1. Introduction
The geological and hydrogeological conditions of coal mines in China are extremely complex, making China a country with one of the worst records for coal mine water disasters in the world [
1,
2]. According to incomplete statistics, coal mines in China suffered 153 water disaster accidents from 2008 to 2021 [
3], causing tremendous economic losses to the country and its people. Applying underground grouting to reinforce the floor aquitard and transform the aquifer is one of the commonly used methods of coal mine water disaster prevention. However, grouting reinforcement projects have been characterized by concealment and complexity, which makes the evaluation of grouting effectiveness extremely difficult and seriously restricts the application of grouting technology. Therefore, how to scientifically, effectively, and accurately evaluate the effectiveness of grouting is an urgent problem to be solved.
Many academics and engineering technicians in China and elsewhere have conducted research on the evaluation of underground grouting effectiveness. Methods commonly used include geophysical detection methods [
4,
5,
6,
7], packer testing [
8,
9,
10], computer numerical simulations [
11,
12,
13,
14], and comprehensive evaluation methods, among others.
In the evaluation of grouting effect, geophysical detection methods are usually used as one means of geophysical exploration to detect the scope and effectiveness of grouting comprehensively. Through a geophysical comparison before and after grouting, the grouting effect can be evaluated macroscopically, especially the horizontal and vertical continuity of the grouting area [
15,
16]. The field water pressure test method can directly reflect the strength and permeability of rock and soil, and can directly evaluate the effectiveness of grouting [
17,
18]. With recent rapid development of computer applications, greater accuracy and simulation realism have led to increased use of numerical analysis methods to simulate the effects of grouting [
19]. Some scholars use numerical simulation software such as FLAC3D 6.0and UDEC 7.00 to simulate and predict the grouting effect [
20,
21], which provides reference for the evaluation of the reinforcement effect of grouting.
Numerical simulation can thus be used to evaluate grouting effects to some extent, but it should not be regarded as the only evidence. Numerical simulation is merely a predictive model. Its results are influenced by various factors, including the original assumptions, parameter selection, and the settings adopted for the initial conditions. Therefore, for comprehensive analysis of grouting effectiveness, numerical simulation should be combined with other evaluation methods.
Evaluating the overall effectiveness of underground grouting is a multifaceted evaluation problem with many uncertain indicators. The ambiguity of such indicators may lead to an uncertain relationship between indicators and evaluation results. The fuzzy comprehensive evaluation method is based on fuzzy mathematics and has been widely applied to handle fuzzy problems. Jin et al. [
22] used the analytic hierarchy process (AHP) cloud model and the fuzzy comprehensive evaluation method to assess the influencing effects of a grouting project at a Pingnan limestone mine. This combination of methods fully considers the ambiguity and randomness of indicator factors, thereby improving the reliability of the results. Subsequent monitoring of the project validated the accuracy of the model. Liu et al. [
23] evaluated the curtain grouting effect at a water station by establishing an objective and reasonable fuzzy evaluation method that combines interval intuitive fuzzy sets, prospect theory, and improved D number theory to further increase the diversity range of the evaluation indicators and take full account of the incompleteness of the decision information generated by experts, proving the consistency and superiority of the model. The fuzzy analytic hierarchy process was employed by Zhu et al. [
24] to quantify the pre-grouting effects on the Tongluo Mountain tunnel using indicators such as integrity, continuity, and solidity. The results agreed with field test outcomes, providing a reference for similar project evaluations.
In summary, the approaches that has been adopted in studies of the detection and evaluation of grouting effects involving single-factor or single-method qualitative or quantitative analysis have certain limitations. Even when multiple indicators are used to evaluate grouting effectiveness, the reliability of the results is not high due to the lack of scientific and reasoned determination of the weights of each indicator, which restricts the application of grouting technology.
In the present study, the grouting project at workface 15,051 in the ancient Han Mountain coal field in Jiaozuo was selected as the objective. The authors selected the grouting volume, the length of the meter grouting, the value of dry material per ton of water, the complexity of faults, and the threat degree of water inburst at the working face as the evaluation index, and proposed a fuzzy variable set comprehensive evaluation method of grouting effectiveness based on the subjective and objective combination of AHP-CRITIC. While the AHP method retains the expert’s mature experience in weight allocation, the CRITIC method is adopted to increase the objectivity of weight allocation by analyzing the relationship between data, and quantitative evaluation of the grouting effect is carried out based on fuzzy variable set theory, which is more suitable for evaluating objects charactized by uncertainty and complexity. It is anticipated that the findings of this study will provide technical support for the quantitative identification of the grouting effects at workfaces.
2. Research Method
2.1. Fractal Dimension Theory
The fractal dimension theory, also known as the dimension theory, is a mathematical concept that describes the morphology and structure of complex systems. This theory primarily investigates the dimensional properties of fractal objects, including both integer and non-integer dimensions. In geological structure research, the self-similar dimension
DS is often used to analyze the complexity of structures, calculated from
where
N(
a) is the number of similar shapes and
a is the scale ratio.
The fractal dimension is positively correlated with the complexity of the study object; that is, the larger the fractal dimension, the more complex the study object is considered to be.
2.2. AHP-CRITIC Combination Weighting Method
The AHP [
25] is a multi-level factor weight decision-making analysis method used to quantify qualitative problems. This method involves breaking down the objective into multiple factors and organizing these factors into a structured model in a hierarchical manner based on their relationships, influences, and dependencies. This hierarchical structure allows for a systematic analysis of complex decisions by comparing and ranking factors at different levels.
The CRITIC method [
26,
27] is an objective weighting technique that determines weights based on the intensity of comparison and the conflict between indicators. This method uses standard deviation to represent the intensity of the comparison between indicators, and correlation coefficients to represent the conflict between them. A large standard deviation of an individual indicator implies greater volatility, hence a higher weighting. Conversely, if the correlation coefficients between indicators are large, it suggests less conflict between them, leading to relatively smaller weightings. The CRITIC method takes both correlation weights and information weights into account, resulting in a more reasonable determination of indicator weights.
The AHP relies on the relative importance of evaluation indicators, which increases the subjectivity of the analysis. By contrast, the CRITIC method uses the inherent properties of the evaluation indicators to calculate weights, which is more objective. Therefore, to establish an optimized combined weighting model that incorporates both subjective and objective weights, a target function was developed on the principle of minimum relative information entropy. The specific target function is
where
F is the information entropy;
is the subjective weight determined by the AHP; and
is the objective weight determined by the CRITIC method.
The Lagrange multiplier is used to determine the combined subjective and objective weights,
Wj, giving
2.3. Fuzzy Variable Set Evaluation Model (FVSEM)
The FVSEM is based on fuzzy mathematics and the theory of variable sets. Firstly, it processes the various indicators of the evaluation object by fuzzifying them to convert them into fuzzy values; it then utilizes the theory of variable sets for weighting or combination to obtain the evaluation. The FVSEM is more flexible and reliable than traditional evaluation methods and better adapted to the evaluation of objects with uncertainty and complexity.
2.3.1. Basic Principle
Let there be a fuzzy concept
A in the universe of discourse
U. For any element
u in
U, at any point on the continuum of the relative membership function the relative membership degree of
u to
A is
µA(
u), and the relative membership of the opposite fuzzy concept
AC to
A is
[
28,
29].
Let
DA(
u) be the relative difference degree of
u with respect to
A, then
Defining the relative difference degree of
u with respect to
A gives its mapping
It is known from the theory of fuzzy variable sets that
Then, from Equations (5) and (6), the relative membership is
2.3.2. Membership Degree Model
Let
X0 = [
a,
b] be the attractive domain of fuzzy variable set
V on the real axis,
X1 = [
c,
d] be the range domain of fuzzy variable set containing
X0,
M be the midpoint value of the attractive domain interval [
a,
b], and let
x be the quantized result value of any index at any point on the real axis, using
x and
X0, The relative position relation of
X1 calculates the relative difference degree
DA(
u). The positional relationship between M and the intervals [
a,
b] and [
c,
d] is shown in
Figure 1.
When
x ∈ [
c,
M], the relative difference is given by
and when
x ∈ [
M,
b], the relative difference is given by
When x ∉ [c, d], the relative difference degree DA(u) = −1. If β is a non-negative exponent, the value β = 1 is usually assumed.
2.3.3. Evaluation Model
After determining the relative membership of the evaluation indicators corresponding to the levels based on the membership function, the comprehensive membership degree
µr is calculated using the fuzzy variable set evaluation model, expressed as
where
j is the index number of the indicator,
j = 1, 2, …,
m;
r is the sequence number of the level,
r = 1, 2, …,
m;
α is the parameter of the optimization criterion, with the least squares criterion given by
α = 1 and the least mean squared criterion given by
α = 2; and
p is the distance parameter (
p = 1 for the Hamming distance,
p = 2 for the Euclidean distance).
The level feature value
H is calculated from
2.4. Comprehensive Model Building
The key steps in establishing and applying a fuzzy variable set evaluation model include:
(1) Determining evaluation indicators and weights: First, determine the indicators that need to be evaluated, then determine the weights of each indicator. These can be obtained through expert consultation, analytic hierarchy process, CRITIC, etc.
(2) Establishing the fuzzy variable set: transform each evaluation index into a fuzzy variable set. The variable set consists of a membership function, which describes the shape of the fuzzy set in which the index is located, and a membership value, which represents the value of the index.
(3) Constructing a set of fuzzy rules and carrying out reasoning: Based on expert knowledge or experience, formulate a series of fuzzy rules to describe the influence of various evaluation factors on the evaluation results. The membership value of the evaluation result is derived by matching the actual value of the evaluation index with the membership function.
(4) Synthesizing evaluation results: According to the membership value of the evaluation results obtained by reasoning, the synthesis method is used to synthesize the results into a comprehensive evaluation result. The results can be normalized as needed.
(5) Interpretation and application: Interpret the fuzzy variable set evaluation results to obtain evaluation decisions about evaluation objects.
In summary, the fuzzy variable set evaluation model introduces the concept of variable sets, which is better able to handle situations with many indicators and factors associated with the evaluation objects. It provides a flexible framework for evaluation that may be adjusted to improve its accuracy and applicability if required in specific circumstances (
Figure 2).
4. Discussion
4.1. Model Reliability Analysis
The accuracy and reliability of the evaluation depends on four aspects: the selection of appropriate indicator factors, their quantification and classification, the determination of weightings, and the feasibility of the method.
(1) Indicator selection: Five common indicators include grouting final pressure, grout volume, permeability coefficient and water absorption rate, borehole water inflow, and water-inrush coefficient. It is generally believed that a good grouting result means that the strength and water resistance properties of the grouted rock layers are significantly improved, and that the risk of water inrush has been reduced accordingly. Based on the experience of water control in northern Chinese coal mines and expert advice, choosing these five factors as evaluation indicators is reasonable.
(2) Indicator quantification and classification: Of the five secondary indicators, the grouting volume, length of grouting in meters, dry material value per ton of water, and water-inrush coefficient are all described directly as numbers. The complexity of fault zones is often quantitatively evaluated using fractal theory [
35]. Since all of the secondary indicators can be quantified in this way, classification can be readily carried out.
(3) Indicator weights: The weighting determination adopted a combination of the AHP and CRITIC methods, which retains subjective expert experience in weighting allocation and simultaneously increases its objectivity by analyzing relationships between data. Therefore, the determination of evaluation indicator weightings is feasible.
(4) Choice of evaluation method: The method of fuzzy variable set evaluation is a mathematical tool for dealing with uncertainty, fuzziness, and incomplete information. It is suitable for solving problems with attributes that are difficult to accurately describe using traditional quantitative methods. Compared to other evaluation methods, the indicator partition construction and membership calculation in fuzzy variable set theory are better able to characterize complex nonlinear relationships between indicator factors and grouting effects. There are many indicators for evaluating the grouting effect on the floor of the working face. Some of them, such as the complexity of the faulting pattern, have to be assessed qualitatively and are therefore subjective. Therefore, using the fuzzy variable set evaluation method to evaluate the grouting effect is a rational approach to the actual situation.
4.2. Evaluation of Grouting Effect
To further verify the accuracy of the model, the same evaluation indicators, weightings and model were used, but with the grouting volume, meter-long grouting amount, and ton-of-water dry material value all set to zero. The index of the water-inrush threat was used for the ungrouted face, with the critical water-inrush coefficient at 0.06 MPa/m. The relationship between the characteristic value
H and the grouting effect is shown in
Table 7.
The quantitative recognition and classification of the working face without grouting is shown in
Figure 15.
Figure 15 shows that before grouting, the areas of poor, qualified, and good grouting effects account for 91.18%, 8.78%, and 0.04% of the face area, respectively. Comparison with
Figure 14 clearly shows the significant improvement due to grouting.
4.3. Grouting Effect Verification
In order to verify the grouting effect, inspection hole new 1 (drilling field No. 4 in the return air lane), hole new 2 (drilling field No. 7 in the return air lane), hole new 3 (drilling field No. 13 in the return air lane), and hole new 4 (drilling field No. 6 in the transport lane) were bored into the 15,051 working face. The outlet points of these four holes were all located in the good areas evaluated by the model, and the holes all passed through the L8 limestone aquifer. The final hole layer was located in the L2 aquifer, and the water inflow was 8 m3/h, 2 m3/h, 7 m3/h, and 2 m3/h, respectively, which meets the requirement that the water inflow of the hole does not exceed 10 m3/h, indicating that the grouting effect was good.
The 15,051 working face of Guhanshan mine was safely mined with no water-inrush events during this period. After the floor of the working face was grouted and transformed, it achieved the effect of isolating the water layer, verifying the reliability of the model.
5. Conclusions
(a) The dimensional values of faults in the 15,051 working face were determined using fractal theory, enabling the working face to be classified in terms of faulting complexity. It was found that the overall fault complexity of the 15,051 working face was simple to relatively simple. These results laid a sound foundation for the subsequent quantitative evaluation of the effectiveness of the grouting.
(b) The water-inrush coefficient of the working face after grouting was calculated based on grouting borehole records of final depth, dip angle, and water pressure measurements. Accordingly, the risk of water inrush at the grouted face was divided into four possible zones: safe, low-threat, high-threat, and danger zones. The results show that the risk of water inrush was reduced after the grouting of the 15,051 working face. It not only shows that the effect of the grouting was good, but also verifies the results of the quantitative evaluation model.
(c) Based on the actual conditions of the working face, and with reference to previous studies, grouting volume, length of grouting in meters, dry material content per ton of water, water-inrush threat level, and fault structure complexity were selected as evaluation indicator factors. The subjective and objective weights of the indicator factors were determined using the AHP and CRITIC methods, respectively, and the overall weights were determined using a combination of weighting methods. This rational approach retained expert advice to be used along with objective weighting methods.
(d) A comprehensive evaluation model based on fuzzy variable set theory was developed to quantitatively evaluate the effect of the floor grouting project at the 15,051 working face in the Guhanshan mine. Optimal, good, qualified, and poor grouting effect accounted for 4.66%, 74.34%, 21.00%, and 0% of the total area, respectively, with a high rate of excellence reaching 79% overall. These values agree closely with on-site observations, underlining the applicability of the evaluation method at the Guhanshan mine and providing a reference for similar projects in the future.