1. Introduction
A slope containing a coal seam in a goaf is a slope formed when the unmined coal seam is exposed to the surface of the slope, during the process of excavation in the goaf, as shown in
Figure 1. Recently, with the large-scale construction of highway projects in China, highways are increasingly passing through goafs, so excavation for road cutting in goafs is required. When the road slope contains shallow unmined coal seams, the slope is prone to collapse, which affects the normal construction and operation of the highway, and even threatens human safety and lives. Therefore, analyzing the factors influencing the goaf slopes containing a coal seam is essential.
To address the problem of slope stability, the current research directions mainly include: (1) new methods for analyzing slope stability, such as for calculating the slope stability, based on the generalized Hoek–Brown criterion [
1], for predicting the slope stability, based on the finite element analysis and field data superposition [
2], and for predicting the slope stability, based on machine learning [
3]; (2) a slope stability analysis of various special soils, such as expansive soil [
4,
5], unsaturated soil [
6], soft soil [
7], etc.; (3) a slope stability analysis under various special conditions, such as earthquake [
8] and rainfall conditions [
9,
10]; (4) measures for slope reinforcement, such as planting plants [
11,
12], injecting a curing liquid [
13], etc. Regarding the stability of goafs, the current research directions are mainly focused on: (1) the subsidence prediction of goafs, such as a numerical simulation subsidence prediction [
14] and intelligent subsidence predictions using computers [
15], etc.; (2) the scope of the goaf detection, to detect water-logged [
16] and old goafs [
17]; (3) goaf treatment methods, such as the application of fly ash geopolymer grouting material [
18] and the grouting method when the goaf is saturated with water [
19]; (4) the influence of various special working conditions on the stability of goafs, such as under water static–dynamic load coupling [
20] and under earthquake loads [
21].
Many studies have focused on the stability of goafs or slopes, but studies are lacking on the stability of goaf slopes. Considering the stability of a goaf slope, Xie et al. [
22] studied the influence of the underlying goaf on an open-pit slope, based on various methods, such as a finite element analysis and mechanical theoretical calculation, and the results showed that the instability and collapse of the goaf roof would lead to the local collapse of the open-pit slope. To study the influence of the goaf span, position, and double-layer goaf working conditions on slope stability, Xu et al. [
23] applied ANSYS software to establish several models, and finally came to the conclusion that all three working conditions would lead to the decline of the slope stability coefficient. To explore the instability mechanism of a red clay slope under the influence of a goaf, Li et al. [
24] revealed the instability and failure development law of this type of slope by combining a numerical simulation analysis with the limit equilibrium theory. The results showed that the instability and failure mechanism of the red clay slope was a ’shear-tensile crack-slip-collapse’. To solve the problem of complicated processes and a low accuracy in the safety evaluation of the goaf slope, Zhao et al. [
25] established a risk evaluation model of the goaf slope using the TOPSIS theory. The results show that the evaluation results of the established model are consistent with reality, and can better evaluate the state of the goaf slope. Zhang et al. [
26], to explore the slope instability process, analyzed the damage, failure, and instability processes of a localized rock mass in the process of multiple minings of a multistage slope, based on the RFPA finite element software. The results showed that the continuous mining of a multistage slope was mainly characterized by local instability and failure, under the influence of time and space effects. Through the above analysis, we found that scholars have studied the stability of goaf slopes, but have mostly focused on the influence of coal seam mining on the stability of the existing slopes that do not contain coal seams. The stability of a goaf slope with a coal seam has not been analyzed.
Based on this, in this study, we considered the excavation of a cutting slope containing a coal seam in the K1641 + 890–K1641 + 950 section of the Jixi Section reconstruction and expansion project of the National Dan-A Highway. We used three-dimensional finite element software Midas GTS as the calculation engine, selected the slope stability coefficient as the analysis index, and identified the factors influencing a slope containing a coal seam stability in a goaf through a single-factor analysis. We quantitatively evaluated the importance of these stability-influencing factors with the orthogonal test method, and then identified the main and minor factors controlling the slope stability. Our results provide a reference for the treatment of coal seams containing a slope in a goaf, so as to improve the slope stability coefficient.
The rest of this paper is structured as follows:
Section 1 introduces our preparatory work, prior to the establishment of the model, including outlining the possible factors influencing slope stability, the method of calculating the stability coefficient, and the model parameters.
Section 2 introduces the modeling process, the related settings, and the stability analysis results under actual working conditions.
Section 3 describes the process of analyzing the major and minor influencing factors.
Section 4 outlines the novelty of the findings and the study results, and provides a discussion of the study shortcomings.
Section 5 describes the conclusions of this study.
4. Analysis of the Influencing Factors
4.1. Single-Factor Simulation
By consulting the data and referring to our engineering experience, we designed a single-factor simulation analysis.
Table 8 shows the values of the coal seam position H, the roadway width W, the slope gradient i, the coal seam thickness T, the roadway position S, the mining depth and mining thickness ratio R, the coal seam cohesion c, the coal seam internal friction angle
, and the coal seam inclination angle α. Taking the slope calculation model in
Section 3.1 as the basic model, we analyzed the influence of the above single factors on the stability of the slope containing a coal seam in a goaf by changing the parameter, while the other factors remained unchanged. The analysis and calculation results are shown in
Figure 8.
When other factors were kept the same, as in the basic model in
Section 3.1, we found, as shown in
Figure 9a, that when the coal seam position was changed, with the decrease in the coal seam position, the slope stability coefficient remained unchanged at first (2.5 < H < 5.5) and then sharply dropped (5.5 < H < 11.5). We found that with increasing roadway width, the slope stability coefficient gradually decreased. Changing the slope gradient, with the increase in the slope gradient, the slope stability coefficient gradually decreased. With the increase in the coal seam thickness, the slope stability coefficient gradually decreased. When changing the roadway position, with the horizontal distance from the slope foot changing from −15 to 15 m, the slope stability coefficient first decreased (−15 < S < 0) and then increased (0 < S < 15), which was almost symmetrical, but the change range was small, at less than 0.05.
Figure 9b shows that with the increases in the mining depth and the mining thickness ratio, the slope stability coefficient first increased (5 < R < 15) and then remained unchanged (15 < R < 35); changing the cohesion of the coal seam, with the increase in the coal seam cohesion, the slope stability coefficient gradually increased. With the increase in the internal friction angle of the coal seam, the slope stability coefficient gradually increased. When the coal seam dip angle changed from −15°to 0°, the slope stability coefficient gradually increased.
From the above analysis results, we found that the coal seam position (between 5.5 m and 11.5 m), the roadway width, the slope gradient, and the coal seam thickness all adversely affected the slope stability, that is, the higher the values of the above four factors, the lower the slope stability coefficient. Additionally, the ratio of the mining depth to the mining thickness (5–15 m), the coal seam cohesion, the coal seam internal friction angle, and the coal seam dip angle favorably influenced the slope stability, that is, the higher the values of these four factors, the higher the stability coefficient of the slope. However, the roadway position had little influence on the stability of the slope, affecting the variation in the stability coefficient by less than 0.05.
According to the above analysis results, we eliminated one factor, the roadway position, which had little influence on the stability of the slope containing a coal seam in a goaf. We then designed the multifactor orthogonal experiments on the coal seam position (5.5–11.5 m), the roadway width, the slope gradient, the coal seam thickness, the coal seam cohesion, the mining depth and mining thickness ratio (5–15), the coal seam dip angle, and the coal seam internal friction angle, which showed a notable influence on the slope stability, to further determine the major and minor factors affecting the slope stability.
4.2. Orthogonal Multifactor Simulation Test
The orthogonal design is the most important method in a multifactor simulation experiment. This method is a multi-factor simulation test method [
29] that is based on the fractional principle of factor design and uses an orthogonal table, derived from a combination theory to arrange and design simulation tests. Then, the results are statistically analyzed.
In this orthogonal design, we selected the eight influencing factors as the study objects, and each factor had three levels, as shown in
Table 9. The factors refer to the items that affected the simulation test results, and the levels refer to the size and level of each factor in the simulation test process. According to the principle of orthogonal design, we used the L
27(3
8) orthogonal table to arrange the orthogonal simulation test of eight factors and three levels, then we obtained the orthogonal design table of the parameter levels of each factor influencing the slope containing a coal seam in a goaf, as shown in
Table 10.
Table 10 shows that we obtained 27 groups of different levels of combinations of slope parameter factors, corresponding to 27 rows in the orthogonal table; that is, the number of simulation tests was 27. We calculated each simulation of the slope stability coefficient, according to a set of parameter levels in
Table 3, and we recorded the calculated slope stability coefficient. The slope stability coefficients of the 27 different parameter level combinations obtained from the simulation are shown in the last column of
Table 10.
4.2.1. Range Analysis of the Slope Stability Coefficient
The purpose of the range analysis is to calculate the range of the R values of the simulation results, corresponding to each column and level in the orthogonal table using mathematical statistics. Because the R of a factor is defined as the difference between the maximum and minimum value of the factor, the relative influence of the factor on the slope stability could be judged, according to the value of R. A large R indicates that the factor has a strong relative influence, so is a relatively main influencing factor. A small R indicates that this factor has a relatively weak influence and is a relatively minor factor [
30]. During the range analysis, the total value (Tij) of the simulation results at each level of each factor should be first calculated, and then the average value (Kij) of the simulation results at each level of each factor should be calculated, according to Formula (4). Finally, the R value (Rij) of each factor can be obtained by Formula (5).
According to the above formula and combined with the simulation results of the slope stability coefficient in
Table 3, we calculated the
R value of the slope stability, and the results are shown in
Table 11.
According to the ranges listed in
Table 11, the R values corresponding to the eight factors
H,
W,
i,
T,
R,
c,
, and
α were 1.21, 1.85, 0.83, 0.72, −0.05, −0.69, −0.71, and −0.57, respectively. The R values of the eight factors in descending order were R
W > R
H > R
i > R
T > R
> Rc > R
α > R
R. That is, among the eight factors that impacted the slope stability that we analyzed, because the R value corresponding to
W was the largest, we found that the change in the roadway width
W had the strongest relative impact on the slope stability coefficient index. Ranked second was
H, followed by
i,
T,
,
c,
α, and R, indicating that the level change of the last had the weakest relative influence on the slope stability coefficient. Therefore, we found that the ranking of the relative influence of each factor on the slope containing a coal seam in a goaf was
W > H > i > T > > c > α > R.
4.2.2. Variance Analysis of the Slope Stability Coefficient
The range analysis method could only be used to determine the relative influence of each factor on the slope stability coefficient, but could not be used to determine whether the influence of each factor on the slope stability coefficient was significant and the magnitude of the significance. The variance analysis, as a method of analyzing experimental data, can be used to study whether the influence of factors on the experimental results is significant. Therefore, through the analysis of variance on the slope stability coefficient, we investigated the significance of the influence of the eight factors H, W, i, T, R, c, and α on the slope stability coefficient.
According to the theory of the variance analysis of the orthogonal test and the data of the slope stability coefficient in
Table 10, we calculated the mean square, degree of freedom, the sum of squares, and
p value of each factor, where
p < 0.05 indicated that the factor significantly influenced the slope stability coefficient. The results are shown in
Table 12.
Table 12 shows that among the eight factors analyzed, the corresponding P values of factors H, W, i, T,
c,
, and α were all less than 0.05, indicating that these seven factors significantly influenced the slope stability coefficient. The P value of factor R was 0.675 > 0.05, indicating that this factor had no significant influence. Combined with the differences in the F values, we further compared the significant differences among the seven factors that had a significant influence. Among them, the F value of the roadway width was 245.375, which was the most significant influence. This showed that reducing the roadway width can considerably improve the stability of a slope containing a coal seam in a goaf, during the implementation of practical projects. The F value of the coal seam position was 104.751, and its influence degree was second only to the roadway width. If the roadway width cannot be changed, the coal seam position plays a decisive role in the stability of the coal seam containing a slope in the goaf. The F value of the slope gradient was 50.375, ranking it third in terms of influence. Although its significance was less than that of the above two factors, the degree of significance was still highly significant, so the slope gradient also played a crucial role in the stability of the slope containing a coal seam. The F values of the coal seam thickness, coal seam internal friction angle, coal seam cohesion, and the coal seam dip angle were 36.522, 35.865, 34.298, and 23.259, respectively, ranking their influence as fourth to seventh, respectively. The significance of these four factors was relatively weak, and they had less influence on the stability of the slope containing a coal seam in a goaf than the above three factors.
From the above analysis, we found that, among the factors affecting the stability of the slope containing a coal seam in a goaf, the roadway width, the coal seam position, and the slope gradient were the main significant factors affecting the stability of the slope. This showed that grouting in goaf roadways, to reduce roadway width, cutting the top of the slope to control the coal seam position, and reducing the slope gradient can considerably improve the stability of slopes in actual projects. Although the coal seam thickness, the coal seam internal friction angle, the coal seam cohesion, and the coal seam dip angle are also significant factors influencing the slope stability, their degree of influence is less than that of the above three factors, so they are minor, but significant, factors influencing slope stability.
5. Discussion
The novelty of this study of the factors influencing the stability of a slope containing a coal seam in a goaf, studied in the coupled analysis of the influence of goaf roadways and coal seams on slope stability. Considering this special working condition, we analyzed the major and minor influencing factors, with the results providing a scientific basis for the analysis for the protection of this type of slope in goafs.
Our findings enrich the literature on goaf slope stability because the previous researchers mostly focused on the influence of goaf excavations on existing slopes. Studies were lacking on unexploited coal seams in a goaf exposed to the slope surface, due to excavation.
From the analysis results of the numerical simulation and the actual working conditions on site, the sliding surface of this type of slope is located near the coal seam. The roadway width, coal seam position, and slope gradient are the main influencing factors affecting the stability of this type of slope, but their influencing mechanisms are different. The influence mechanism of the roadway width: the collapse of the roadway roof causes the deformation of the upper slope, with the increase of roadway width, the deformation of the slope, caused by the collapse, also increases, and worsens the overall stability of the slope. The influence mechanism of the coal seam position: the contact part between the coal seam and the rock stratum is the rock stratum structural plane, and the upper rock stratum of the structural plane generates a down-sliding force along the structural plane under the action of gravity. The lower the coal seam position, the greater the down-sliding force at the upper part, and the worse the overall stability of the slope. The influence mechanism of the slope gradient is similar to that of the coal seam. The larger the slope gradient, the greater the down-sliding force generated by the upper part of the coal seam, and the worse the overall stability of the slope.
As mentioned above, our findings provide both a scientific basis for the protection of slopes containing coal seams in goafs and a reference for similar engineering construction projects. However, in this study, we considered only a practical project for a modeling analysis. In future work, similar simulation tests can be used with a larger number of samples to analyze the factors influencing the stability of this type of slope.
6. Conclusions
In this study, considering the cutting slope containing a coal seam that was excavated in the section K1641+890-K1641+950 of a reconstruction and extension project of the Jixi Section of the Dan-A National Highway, we analyzed the factors affecting the stability of the slope containing a coal seam in a goaf by a single-factor numerical simulation and orthogonal multifactor numerical simulation. Our main conclusions are as follows:
(1) From our engineering experience, we identified nine factors that may affect the stability of this type of slope, and we analyzed the proposed factors with a single-factor numerical simulation. The results showed that the factors that affected the stability of a slope containing a coal seam in a goaf were the coal seam position, the roadway width, the slope gradient, the coal seam thickness, the coal seam cohesion, the mining depth and mining thickness ratio, the coal seam dip angle, and the coal seam internal friction angle.
(2) We arranged the numerical simulation scheme of the influencing factors using an orthogonal design, and we analyzed the influence of each factor with range and variance analyses. The results showed that the roadway width, the coal seam position, and the slope gradient were the main significant factors influencing the slope stability; the coal seam thickness, coal seam internal friction angle, coal seam cohesion, and the coal seam dip angle were the minor significant influencing factors. The influences of the mining depth and mining thickness ratio were not significant.
(3) Because the roadway width, the coal seam position, and the slope gradient were the three main factors controlling the stability of the slope containing a coal seam in a goaf, when this type of slope is treated in practical engineering applications, the stability of this type of slope should be improved by grouting in the roadway to reduce the roadway width and cutting the top of the slope to control the coal seam position, and the slope gradient should be reduced.