	Definition of Indicators
Roadway rib movement	C1	Difference between the original width of the roadway and the deformed width
Roadway roof movement	C2	Difference between the original height of the top plate and the height after deformation
Maximum depth of distribution of roof cracks	C3	Maximum depth of the roof slab from the surface to the appearance of fissures
Trimmed depth of distribution of roof cracks	C4	The mean value of the roof slab after removing the maximum and minimum values at each depth from the surface to the inner part where the fissure occurs
Number of roof cracks	C5	Number of fissures present around the perimeter of the roof
Maximum depth of distribution of rib cracks	C6	Maximum depth of the rib slab from the surface to the appearance of fissures
Trimmed depth of distribution of rib cracks	C7	The mean value of the rib slab after removing the maximum and minimum values at each depth from the surface to the inner part where the fissure occurs
Number of rib cracks	C8	Number of fissures present around the perimeter of the rib
Seepage	C9	Whether the water seepage conditions occurred

The rock mass damage evaluation system is shown in Figure 1:

Figure 1. Destruction of the evaluation system diagram.

After obtaining the basic data, for ease of calculation and to eliminate the influence of dimensions, we need to use expert scoring to perform fuzzy processing. Expert scoring uses a 10-point scale, and the fuzzy membership degrees are as shown in Table 2.

Table 2. Fuzzy quantification table of membership of grading parameters.

Score	0–2	2–4	4–6	6–8	8–10
Roadway rib movement/m	0–0.4	0.4–0.8	0.8–1.2	1.2–1.6	>1.6
Roadway roof movement/m	0–0.3	0.3–0.6	0.6–0.9	0.9–1.2	>1.2
Maximum depth of distribution of roof cracks/m	0–3	3–5	5–7	7–9	>9
Trimmed depth of distribution of roof cracks/m	0–2	2–3	3–4	4–6	>6
Number of roof cracks	0–5	5–7	7–9	9–11	>11
Maximum depth of distribution of rib cracks/m	0–3	3–4.5	4.5–6	6–7.5	>7.5
Trimmed depth of distribution of rib cracks/m	0–2	2–3	3–4	4–6	>6
Number of rib cracks	0–5	5–6	6–7	7–8	>8
Seepage	No				Yes

3. Basic Principles of Combined Weighting Evaluation Using FAHP–Entropy Weight TOPSIS Method

Completing rock mass classification requires a quantifiable metric. Based on this metric, differences in rock mass properties are described through varying metric values, thereby enabling the classification of rock mass grades. In the preceding sections, we identified the selected rock mass parameter metrics and further subjected them to fuzzy processing to eliminate dimensional effects. Subsequently, it is necessary to investigate the extent to which these parameters influence rock mass failure and establish a numerical model to reflect this relationship. This numerical model must calculate the relative weights of each factor in the comprehensive assessment of rock mass failure while maintaining objective scientific rigor. Therefore, this paper adopts a combined weighting evaluation to describe the corresponding relationships. The numerical model comprises three components: the fuzzy analytic hierarchy process, the entropy weighting method, and the TOPSIS method.

Fuzzy Analysis Hierarchical Method (FAHP) is an extension of the Analysis Hierarchical Method (AHP), where indicators are subjected to fuzzy processing to eliminate the nonlinear effects of units of measurement and data during the calculation of composite scores. However, since the analytic hierarchy process relies on the professional experience of the evaluators and is subjective, we have introduced the entropy weighting method, which is objective. The two methods are weighted together to determine the final weights, which are then combined with the TOPSIS method to calculate the degree of proximity, serving as the basis for classification.

3.1. Principles of Fuzzy Analysis Hierarchical Method (FAHP)

The fuzzy analytic hierarchy process requires the construction of a three-layer evaluation system comprising the target layer, principles layer, and indicator layer. In this paper, the target layer is degree of rock mass damage (A); the principles layer is roadway deformation (B1), degree of development of rock mass fractures (B2), and watering seepage conditions (B3); and the indicator layer is roadway rib movement (C1), roadway roof movement (C2), maximum depth of distribution of roof cracks (C3), trimmed depth of distribution of roof cracks (C4), number of roof cracks (C5), maximum depth of distribution of rib cracks (C6), trimmed depth of distribution of roof cracks (C7), number of rib cracks (C8), and seepage (C9). The method for calculating weights using FAHP is as follows [30]:

3.1.1. Establish a Fuzzy Complementary Judgment Matrix

The fuzzy complementary judgment matrix $\mathrm{R}={({\mathrm{r}}_{\mathrm{i}\mathrm{j}})}_{\mathrm{n}*\mathrm{m}},(\mathrm{i},\mathrm{j}=1,2,\dots ,\mathrm{n})$. Each indicator in the indicator layer is compared pairwise, and a scale of 0.1–0.9 is assigned based on its relative importance to the upper layer, as shown in Table 3.

Table 3. Scaling and what it means.

Scale	Degree of Importance	Clarification
0.5	equal importance	Both factors are equally important
0.6	slightly important	The former factor is slightly more important than the latter factor
0.7	clearly important	The former factor is clearly more important than the latter factor
0.8	far more important	The former factor is far more important than the latter factor
0.9	vital	The former factor is vital, more important than the latter factor
0.1, 0.2, 0.3, 0.4	Contrary to the above	Factor $r_j$ Than Factor $r_i$ Scale and Factor $r_i$ Than Factor $r_j$ Add up to 1

3.1.2. Weight Calculation

$$W_i={\displaystyle \frac{{\displaystyle {\sum }_{i,j=1}^n{r}_{ij}+\frac{n}{2}-1}}{n(n-1)}}$$

(1)

For the fuzzy complementary judgment matrix $\mathrm{R}={(r_{ij})}_{n\times n}$, its weight vector is $W=\left(W_1, W_2, \dots , W_i, \dots , W_n\right)$. According to the formula, the formula to be solved is expressed as.

$$W_i={\displaystyle \frac{{\displaystyle {\sum }_{i,j=1}^n{r}_{ij}+\frac{n}{2}-1}}{n(n-1)}}$$

(2)

In the formula, $W_i$ is the weight of factor $r_j$.

3.1.3. Consistency Test

After obtaining the weights of the fuzzy complementary judgment matrix, it is necessary to determine whether they are reasonable, so a consistency test is required. To perform a consistency test, it is necessary to calculate the judgment matrix and the feature matrix $W^{*}$, and then find the compatibility index $I\left(A,B\right)$ between them, which is expressed as

$$I(A,B)={\displaystyle \frac{1}{n^2}}{\displaystyle \sum _{i,j=1}^n|a_{ij}+b_{ij}-1|}$$

(3)

$$A={(a_{ij})}_{n\times n},B={(b_{ij})}_{n\times n}$$

$$W^{*}={(W_{ij})}_{n\times n}$$

(4)

$$W_{ij}={\displaystyle \frac{W_i}{W_i+W_j}},\forall i,j=1,2,\dots ,n$$

Compare matrices A and B. When their compatibility index is less than 0.1, we can regard them as satisfactory consistency matrices, and the weight values are reasonable and reliable.

3.2. Entropy Weighting Method Principle

The entropy weighting method is an objective weighting method that avoids the arbitrariness of subjective weighting [31]. Its core principle is as follows: the greater the degree of variation in an indicator, the more information it contains, and the greater its weight should be; the smaller the degree of variation, the less information it contains, and the smaller its weight should be.

3.2.1. Constructing the Judgment Matrix and Standardization

Establish the judgment matrix X between object $i \left(i = 1, 2, 3, \dots , m\right)$ and indicator $j \left(j = 1, 2, 3, \dots , n\right)$:

$$X=\left(\begin{array}{ccc}{x}_{11}& \dots & x_{1n}\\ ⋮& \ddots & ⋮\\ x_{m1}& \dots & x_{mn}\end{array}\right)$$

(5)

Perform normalization processing on the data:

$$y_{ij}={\displaystyle \frac{x_{ij}-x_j^{\min }}{x_j^{\max }-x_j^{\min }}}$$

(6)

In the formula, $x_j^{\max }$ is the maximum value under indicator $j$, and $x_j^{\min }$ is the minimum value under indicator $j$.

After normalization, standardization is performed using the column sum method:

$$z_{ij}={\displaystyle \frac{y_{ij}}{{\displaystyle \sum _{i=1}^m{y}_{ij}}}}$$

(7)

In the formula, $y_j^{\max }$ is the maximum value under the normalized indicator $j$, and $y_j^{\min }$ is the minimum value under the normalized indicator $j$.

3.2.2. Calculate the Weightings of Each Indicator

$$E_j=-{\displaystyle \frac{1}{\ln m}}{\displaystyle \sum _{i=1}^m{z}_{ij}\ln }{z}_{ij},(j=1,2,3,\dots ,n)$$

(8)

$$G_j=1-E_j$$

(9)

$$W_j={\displaystyle \frac{G_j}{{\displaystyle \sum _{j=1}^n{G}_j}}}$$

(10)

In the formula, $E_j$ is the entropy value, $G_j$ is the differentiation coefficient, and $W_j$ is the final weight.

3.3. TOPSIS Method Principle

TOPSIS is an evaluation method based on multi-indicator data. Its core idea is to measure the relative superiority or inferiority of objects by calculating the distance from the ideal and negative ideal solution. Objects that are closer to the ideal solution receive a higher comprehensive evaluation [32].

In a comprehensive scoring matrix P:

$$P=\left(\begin{array}{cccc}{\omega }_1\ast p_{11}& {\omega }_2\ast p_{12}& \dots & {\omega }_n\ast p_{1n}\\ {\omega }_1\ast p_{21}& {\omega }_2\ast p_{22}& \dots & {\omega }_n\ast p_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ {\omega }_1\ast p_{m1}& {\omega }_2\ast p_{m2}& \dots & {\omega }_n\ast p_{mn}\end{array}\right)$$

(11)

The maximum value in each column is the positive ideal solution $p_j^{+}$, and the minimum value in each column is the negative ideal solution $p_j^{-}$. Using Euclidean distance, calculate the positive ideal solution distance $D_i^{+}$ and negative ideal solution distance $D_i^{-}$ for each object.

$$D_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{(p_j^{+}-{\omega }_j\ast p_{ij})}^2}},D_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{(p_j^{-}-{\omega }_j\ast p_{ij})}^2}}$$

(12)

Use negative ideal solutions to calculate the degree of proximity to the object:

$$S_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}}$$

(13)

The score ranges from 0 to 1, with higher scores indicating greater deviation from the negative ideal solution and better results.

3.4. Establishment of the FAHP–Entropy Weighting TOPSIS Combined Weighting Evaluation Model

Within the three-tier evaluation system, the criterion layer comprises three elements: roadway deformation, degree of rock mass joint development, and watering seepage conditions. These three elements cannot be measured as a single composite parameter and must be described through their respective secondary indicators. Consequently, they cannot be processed using the entropy increase method. Considering these three elements are common factors, they can be assessed based on experts’ experience. Therefore, the weights $W_{A\text{-}B}$ of the objective layer and criterion layer are calculated using the analytic hierarchy process.

The indicator layer comprises nine indicators, whose weights can still be calculated using the analytic hierarchy process. However, since both the criterion layer and indicator layer involve substantial specific data, results derived solely from expert experience exhibit strong subjectivity and weak objectivity. Moreover, these indicators can yield actual parameters through measurement. Therefore, weights obtained via the entropy increase method demonstrate greater objectivity. However, considering that the purpose of rock mass classification is to provide support for reinforcement, describing the extent of roadway damage must not only reflect objective conditions but also prioritize subsequent reinforcement efforts—something the entropy increase method cannot achieve. Thus, the analytic hierarchy process retains its value. Therefore, the weights obtained from the AHP and entropy weight method are coupled to derive the weights of the criterion layer and indicator layer. Using the weights $W_{B\text{-}C}$ obtained from the entropy weight method as the primary weights, with $W_M$ weighting coefficient of 0.6, and the weights $W_N$ obtained from the AHP as the corrective weights, with a weighting coefficient of 0.4, the final comprehensive weights $W_{A\text{-}C}$ for the objective layer and indicator layer are

$$W_{A\text{-}C}=W_{A\text{-}B}\times (0.6\times W_M+0.4\times W_N)$$

(14)

By establishing a comprehensive scoring matrix through weighted integration, we obtain the weighted scores for each of the nine indicators. Scores derived solely by simple addition only reflect numerical magnitude. However, field observations reveal that even with identical scores, the extent of damage to roadways varies significantly. Therefore, simple addition cannot serve as the method for calculating the comprehensive score. Here, we employ the TOPSIS method. By defining positive and negative ideal solutions—the maximum and minimum damage scores—we calculate the proximity of each section of the roadway to the negative ideal solution. This transforms the scores into values that accurately reflect the roadway damage condition, aligning with human decision-making intuition. Higher scores indicate greater proximity to maximum damage, while lower scores indicate proximity to minimum damage. This serves as the standard for rock mass classification.

4. FAHP–Entropy Weighting TOPSIS Method for Rock Mass Zoning Classification and Repair Design

4.1. Rock Mass Classification Based on the FAHP–Entropy Weighting TOPSIS Method

After determining the required indicator parameters, this paper took the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine as the background and measured the roadway deformation. To study the development of rock fractures in the northern wing auxiliary transportation roadway, a drilling inspection plan is formulated. Preliminary design involves arranging three drill holes every 20 m to probe the internal structure and fissure development of the rib and roof. The roadway center is constructed perpendicular to the rib and roof. Based on the bolt and cable support range, the depth of the rock mass fissure probe holes is preliminarily determined. (roof borehole depth 9 m, sidewall borehole depth 5 m. If during on-site exploration it is found that rock mass fractures remain well developed near the bottom of the boreholes at this depth (roof above 8 m, sidewalls above 4 m), supplementary exploration will be conducted, with the roof borehole depth increased to 15 m and the sidewall borehole depth increased to 10 m), with a borehole diameter of 32 mm. The final statistics are as shown in Table 4.

Table 4. Damage of surrounding rock.

Distance from the Start of the Roadway/m	C1	C2	C3	C4	C5	C6	C7	C8	C9
10	0.6	0.2	2.85	2.31	5	3.29	1.9	5	No
30	1.1	0.2	3.51	1.95	6	3.56	1.97	6	No
50	0.8	0.4	3.28	2.35	8	3.11	2.56	6	No
70	0.8	0.2	3.56	2.26	9	3.21	2.56	7	No
90	0.9	0.3	4.23	1.99	8	2.57	2.34	6	No
110	0.2	0.1	2.03	1.85	7	2.11	1.75	4	No
130	0.2	0.1	2.03	1.55	4	2.23	1.56	5	No
150	0.1	0	2.11	1.35	5	2.76	1.64	6	No
170	0.3	0.1	2.25	2.25	5	2.51	1.78	5	No
190	0.2	0.3	2.89	2.89	5	3.03	2.31	6	No
210	0.2	0.5	3.03	1.13	6	3.45	2.58	7	No
230	0.8	0.5	4.06	1.55	7	3.91	1.5	5	No
250	1.2	0.1	4.81	2.85	7	4.21	2.97	5	No
270	1	0.3	5.42	3.34	9	3.94	3.2	7	No
290	0.6	0.1	6.65	3.18	8	4.34	2.98	7	No
310	0.9	1	4.77	3.59	8	3.75	2.57	5	No
330	1.1	0.8	6.75	3.29	6	4.21	3.75	7	No
350	1	0.9	5.26	2.54	6	4.46	2.79	7	No
370	1.4	0.7	8.15	3.47	11	4.99	3.45	6	No
390	1.6	0.8	7.55	4.62	8	4.75	2.58	7	No
410	1.8	0.9	8.32	4.51	8	6.21	3.66	8	No
430	1.7	1.2	10.25	6.98	12	5.89	4.25	8	No
450	1.5	1	11.33	5.12	9	6.67	5.33	8	No
470	1.2	0.3	2.56	1.58	5	7.01	6.12	7	No
490	1.9	1.3	12.22	6.21	12	7.24	6.35	8	No
510	1.9	0.8	7.95	4.95	10	7.98	6.11	9	No
530	2.3	0.9	13.01	10.25	13	7.21	6.19	9	No
550	1.7	1.5	10.25	8.86	10	7.29	5.77	7	No
570	1.7	1.5	12.85	8.64	12	8.21	5.65	9	Yes
590	1.5	1.1	10.35	6.21	12	8.45	5.23	10	Yes
610	1.6	1.2	10.45	10.45	10	8.67	7.21	9	Yes
630	2.4	1.4	12.84	6.57	12	8.91	7.38	11	Yes

4.1.1. Weight Solution

(1)

A-B Layer Weights

Based on mutual comparisons between criteria layer and indicator layer parameters, the following AHP judgment matrix is determined.

$${\mathrm{R}}_{A\text{-}B}=\left(\begin{array}{ccc}0.5& 0.4& 0.7\\ 0.6& 0.5& 0.9\\ 0.3& 0.1& 0.5\end{array}\right)$$

The solution is ${\mathrm{W}}_{N1}$ = (0.350, 0.417, 0.233).

(2)

B1-C Layer Weights

$$R_{B1\text{-}C}=\left(\begin{array}{cc}0.5& 0.4\\ 0.6& 0.5\end{array}\right)$$

The solution is ${\mathrm{W}}_{\mathrm{N}1}$ = (0.45, 0.55).

Calculating weights using entropy weight method, the solution is ${\mathrm{W}}_{\mathrm{M}1}$ = (0.50, 0.50).

(3)

B2-C Layer Weights

$$R_{B2\text{-}C}=\left(\begin{array}{cccccc}0.5& 0.75& 0.6& 0.55& 0.8& 0.65\\ 0.25& 0.5& 0.35& 0.3& 0.6& 0.35\\ 0.4& 0.65& 0.5& 0.4& 0.55& 0.45\\ 0.45& 0.7& 0.6& 0.5& 0.75& 0.6\\ 0.2& 0.4& 0.45& 0.25& 0.5& 0.1\\ 0.35& 0.65& 0.55& 0.4& 0.9& 0.5\end{array}\right)$$

The solution is ${\mathrm{W}}_{\mathrm{N}2}$ = (0.195, 0.145, 0.165, 0.187, 0.130, 0.178).

Calculate weights using entropy weight method, the solution is ${\mathrm{W}}_{\mathrm{M}2}$ = (0.166, 0.165, 0.168, 0.167, 0.165, 0.170).

(4)

A-C layer weights

In summary, the A-C layer weights are ${\mathrm{W}}_{\mathrm{A}\text{-}\mathrm{C}}$ = (0.168, 0.182, 0.074, 0.065, 0.070, 0.073, 0.063, 0.072, 0.233)

4.1.2. Score Calculation

Referring to Table 2, the fuzzy quantification table of grading parameters, the rock mass damage situation is converted into corresponding indicator membership degrees. Combined with the weights of layers A-C, a comprehensive score matrix is formed, as shown in Table 5.

Table 5. Comprehensive scoring matrix.

Distance from the Start of the Roadway/m	C1	C2	C3	C4	C5	C6	C7	C8	C9
10	0.168	0.546	0.074	0.195	0.07	0.073	0.189	0.072	0
30	0.168	0.91	0.222	0.065	0.21	0.073	0.189	0.216	0
50	0.504	0.546	0.222	0.195	0.35	0.219	0.189	0.216	0
70	0.168	0.546	0.222	0.195	0.35	0.219	0.189	0.36	0
90	0.168	0.91	0.222	0.065	0.35	0.219	0.063	0.216	0
110	0.168	0.182	0.074	0.065	0.21	0.073	0.063	0.072	0
130	0.168	0.182	0.074	0.065	0.07	0.073	0.063	0.072	0
150	0.168	0.182	0.074	0.065	0.07	0.073	0.063	0.216	0
170	0.168	0.182	0.074	0.195	0.07	0.073	0.063	0.072	0
190	0.168	0.182	0.074	0.195	0.07	0.219	0.189	0.216	0
210	0.504	0.182	0.222	0.065	0.21	0.219	0.189	0.36	0
230	0.504	0.546	0.222	0.065	0.21	0.073	0.189	0.072	0
250	0.168	0.91	0.222	0.195	0.21	0.219	0.189	0.072	0
270	0.168	0.91	0.37	0.325	0.35	0.365	0.189	0.36	0
290	0.168	0.546	0.37	0.325	0.35	0.219	0.189	0.36	0
310	1.176	0.91	0.222	0.325	0.35	0.219	0.189	0.072	0
330	0.84	0.91	0.37	0.325	0.21	0.365	0.189	0.36	0
350	0.84	0.91	0.37	0.195	0.21	0.219	0.189	0.36	0
370	0.84	1.274	0.518	0.325	0.49	0.365	0.315	0.216	0
390	0.84	1.274	0.518	0.455	0.35	0.219	0.315	0.36	0
410	0.84	1.638	0.518	0.455	0.35	0.365	0.441	0.504	0
430	1.176	1.638	0.666	0.585	0.63	0.511	0.315	0.504	0
450	1.176	1.274	0.666	0.455	0.35	0.511	0.441	0.504	0
470	0.168	0.91	0.074	0.065	0.07	0.657	0.441	0.36	0
490	1.512	1.638	0.666	0.585	0.63	0.657	0.441	0.504	0
510	0.84	1.638	0.518	0.455	0.49	0.657	0.567	0.648	0
530	0.84	1.638	0.666	0.585	0.63	0.657	0.441	0.648	0
550	1.512	1.638	0.666	0.585	0.49	0.511	0.441	0.36	0
570	1.512	1.638	0.666	0.585	0.63	0.511	0.567	0.648	2.33
590	1.176	1.274	0.666	0.585	0.63	0.511	0.567	0.648	2.33
610	1.176	1.274	0.666	0.585	0.49	0.657	0.567	0.648	2.33
630	1.512	1.638	0.666	0.585	0.63	0.657	0.567	0.648	2.33

The positive ideal solution for each object in the judgment matrix is (1.512, 1.638, 0.666, 0.585, 0.63, 0.657, 0.567, 0.648, 0.233), and the negative ideal solution is (0.168, 0.182, 0.074, 0.065, 0.070, 0.073, 0.063, 0.072, 0). After sorting the scores, when two adjacent scores exhibit a significant difference, we consider these two scores as the boundary points for dividing the grades. Based on the site conditions and borehole inspection results, combined with the requirements for support, the rock mass is divided into five damage grades: 0.000–0.010 is Grade I damage, 0.010–0.100 is Grade II damage, 0.100–0.250 is Grade III damage, 0.250–0.900 is Grade IV damage, and 0.900–1.000 is Grade V damage. The results of rock failure classification are shown in Table 6.

Table 6. Rock failure classification.

Distance/m	Score	Damage Grade	Distance/m	Score	Damage Grade
10	0.017	II	330	0.161	III
30	0.064	II	350	0.146	III
50	0.048	II	370	0.264	IV
70	0.039	II	390	0.260	IV
90	0.071	II	410	0.359	IV
110	0.002	I	430	0.445	IV
130	0.000	I	450	0.363	IV
150	0.002	I	470	0.112	III
170	0.002	I	490	0.504	IV
190	0.007	I	510	0.404	IV
210	0.028	II	530	0.423	IV
230	0.033	II	550	0.484	IV
250	0.068	II	570	0.998	V
270	0.103	III	590	0.972	V
290	0.051	II	610	0.972	V
310	0.206	III	630	1.000	V

The results of the classification indicate that damage patterns of the same grade are generally distributed continuously. There is one area of Grade II damage located within a Grade III damage zone and one area of Grade III damage located within a Grade III damage zone. For the sake of consistency and safety in support design, both of these areas are treated as higher-grade damage during support design. The grading range of the roadway is shown in Figure 2:

Figure 2. The grading range.

4.1.3. Classification of Rock Mass Damage

(1)

Grade I Damage

When the rock mass is in Grade I damage, the deformation of the roadway is minimal, there are no significant cracks within the rock layers, the overall damage to the rock mass is slight, and it has strong stability. Its inherent strength is sufficient to meet the requirements for support. In subsequent decisions regarding roadway support, no additional support measures need to be added.

(2)

Grade II Damage

When the surrounding rock is in Grade II damage, the rock mass has undergone a certain degree of deformation, requiring additional support measures to maintain roadway stability. However, the deformation of the roadway is not significant, causing minimal impact on pedestrian traffic and material transportation, and no roadway widening is necessary. Drill hole inspection results indicate that fracture development is concentrated in the shallow areas, with no significant fractures, ensuring good anchorage properties.

(3)

Grade III Destruction

When the surrounding rock is in Grade III destruction, the roadway deformation is significant, obstructing pedestrian and material transportation. During repair, roadway widening must be performed. Within the surrounding rock, fractures have extended into the middle region, with fractures still present at depths of 5–7 m. Anchor rod support is insufficient to meet support requirements, necessitating using high-preload long and short cables for coordinated support.

(4)

Grade IV damage

In Grade IV damaged surrounding rock, fracture development is more severe. Most other roadways above 7 m have no significant fracture development, with stable deep regions. However, in Grade IV damage, two or more fractures are distributed in the deep region above 7 m, with poor rock mass integrity and poor anchorability. Considering the severe deformation and damage of the roadway, additional channel steel beams are required for reinforcement.

(5)

Grade V Damage

The classification criteria for Grade V damage differ from the previous four grades and are added specifically to address certain watering seepage roadways. In these sections, the rock layers are significantly affected by mining activities from the 1303 working face, resulting in increased fragmentation of the surrounding rock. Severe fragmentation in shallow areas has led to water flow formation. Within the region, the surrounding rock softens upon contact with water, further developing plastic zones, making it difficult to ensure cable fixation effectiveness and thereby achieving high-stiffness support.

4.2. Rock Mass Zone Repair Design

4.2.1. Zone Repair Plan

For high-stress soft rock roadway, effective control of rock mass deformation can be achieved through the following measures: implementing rock mass grouting and enhancing support strength to control the extent of rock mass fragmentation. Once the roadway’s burial depth and cross-sectional form are determined, the degree of rock mass fragmentation is closely related to its residual strength. Rock mass grouting and enhancing support strength can increase the confining pressure of the shallow rock mass, thereby enhancing its residual strength, reducing the degree of fragmentation, and ultimately achieving the goal of controlling rock mass deformation and failure. The schemes for each region are shown in Table 7.

Table 7. Partition repair scenarios.

Shore	Regional Descriptions	Control Program
I	Small amount of deformation, overall stability	No additional support methods for the time being
II	Shallow fractured perimeter rock, overall integrity is fair, good anchorage	Tensioned high prestressing long bolts and cables with synergistic support, lagging grouting
III	Enclosed rock is more fractured, low integrity, fair anchorage	High prestressing long and short cables with synergistic support and lagging grouting
IV	Severe damage to the surrounding rock, deep fissure development, poor anchorage	Highly prestressed long and short cables with coordinated support, cable channel steel beams, lagging grouting
V	Internal water seepage, softening of surrounding rock, high stress, poor anchoring	Advanced high-pressure grouting modification water blocking, high pre-stress long and short cables

4.2.2. Support Parameter Design

Based on the schemes in Table 7, specific support schemes for each area are proposed as follows:

(1)

Bolt and Cable Parameters

Bolt and cable parameters are calculated using the limit equilibrium theory and suspension theory:

The length of the long cable is calculated using the following formula:

$$L=L_1+L_2+L_3+L_4$$

(15)

In the formula: $L$—cable length, m; $L_1$—cable anchoring length in stable rock layer, m; $L_2$—thickness of unstable rock layer requiring suspension, m; $L_3$—length used for upper tray and lock, taken as 0.15 m; $L_4$—length requiring external tensioning, taken as 0.25 m.

The value of $L_1$ is calculated using the following formula:

$$L_1=L\prime \times {\displaystyle \frac{D_1^2}{D_2^2-D^2}}$$

(16)

In the formula: $L\prime$—anchorage agent length; $D_1^2$—resin anchorage agent diameter, taken as 23 mm; $D_2^2$—anchorage eye diameter, taken as 32 mm; $D$—anchorage inner diameter, taken as 22 mm. The calculation results for each area are as shown in Table 8.

Table 8. Long cable length calculation.

Parameters	Region II	Region III	Region IV	Region V
$L^{\prime }$	60 cm3	60 cm3	70 cm3	70 cm3
$L_1$	1763 mm	1763 mm	2057 mm	2057 mm
$L_2$	4500	6000	7100	7000
$L$	6663	8163	9557	9457

The length of bolt is calculated using the following formula:

$$L=L_1+\mathrm{\Delta }+L_3$$

(17)

In the formula: $L$—the bolt length, m; $L_1$—the bolt anchorage segment length, m; $\mathrm{\Delta }$—the depth of the limit equilibrium zone penetrating the surrounding rock, m; $L_3$—the exposed length of the bolt, typically taken as 0.05 m. When short cables replace bolts for support, their length values are the same as those of the bolts.

The calculated bolt length for the north wing main roadway should be $L \ge 3.48 \mathrm{m}$, with the bolt length set to 3.5 m, and the subsequent short cable length set to 4.5 m.

The spacing $L_j$ and row spacing $L_p$ between long cables is determined by the following formula:

$$L_{\mathrm{j}}\le {\displaystyle \frac{1}{2}}\times L,L_{\mathrm{p}}={\displaystyle \frac{nN}{krB{L}_1}}$$

(18)

In the formula: $n$—number of cables arranged in each row of the roof; $N$—anchorage force of a single cable; $k$—safety factor, taken as $k$ = 1.5; $r$—unit weight of the roof rock layer; $B$—roadway width, 5.2 m; $L_1$—height of the fractured zone at the top of the roadway.

The prestressing force of bolts and cables is determined by the following formula:

$${\mathrm{F}}_{\mathrm{p}}\le 0.6\times {\mathrm{N}}_{\mathrm{b}}$$

(19)

In the formula: ${\mathrm{F}}_{\mathrm{p}}$—breaking load of bolts and cables; bolts: 254 kN, cables: 587 kN.

The calculation results for each area are as shown in Table 9.

Table 9. Calculation of the distance between long cables.

Parameters	Region II	Region III	Region IV	Region V
n	3	4	5	5
$L_1$	4500	6000	7100	7000
$L$	6663	8163	9557	9457
$L_{\mathrm{j}}$	≤3331 mm	≤4081 mm	≤4778 mm	≤4728 mm
$N$	607 kN	607 kN	607 kN	607 kN
$r$	2560 N/m3	2650 N/m3	2650 N/m3	1410 N/m3
$L\mathrm{p}$	2027 mm	1958 mm	2068 mm	3942 mm

The anchoring force of the bolts must be greater than the self-weight of the rock. Generally, the spacing between bolts is equal, denoted as a, then

$$a=\sqrt{{\displaystyle \frac{Q}{K\mathsf{\gamma }\mathrm{\Delta }}}}$$

(20)

In the formula: $Q$—anchorage force, taken as 300 kN; $K$—bolt safety factor, taken as 4; $\mathsf{\gamma }$—rock volume force, 25 kN/m³. The calculation yields the required spacing for the roadway $a\le 1.004 \mathrm{m}$. The spacing for short cables replacing bolts support is the same as that for bolts.

The value range for the long cables is calculated earlier, and the value was obtained by rounding up. The values for the bolts and short cables have already been specified. Similarly, the spacing and row spacing value ranges for the bolts, short cables, and long cables have been determined. Based on site conditions and construction experience, values should be obtained within these ranges. The final parameters selected for bolts and cables are as shown in Table 10.

Table 10. Summary of bolt and cable support parameters.

Shore	Region II	Region III	Region IV	Region V
Length of bolt (short cable)	3500	4500	4500	4500
Bolt (short cable) spacing	1000 × 1000	900 × 900	800 × 800	800 × 800
Length of long cable	6700	8200	9600	9700
Long cable spacing	2200 × 2200	1900 × 1900	1600 × 1600	1500 × 1500

(2)

Channel steel beams

18#A channel steel (height 180 mm, flange width 68 mm, web thickness 7 mm) is arranged along the roadway alignment. The channel steel is arranged in a 3-2-3-2 pattern, with a length of 3600 mm.

(3)

Sprayed Concrete

The total thickness of the sprayed concrete is 90 mm, with coverage of the metal mesh as the standard, and the concrete strength is no less than C20.

(4)

Water-blocking Materials

Based on the actual conditions at the mine site, a two-component rapid-setting inorganic filling and reinforcement material for mining applications is selected, with a water–cement ratio of 0.3:1. The A/B material ratio is 1:1, and the final grouting pressure is tentatively set between 3 MPa and 12 MPa (subject to on-site conditions).

Support diagrams for each section are shown in Figure 3:

Figure 3. Schematic diagram of support. (a) Region II, (b) Region III, (c) Region IV, (d) Region V.

4.2.3. Numerical Simulation Verification of Support Effectiveness

(1)

Model Establishment

Based on the graded control schemes for each damage zone and support parameters derived from the preceding sections, numerical simulations are conducted. The inclined section of the auxiliary transportation roadway of the northern wing is over 600 m in length, making overall modeling impractical. Therefore, except for the Grade I damage zone that does not require support, segments are selected from the remaining four damage zones based on the distribution of rock layers in the borehole columnar diagrams for modeling. The model dimensions are all 60 m × 30 m × 60 m, employing the Mohr–Coulomb constitutive relationship. A 10 MPa load is applied to the top surface with a pressure coefficient of 0.9. No displacement occurs on the remaining five surfaces. In the simulation, bolts and cables are modeled using cable elements, and the channel steel beams in Region IV are modeled using shell elements. The parameters of each rock layer are as shown in Table 11, and the numerical model is shown in Figure 4 (with surrounding rock layers of the roadway hidden).

Table 11. Rock mass parameters.

Name	Modulus of Elasticity/GPa	Poisson’s Ratio	Tensile Strength/MPa	Angle of Internal Friction/°C	Cohesion/MPa	Density/(g/cm3)
Siltstone	1.071	0.25	2.14	36.51	1.87	2.56
Mudstone	1.064	0.25	2.13	34.71	2.24	2.65
Coal	1.551	0.23	3.10	34.71	3.26	1.44
Middle Sandstone	1.384	0.24	3.16	34.59	3.05	2.63
Fine Sandstone	1.357	0.24	1.97	35.43	2.68	2.60

Figure 4. Numerical model for each district. (a) Region II model, (b) Region III model, (c) Region IV model, (d) Region V model.

(2)

Numerical simulation results for each region

After the initial model is established, excavation without support and with support is carried out on the model to check whether the support strength is up to standard by comparing the roadway deformation. The simulated deformation is as shown in Figure 5, Figure 6, Figure 7 and Figure 8:

Figure 5. Numerical simulation of region II. (a) X−displacement without support, (b) Z−displacement without support, (c) X−displacement after support, (d) Z−displacement after support.

Figure 6. Numerical simulation of region III. (a) X−displacement without support, (b) Z−displacement without support, (c) X−displacement after support, (d) Z−displacement after support.

Figure 7. Numerical simulation of region IV. (a) X−displacement without support, (b) Z−displacement without support, (c) X−displacement after support, (d) Z−displacement after support.

Figure 8. Numerical simulation of region V. (a) X−displacement without support, (b) Z−displacement without support, (c) X−displacement after support, (d) Z−displacement after support.

(3)

Verification of support effect

From Table 4 the amount of deformation in each area of the roadway is known, and compared with the simulation results, see Table 12. Simulated vs. actual.

Table 12. Simulated vs. actual.

Region	Range of Actual Rib Movement/m	Simulation of Rib Movement/m	Range of Actual Roof Movement/m	Simulation of Roof Movement/m
II	0.6–1.2	1.03	0.2–0.6	0.61
III	0.9–1.5	1.10	0.3–1.0	0.65
IV	1.2–2.4	1.65	0.6–1.5	1.02
V	1.3–2.4	2.18	0.4–1.8	1.31

Results obtained from numerical simulation are all within the range of the actual situation, prove that this simulation is reliable.

Compare the deformation obtained from the simulation of the roadways before and after support in each area obtained from the simulation, as shown in Figure 9:

Figure 9. Comparison of deformation before and after numerical simulation support.

Before the increase in support measures, the four areas of the roof sinking amount are 0.61 m, 0.65 m, 1.02 m, 1.31 m, and the two gangs move close to the amount of 1.03 m, 1.10 m, 1.65 m, and 2.18 m, respectively. After adding support measures, the deformation is significantly reduced, the roof sinking amount is 0.23 m, 0.22 m, 0.21 m, 0.29 m, reduced by 62%, 66%, 79%, 78%, respectively; the amount of two gangs approaching is 0.32 m, 0.21 m, 0.30 m, 0.44 m, reduced by 69%, 80%, 82%, 80%, respectively. And the final deformation are less than 0.45 m, within the allowable deformation, so the zoning repair program meets the safety requirements of supporting.

5. Industrial Test

To observe the activity pattern of surrounding rock in the auxiliary transportation roadway of the northern wing, examine the maintenance effect of the roadway, and study the reasonableness of the support parameters, set up the corresponding measuring station, and carry out the observation of the roadway surface displacement through the laser rangefinder in the area IV and V, which are originally damaged seriously, and the results are as shown in Table 13 and Table 14.

Table 13. Data record table for Stations 1 and 2 in Region IV.

Days/d	Station 1 Roadway Rib Movement/mm	Station 1 Roadway Roof Movement/mm	Station 2 Roadway Rib Movement/mm	Station 2 Roadway Roof Movement/mm
1	0.5	1	0	1
3	1	2	1.5	3
6	5	5	5.5	7
9	10	9	11.5	12
12	14	12	16.5	15
15	18	16	20.5	17
18	22	18	23.5	19
21	26	21	25.5	21
24	27	21	25.5	21
27	28	21	26.5	21
30	30	21	27.5	22
33	30	21	27.5	22.5
36	31	22	27.5	22.5
39	31	22	27.5	22.5
42	31	22	27.5	22.5
45	31	22	27.5	22.5
48	31	22	27.5	22.5

Table 14. Data Record Table for Stations 3 and 4 in Region V.

Days/d	Station 3 Roadway Rib Movement/mm	Station 3 Roadway Roof Movement/mm	Station 4 Roadway Rib Movement/mm	Station 4 Roadway Roof Movement/mm
1	0	1	0	1
3	0.5	0.5	0	1
6	3	2	1	3
9	5	5	5	7
12	9	8	11	11
15	13	11	16	13
18	17	15	20	15
21	22	17	23	17
24	26	20	25	20
27	27	21	25	22
30	27	21	26	22

Measuring Stations 1 and 2 are arranged in area IV, the roadway section in this area is large, and the preliminary support has been completed, but the supplementary support has not been constructed yet; as shown in Figure 10 after 20 to 25 days of slow growth, the roadway surface deformation enters the creep deformation stage, and the deformation speed of the rib is larger than the roof; at present, the roadway deformation in this area is relatively small, and the full-anchor support combining the short and long cables greatly improves the range of the anchor circle and provides a large preload force. Under the high-preload active support, the development of fissures in surrounding rock is effectively controlled, the filling effect of lagging grouting on the fissures improves the stability of roadway.

Figure 10. Measurement stations 1 and 2.

Measuring Stations 3 and 4 are located in area V, which has been significantly affected by the mining activities of the 1303 working face. As shown in Figure 11, as the degree of rock fragmentation in the roadway increases and fractures become more permeable, watering seepage occurs, resulting in widespread moisture in the roadway roof and rib in this area. After repairs are completed, the number of seepage areas in the rib has significantly decreased. Currently, there is still one seepage area, where the shallow rock mass in the roadway is soft, but no significant deformation has occurred. The roadway remains in a stable condition overall.

Figure 11. Measurement stations 3 and 4.

6. Conclusions

This paper takes the repair of the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine as its background. After collecting the deformation parameters of the site, the data are analyzed using the FAHP–entropy weight TOPSIS method, and the rock mass damage grades are classified, with corresponding support schemes provided. Numerical simulations are conducted using FLAC3D to verify the support effectiveness, proving the feasibility of the scheme, and field tests are also carried out.

After all work is completed, the following conclusions are drawn:

(1)

Statistical results indicate that roadway deformation and fissure development exhibit a high degree of consistency, effectively reflecting the extent of roadway damage.

(2)

A grading scheme is established with the actual damage condition of the roadway as the primary influencing parameter. Based on nine primary parameters, including rib movement, roof movement, seepage, and maximum depth of distribution of rib cracks, the comprehensive damage score for the roadway is calculated using the FAHP–Entropy Weighting TOPSIS combined weighting evaluation model, and the roadway is classified into five damage grades. This scheme effectively quantifies the actual damage condition of the roadway. For other roadways with varying degrees of internal damage, integrating their geological conditions with the solutions presented in this paper can provide valuable reference for enhancing the rationality, reliability, and cost-effectiveness of support design.

(3)

Based on the classification results, a graded control plan is developed for the auxiliary transportation roadway of the northern wing. Except for the Region I damage area, which does not require additional support measures, Region II are supported using “Tensioned high prestressing long bolts and cables with synergistic support, lagging grouting”, Region III are supported using “High prestressing long and short cables with synergistic support and lagging grouting”, Region IV are supported using “Highly prestressed long and short cables with coordinated support, cable channel steel beams, lagging grouting”, and Region V are supported using “Advanced high-pressure grouting modification water blocking, high pre-stress long and short cables”.

(4)

After verifying the results through numerical simulation, the deformation of the roadways in these areas showed significant improvement following the addition of the support structures required by the design. The results indicate that the scheme is reasonable and effective, ensuring the safe use of the auxiliary transportation roadway of the northern wing.

(5)

On-site displacement monitoring showed that after the support is completed, the roadway deformation stabilized after 35 days, with the rib movement controlled within 35 mm and the roof movement controlled within 25 mm. The deformation of the roadway is effectively controlled. This plan has good support effects and can meet the needs of safe production. The rock mass failure classification based on FAHP–Entropy Weight TOPSIS method is reasonable and feasible.