1 Introduction

In coal deposits, monoclinic, fold, fault, and other geological structures are formed under the internal and external dynamic actions of the earth [1]. Geological structures within the boundary of an open-pit coal mine result in drastic changes in geological conditions that affect the safe, economical, and efficient production of the open-pit coal mine.

In view of the problems caused by geological structures developed in open-pit coalfields, many researchers have conducted extensive research and achieved fruitful results.

Regarding the stability of open-pit coal mine slopes with faults, some researchers focused on analyzing the factors influencing slope stability with faults with the goal of determining the dominant factors and correlations among them [2,3,4,5]. Based on the different dip direction relationships between faults and slopes, some researchers focused on the sliding mode, deformation and failure mechanism, and mechanical models for slope stability analysis [6,7,8,9]. To study the influence of fault geometry, fault thickness on the safety factor of open-pit mine slope, and prevent underestimate or overestimate design, Azarfar [10, 11] focused on numerical and experimental fault modeling. According to the different occurrence conditions of planar, wedge and toppling failures [12], Kincal [13] conducted kinematic analyses to determine the failure orientation of slopes where different failures were likely to develop from the existing faults, and suggested the safe slope excavation orientations for the slopes of the Yörgüç Y2-panel site.

The collapse column developed within the open-pit coalfield destroys the continuity of the coal seam and results in a series of problems, such as an increase in the invalid stripping amount, shortening of the working line, and complications of the haulage system layout. The aforementioned problems in some open-pit coal mines have been solved by optimizing the mining scheme and haulage system layout in the collapsed column region [14,15,16]. To ensure the stability of the slope within the collapse column influencing region, Wang et al. [17] studied the deformation and failure mechanisms of the slope and proposed technical measures to prevent landslides.

Anticlines cause the occurrence conditions of coal seams to change dramatically and have many adverse effects on open-pit coal mine production. Liu [18], Duan [19], Wei [20], and Zhao [21] optimized the mining procedure, production continuity, and layout of the haulage system during mining over the anticline region in the Anjialing Open-pit Coal Mine. Xue [22], Liu [23], and Zhao [24] optimized the trenching schemes, internal dump parameters, and reasonable working-line length of the Antaibao Open-pit Coal Mine during mining over the Luzigou anticline. To solve the stability problem of internal dump slopes caused by the large dip angle of anticlines in open-pit coal mines, Zhao [25] proposed three schemes for inclined basement treatment in anticline regions. The best scheme was determined by a TOPSIS model based on indices of cost, stability factor of the internal dump slope and dumping volume.

There are also other studies related to the geological structure of open-pit coal mines, mainly focusing on the capacity calculation under different geological conditions [26], the geological structure analysis [27, 28], coal losses calculation for complex geological conditions [29, 30] and so on. Although some achievements have been made in the research of geological structures on the production and safety of open-pit coal mines, there are few reports on the coordination development schemes of mining and dumping engineering in the steeper anticline region of open-pit coal mines with nearly flat coal seams.

In an open-pit coal mine with a nearly flat coal seam, a steeper anticline typically refers to an anticline with a dip angle greater than 12°. Because of the drastic change in geological conditions in the steeper anticline region, mining and dumping engineering cannot develop as in the non-anticline region. Therefore, the study of mining and dumping engineering coordination development schemes in steeper anticline regions is of great significance for open-pit coal mines with nearly flat coal seams. This will be helpful for sustainable and stable coal production, timely release and utilization of internal dumping space, shortening transportation distances, and reducing mining costs.

The rest of this paper is organized as follows: Sect. 2 analyzes the impact of the steeper anticline on the efficient and economical production of an open-pit coal mine with a nearly flat coal seam. In Sect. 3, the key technological issues and schemes related to mining and dumping engineering coordination development in steeper anticline regions are discussed. In Sect. 4, considering the Antaibao Open-pit Coal Mine as a case study, two schemes for mining and dumping engineering coordination development in the steeper anticline region are proposed. Key indices were computed based on the prepared mining and dumping coordination development plans of the two proposed schemes. Using the six selected key indices, a multi-index comprehensive evaluation model based on CRITIC-TOPSIS was established to evaluate the two schemes, and the optimal scheme was determined. Finally, the study concludes in Sect. 5.

2 Impact of steeper anticline on production of open-pit coal mine with nearly flat coal seam

If a steeper anticline develops within the boundary of an open-pit coal mine with a nearly flat coal seam, once the working line advances into the anticline region, the drastic changes in geological conditions will have a significant impact on the efficient and economical production of the mine.

  1. (1)

    Production quantity and quality of coal.

For open-pit coal mines with flat, nearly flat, or gently inclined coal seams, coal can be mined with a separate bench in the non-anticline region, and the coal production quantity depends mainly on the horizontal advancing speed of the working line lkt (from position ① to position ②, as shown in Fig. 1). When the mining working line advances into the steeper anticline region, the coal seam cannot be mined with a separate bench because of the steeper dip angle. Therefore, coal exposure and mining methods should be adapted accordingly. In this case, sustainable and stable coal production mainly depends on both the horizontal advance speed lkt and the vertical deepening speed Hc (from position ③ to position ④, as shown in Fig. 1).

Fig. 1
figure 1

Diagram of coal exposure in anticline region

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As the efficiency of the excavator declines during trenching (efficiency decreases by 10–15% when excavating the access ramp and 10–20% when excavating the working trench), the deepening speed also declines, especially when the hydrogeological conditions of the deposit are poor. As a result, with the shortening of the coal mining working-line length and reduction in the number of coal mining benches, it is challenging to maintain the sustainability and stability of the coal production quantity.

If the anticline dip angle is greater than 12°, the coal seam cannot be mined in the inclined stratification mode but in the horizontal stratification mode. In the horizontal stratification mode, coal and rock are mixed in some benches, making selective mining of coal difficult and complicated. A difficult and complicated coal selective mining procedure results in a decline in the quantity and quality of coal produced.

  1. (2)

    Release and utilization of internal dumping space

The variation in the dip angle of the anticline leads to an imbalance between the release and utilization of the internal dumping space. In the steeper anticline region, if the anticline dip angle (α) is steeper than the working slope angle of the internal dump (β), then internal dumping benches will not be constructed because of limited space conditions (Fig. 2a). Because the mined-out area (i.e., released internal dumping space) in the steeper anticline zone cannot be utilized to dump in time, the internal dumping space is insufficient for the normal production of open-pit coal mines. To alleviate the lack of internal dumping space, solutions such as dumping to an external site or increasing the internal dump height result in a longer transportation distance, higher lifting height, and higher mining costs.

Fig. 2
figure 2

Diagram of internal dump construction conditions in anticline region

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The released internal dumping space can be utilized to dump in time only when the anticline dip angle (α) is less than the working slope angle of the internal dump (β) (Fig. 2b). At this point, the internal dumping space is sufficient.

  1. (3)

    Transportation distance and cost

The lack of internal dumping space in the steeper anticline region can be alleviated only by external dumping or by increasing the height of the internal dump. Consequently, the height differences between the stripping and dumping sites were large, indicating a longer transportation distance and higher transportation costs.

To overcome the large height difference under limited space conditions in the steeper anticline region, many haulage roads with a greater gradient and longer ramp have to be located on the end wall of the stope (Fig. 3), which results in deterioration of transportation conditions, transportation efficiency, and road-passing capacity. In this situation, energy consumption and transportation costs increase.

Fig. 3
figure 3

Haulage roads located on end wall of stope

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3 Technical issues and solutions for coordination development of mining and dumping engineering in steeper anticline region

Technical issues related to the coordinated development of mining and dumping engineering include coal exposure, working-line layout and development, internal dump construction and development, haulage system layout, and the selective mining of coal. Owing to the great difference in geological conditions between the steeper anticline and non-anticline regions in an open-pit coal mine with a nearly flat coal seam, solutions for the technical issues mentioned above must be dug over according to the geological features of the anticline region.

3.1 Coal exposure

In an open-pit coal mine with a nearly flat coal seam, coal can be mined separately by inclined stratification in a non-anticline region. However, in the steeper anticline region, the steeper dip angle of the coal seam renders inclined stratification impossible. With the horizontal stratification mode, two coal exposure methods can be adopted: trenching and deepening along the roof of the coal seam and trenching and deepening along the floor of the coal seam.

  1. (1)

    Trenching and deepening along roof of coal seam

As shown in Fig. 4, trenching and deepening occurred along the roof of the coal seam, the stripping bench advanced forward, and the coal seam was exposed and mined in the opposite direction. The deepening direction was approximately parallel to the roof of the coal seam. This mode is beneficial for the selective mining of coal. However, when the coal seam is thicker in the horizontal direction, the working slope angle of the stope is usually gentle, which results in a more advanced stripping amount, a greater production stripping ratio, and higher mining costs. Some measures can be applied to control the production stripping ratio, including grouped bench mining, transverse working lines, and tracking such as wild goose flying [31].

  1. (2)

    Trenching and deepening along coal seam floor

Fig. 4
figure 4

Coal exposure method of deepening along coal seam roof and advancing to both sides

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As shown in Fig. 5, trenching and deepening occurred along the floor of the coal seam, and stripping and mining benches advanced in the same direction. The deepening direction was approximately parallel to the coal floor.

Fig. 5
figure 5

Coal exposure method of deepening along coal seam floor and advancing to one side

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Compared with the coal exposure method shown in Fig. 4, the method shown in Fig. 5 is not conducive to selective mining of the coal seam. However, the advantages of this method are the steeper working slope angle of the stope, lower production stripping ratio, and mining cost.

When the horizontal thickness of the coal seam is not too large, the first coal exposure method is preferred; otherwise, the second method is selected.

3.2 Layout and development of working line

Normally, the layout and development of the working line in an open-pit coal mine are determined based on the principles of maintaining sustainable coal production and controlling the production stripping ratio (i.e., efficient and economical production). However, due to the insufficient internal dumping space in the steeper anticline region, the layout and development modes of the working line, which are conducive to the release and utilization of the internal dumping space, should be adapted in the steeper anticline region.

  1. (1)

    Layout and development of stripping and mining working lines

To take full advantage of the characteristics of the coal floor dip angle variation in different parts of the anticline, the stripping and mining working line is arranged obliquely with the anticline axis or in the shape "Z" and develops in parallel or fan mode (Figs. 6, Fig. 7).

  1. (2)

    Layout and development of dumping working-line

Fig. 6
figure 6

Layout and development mode of oblique working line in steeper anticline region

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Fig. 7
figure 7

Layout and development mode of Z-shaped working line in steeper anticline region

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As the internal dump usually keeps a certain tracking distance from the stope, the layout and development mode of the dumping working line are consistent with those of the mining working line. When the anticline dip angle varies significantly along the axis, restricted by the space required for internal dump construction, only the mined-out space that meets the condition of internal dump construction can be utilized preferentially. The dumping working line extends in both directions and develops in L-shaped that parallels the stripping and mining working lines as well as the anticline axis (Fig. 8).

Fig. 8
figure 8

Layout and development of internal dump working line in steeper anticline region

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3.3 Construction and development of internal dump

Normally, the number of benches in the stope or internal dump will not increase when stripping and mining engineering has deepened to the floor boundary of an open-pit coal mine with a nearly flat coal seam. However, in the steeper anticline region, stripping and mining engineering must be deepened to the floor boundary of the stope owing to the descent of the coal seam floor. In this case, the number of benches in the stope and internal dump increased with deepening. This type of unconventional situation is sustained until mining occurs over the anticlinal region.

The construction and development of new lower dumping benches creates the space necessary for the development of upper dumping benches. In other words, only when new lower dumping benches have been constructed and advanced to a certain distance can the construction and development of upper dumping benches continue. As shown in Fig. 9, during Phase I of internal dump construction, only benches with elevations of + 30 and + 40 were constructed (Fig. 9a). With the deepening of stripping and mining engineering, two new mining benches with elevations of ± 0 and − 10 were formed, a new lower dumping bench with elevation + 10 was constructed, and the development of upper dumping benches with elevations of + 30 and + 40 can continue Fig. 9b).

Fig. 9
figure 9

Construction and development of internal dumps in anticline regions

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Because the newly constructed dumping benches at the foot of the internal dump are generally constructed in the mode of reverse dumping, the construction and development of the internal dump in the steeper anticline region is a combination of forward advancing and reverse dumping.

3.4 Haulage system layout

Under the impact of a steeper anticlinal dip angle, the elevation differences between some stripping and dumping sites are larger. To overcome the elevation difference, the roads and ramps of the haulage system can be built in two ways: dumping and ascending at the dump site and deepening and descending along the end wall of the stope (Fig. 10).

Fig. 10
figure 10

Diagram of haulage system layout in anticline region

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Dumping and ascending at the dump site have some disadvantages such as frequent haul road relocation, lower transportation efficiency, and poor road quality. Deepening and descending along the end wall are more effective [32].

3.5 Selective mining of coal

As the dip angle of the coal seam in the anticline region is steeper, coal cannot be mined on a separate coal bench by inclined stratification. To reduce the dilution and loss rate of coal, an appropriate selective mining scheme can be adopted based on the occurrence characteristics of the coal seam and the relative position relationship between the coal seam and the rock stratum.

Solutions to the selective mining of coal have matured in the field of open-pit coal mining [33, 34], so no further details are provided in this paper.

4 Case study

4.1 Background

Antaibao Open-pit Coal Mine (ATB) is located in Pinglu District, Shuozhou City, Shanxi Province, China. The main minable coal seams are #4, #9, and #11, with an average total thickness of approximately 32 m. Except for the northeast flank of the Luzigou anticline being steeper (12°–23°), the dip angle of most coal seams is less than 5°, indicating a nearly flat coal seam. A shovel-truck mining system was adopted in ATB, and some technical parameters of ATB are listed in Table 1.

Table 1 Technical parameters of Antaibao open-pit coal mine
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Within the boundary of the first mining district of the ATB, the northeast flank of the Luzigou anticline extends more than 1.0 km along the working-line advancing direction, and the vertical drop of the coal seam is as high as 270 m. The dip angles of the coal seams are 12°–13° north of the anticline, 13°–17° in the middle, and 19°–23° south (Fig. 11, Table 2).

Fig. 11
figure 11

Geological features of Luzigou anticline region in ATB

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Table 2 Variation in coal seam dip angle in Luzigou anticline region
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The Luzigou anticline dip angle is steeper than that of the typical nearly flat coal seam (dip angle is less than 5°). The steeper dip angle of the coal seam in the Luzigou anticline region causes a series of problems in the mining and dumping engineering coordination development of ATB such as insufficient internal dumping space, higher lifting height, longer transportation distance, complicated coal exposure procedure, greater production stripping ratio, and higher mining cost, as mentioned in Sect. 3 of this paper.

Because of these problems, schemes for mining and dumping engineering coordination development in the Luzigou anticline region of the ATB were proposed and evaluated in order to select the best scheme.

4.2 Coordination development schemes of mining and dumping engineering in Luzigou anticline region

Based on the variations in the coal seam dip angle shown in Table 2, two mining and dumping engineering coordination development schemes are proposed: the northern priority development scheme and the pseudo-longitudinal mining scheme.

Some technical decisions adopted by the two proposed schemes were the same, such as coal exposure (trenching along the roof of the coal seam with horizontal stratification), deepening procedure (deepening along the roof of the coal seam and advancing to both sides), and haulage system layout (deepening and descending along the end wall of the stope). The details of these technical issues are elaborated in Sect. 3 of this paper; therefore, they are not repeated here.

4.2.1 Northern priority development scheme

The northern priority development scheme accelerates the development of the northern working line in the Luzigou anticline region, making the northern working line advance a certain distance from the south. The entire working line of the stope was similar to the shape “Z” (original working line is straight and parallel to the coal seam strike) (Fig. 12).

Fig. 12
figure 12

Diagram of northern priority development scheme in Luzigou anticline region

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As coal is buried shallowly and the dip angle is relatively minor in the northern Luzigou anticline, the mined-out space will be preferentially ready for internal dumping. Therefore, the layout of the internal dump working line is vertical or oblique to the anticline axis, which can reduce the danger of internal dump slope instability and make full use of the internal dumping space in the northern anticline region. The dip angle of the coal seam in the south of the anticline region was steeper, and the internal dump development in this region lagged behind that in the north. Once the southern coal seam floor becomes flat (dip angle less than 12°), the internal dump working line can be extended to the southern end wall of the stope along the strike.

Some key parameters of the northern priority development scheme are as follows:

  1. (1)

    Length of the northern priority developing working line

In the northern priority development scheme, the length of the priority-developing working line is determined by concentrating on two aspects: one is to meet the needs of the mining equipment working space at the lowest mining bench, and the other is to facilitate the release of the internal dumping space in the anticline region.

Hydraulic backhoes with a 2-m3 bucket are the main equipment used for coal mining in ATB. The minimum length of the mining region required for each backhoe can be computed as follows:

$$l_{\min } = \frac{{Q_{d} \cdot n}}{H \cdot A},m$$
(1)

where lmin denotes the minimum mining region length required by 2-m3 hydraulic backhoes (m), Qd is the daily production capacity of 2-m3 hydraulic backhoes (6000 m3/d), n is the number of days in which the mining volume reserved in the mining region can be excavated (10 d), H is the bench height (15 m), and A is the dass width (40 m).

According to Eq. (1), the minimum length of the mining region required by a 2-m3 hydraulic backhoe is approximately 100 m.

The range of the prior developing working line in the north should also facilitate the release of the internal dumping space in the anticline region. In the south of section No. V (Fig. 11), the dip angle of the coal seam floor is greater than the maximum working slope angle (16°) of the internal dump site; therefore, north of section No. IV (Fig. 11) should be preferentially mined out to dump. This is beneficial for alleviating the problem of insufficient internal dumping space.

Based on the above principle and the boundary of the first mining district of ATB, the working-line length of each bench in the northern priority developing part was determined, as shown in Table 3.

  1. (2)

    Preceding distance of northern priority developing working line

Table 3 Length of northern priority working line in Luzigou anticline region
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To release and utilize the internal dump space as soon as possible, the working line in the northern priority developing part must advance at the maximum horizontal speed, which is defined as VN. Assuming that the amount of coal mined in the northern priority developing part is AN and the annual planned coal output is Ap, the development speed of the southern working line is determined according to the required coal output Ap-AN. The difference between the developing speeds of the southern and northern working lines is the distance that the northern working line precedes the southern working line [35]:

$$d_{N - S} = V_{N} - \frac{{Ap - A_{N} }}{{\overline{H}_{S - C} \cdot \overline{l}_{S - C} \cdot \gamma_{C} }},m$$
(2)
$$A_{N} = V_{N} \cdot \overline{H}_{N - C} \cdot \overline{l}_{N - C} \cdot \overline{{\gamma_{C} }} ,t$$
(3)

where dN-S is the distance that the northern working line precedes the southern working line (m), VN denotes the developing speed of the northern working line (400 m/a), Ap is the planned coal output (Mt), AN is the amount of coal mined in the northern priority part (Mt, \(\overline{H}_{S - C}\) is the average thickness of coal seams in the southern part (33.0 m), \(\overline{l}_{S - C}\) denotes the average length of the southern working line (850 m), γC is the average unit weight of the coal (1.41 t/m3), \(\overline{H}_{N - C}\) is the average thickness of the coal seam in the northern priority part (31.6 m), and \(\overline{l}_{N - C}\) is the average length of the working line in the northern priority part (415 m).

If the planned coal output is 15.0 Mt, then according to Eqs. (2) and (3), the development speed of the southern working line was 193 m, and the preceding distance of the northern working line was 207 m.

  1. (3)

    Construction and development of internal dump in northern anticline region

To enhance the internal dump slope stability and make full use of the internal dump space in the anticline region, the initial working line of the internal dump was obliquely arranged and developed parallel to the coal seam strike. As the coal seam dip angle gradually decreases, the dumping working line gradually parallels the coal seam strike and mining working lines.

In the anticline region, a steeper coal seam dip angle causes mining engineering to continue to deepen downward at a certain speed, and it is necessary to maintain sustainable coal production. To make full use of the internal dump space, the lower dump benches in the Luzigou anticline region synchronously “deepen” downward when the dumping space is available. As shown in Fig. 13, the initial elevations of the lowest and uppermost dump benches in the anticline region were + 1120 and + 1240, respectively (Fig. 13a). With the deepening of stripping and mining engineering, the lowest dump bench with an elevation of + 1090 was constructed, and upper dumping benches with elevations of + 1270 and + 1300 were constructed with the necessary dumping space (Fig. 13b). This is the internal dump development mode of forward advancing and reverse dumping, as mentioned in Sect. 3.3.

Fig. 13
figure 13

Diagram of internal dump construction and development procedure in Luzigou anticline region

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4.2.2 Pseudo-longitudinal mining scheme

As shown in Fig. 14, the internal dumping working line in the anticline region is perpendicular to the north end wall of the stope and obliquely intersects the Luzigou anticline axis. The mining working line is parallel to the internal dumping working line and obliquely intersects the strike of the coal seam (the original working line is straight and parallel to the coal seam strike). A fan development mode (the original development mode of the working line is the parallel mode) is adopted to accelerate the development of the northern working line. Thus, the internal dumping space in the north of the anticline region can be released and utilized as soon as possible.

Fig. 14
figure 14

Diagram of pseudo-longitudinal mining scheme in anticline region

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Some key parameters of the pseudo-longitudinal mining scheme are determined as follows:

  1. (1)

    Development speed of working line

When mining engineering deepens along the coal seam floor, the relationship between the horizontal advancing speed lkt of the working line and the vertical deepening speed HBC of mining engineering (Fig. 15) is defined as follows:

$$H_{BC} = \frac{{l_{kt} }}{ctg\beta + ctg\varphi }$$
(4)

where HBC is the vertical deepening speed of the mining engineering (m/a); lkt is the horizontal advancing speed of the working line (m/a); β is the coal seam dip angle, which is also the deepening angle of the mining engineering (°); and φ is the working slope angle of the stope (10°).

Fig. 15
figure 15

Diagram of relationship between horizontal advancing speed and vertical deepening speed

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If the northern working line of the pseudo-longitudinal mining scheme advances at a maximum horizontal speed of 400 m/a, then according to Eq. (4), the vertical deepening speed of the stripping and mining engineering at section No. I (Fig. 11) was 37.0 m/a.

Considering the influence of some uncertain factors on the development of mining engineering, the horizontal advancing speed at the corresponding position of each section (Fig. 11) was calculated using a vertical deepening speed of 30 m/a. The results are presented in Table 4.

Table 4 Horizontal advancing speed of mining working line
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The results listed in Table 4 are the theoretical values calculated using Eq. (4). Owing to the nonlinear variation in the coal seam dip angle, the zigzag shape of the pseudo-longitudinal mining working line is not applicable. Therefore, it was necessary to linearly fit the horizontal advancing speed of the working line (as shown in Fig. 16). The fitted results for the horizontal advancing speed of the working line at each section are listed in Table 5.

  1. (2)

    Construction and development of internal dump.

Fig. 16
figure 16

Linear fitting of horizontal advancing speed of working line in pseudo-longitudinal mining scheme

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Table 5 Linear fitted horizontal advancing speed of working line
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This is similar to the northern priority development scheme; therefore, there is no repetition.

4.3 Mining and dumping coordination plan in Luzigou anticline region

Based on the parameters listed in Table 1 and the above technical decisions, the mining and dumping coordination development plans from year 1 to 4 during mining over the Luzigou anticline of the two proposed schemes are prepared (by the fifth year, the coal seam becomes flat, and mining and dumping engineering develop as usual).

4.3.1 Mining and dumping plan for northern priority development scheme

Plane drawings of the mining and dumping coordination plan for the northern priority development scheme from year 1 to year 4 during mining over the Luzigou anticline region are shown in Fig. 17, and a summary of the key technical indices is listed in Table 6.

Fig. 17
figure 17figure 17

Plane drawings of mining and dumping plan of northern priority development scheme

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Table 6 Technical index summary of mining and dumping plan of northern priority development scheme
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4.3.2 Mining and dumping plan for pseudo-longitudinal mining scheme

Plane drawings of the mining and dumping coordination plan for the mining scheme from year 1 to 4 during mining over the Luzigou anticline region are shown in Fig. 18. A summary of the plan’s key technical indices is listed in Table 7.

Fig. 18
figure 18figure 18

Plane drawings of mining and dumping plan of pseudo-longitudinal mining scheme in anticline region

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Table 7 Technical index summary of mining and dumping plan of pseudo-longitudinal mining scheme
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4.4 Evaluation of mining and dumping engineering coordination development schemes based on CRITIC-TOPSIS

4.4.1 Selection of evaluation methods

Comparing the data in Tables 6 and 7, it can be seen that the two mining and dumping engineering coordination development schemes in the Luzigou anticline region have their own advantages and disadvantages in six key technical indices including the production stripping ratio, weighted average transportation distance and lifting height of coal and stripped rock, and internal dumping volume from year 1 to 4 during mining over the Luzigou anticline region. It was impossible to determine the optimal scheme directly; therefore, a multi-index comprehensive evaluation is necessary.

Common multi-index comprehensive evaluation methods include the analytical hierarchy process (AHP), fuzzy comprehensive evaluation method (FCE), gray relational analysis (GRE), technique for order of preference by similarity to ideal solution (TOPSIS), and principal component analysis (PCA). Among the abovementioned methods, the TOPSIS method is a scientific method commonly used in the multi-index decision analysis of limited schemes. The TOPSIS method judges the advantages and disadvantages of the evaluated object by calculating the distance between the evaluation object and the optimal scheme and the worst scheme [36, 37]. It has no strict restrictions on the data distribution, sample size, or index amount, and its calculation is simple. The TOPSIS method is applicable to both small sample datasets and large-scale systems with large sample datasets, and the evaluation object can be both spatial and temporal. Moreover, the TOPSIS method makes full use of the original data and has less information loss [38]. The TOPSIS method has been a leading tool in multi-index comprehensive evaluation domain [39] because of the above advantages. Therefore, we select the TOPSIS method to evaluate the proposed mining and dumping coordination development schemes during mining over the anticline region.

In the process of applying the TOPSIS method to evaluate the proposed mining and dumping engineering coordination development schemes in this paper, it is necessary to determine the weight of each index in the evaluation system. The commonly used subjective weighting methods include the expert evaluation method (Delphi method) and the analytic hierarchy process (AHP method), and the objective weighting methods include the variation coefficient method, entropy method, and criteria importance through the inter criteria correlation (CRITIC) method. The subjective weighting method is subjective in determining the weight of evaluation indices, which usually leads to a large deviation between the evaluation results and the actual situation.

The CRITIC method was proposed by Diakoulaki [40] in 1995. It is an objective weighting method based on index correlation. The CRITIC method quantifies the contrast intensity (i.e., divergence) of the index value and obtains the index weight [41]. The greater the weight value given, the more different the values of the corresponding indices. Compared with the objective weight given by the entropy method, this method not only considers the contrast strength but also solves the contradictions between indices to cope with the interdependence between indices [42]. Therefore, it is critical to capture more information embedded between indices, which is obviously more suitable for multi-index decisions [43, 44].

CRITIC-TOPSIS combines the advantages of TOPSIS and CRITIC method to provide a sturdy model and the reliable evaluation result, it has been applied in sustainable supply chain risk management [45], optimization of the wind/PV/hydrogen system [46], shipboard crane selection [47] and other domains [48].Therefore, in this paper, the TOPSIS method is selected as the comprehensive evaluation method for the proposed mining and dumping schemes in steeper anticline region. The weights of the evaluation indices used in TOPSIS are objectively determined by the CRITIC method to reduce the subjectivity of evaluation results and improve the scientificity of decision-making.

4.4.2 Evaluation model based on CRITIC-TOPSIS

By combining TOPSIS and CRITIC, an objective multi-index comprehensive evaluation model based on CRITIC-TOPSIS with the above six indices was established to evaluate the mining and dumping engineering coordination development schemes.

  1. (1)

    Establishing the decision matrix

Assuming that m evaluation objects and n evaluation indices are defined for each evaluated object, the decision matrix A is defined as [49]

$$A = \left[ {\begin{array}{*{20}c} {a_{11} } & {a_{12} } & \cdots & {a_{1n} } \\ {a_{21} } & {a_{22} } & \cdots & {a_{2n} } \\ \vdots & \vdots & \cdots & \vdots \\ {a_{m1} } & {a_{m2} } & \cdots & {a_{mn} } \\ \end{array} } \right] = \left( {a_{ij} } \right)_{m \times n} \left( {i = 1,2, \ldots ,m;\,\,j = 1,2, \ldots n} \right)$$
(5)

where A is the decision matrix, and aij is the j-th evaluation index of the i-th object to be evaluated.

  1. (2)

    Decision matrix normalization

The evaluation index can be normalized as follows [50]:

$$a_{ij}^{*} = \frac{{a_{ij} }}{{\sum\nolimits_{i = 1}^{m} {a_{ij} } }}$$
(6)

where aij is the j-th evaluation index of the i-th object to be evaluated, and a*ij is the evaluation index after normalization.

  1. (3)

    Establishing a weighted standardized decision matrix

The weighted standardized decision matrix C is defined as

$$\begin{gathered} C = \left[ {\begin{array}{*{20}c} {\omega_{11} a_{11}^{*} } & {\omega_{12} a_{12}^{*} } & \cdots & {\omega_{1n} a_{1n}^{*} } \\ {\omega_{21} a_{21}^{*} } & {\omega_{22} a_{22}^{*} } & \cdots & {\omega_{2n} a_{2n}^{*} } \\ \vdots & \vdots & \cdots & \vdots \\ {\omega_{m1} a_{m1}^{*} } & {\omega_{m2} a_{m2}^{*} } & \cdots & {\omega_{mn} a_{mn}^{*} } \\ \end{array} } \right] = \left( {\omega_{ij} a_{ij}^{*} } \right)_{m \times n} \hfill \\ = \left( {c_{ij} } \right)_{m \times n} \left( {i = 1,2, \ldots ,m;j = 1,2, \ldots n} \right) \hfill \\ \end{gathered}$$
(7)

where C is the weighted standardization, a*ij is the normalized evaluation index, ωij is the index weight determined by the CRITIC method, and cij is the evaluation index after the weighted standardization.

  1. (4)

    Calculating the ideal proximity solution of the mining and dumping coordination development schemes.

The ideal proximity solution of the mining and dumping schemes is calculated as follows:

Step 1 Establish an ideal solution matrix.

The ideal solution is calculated according to the following equations:

$$\left\{ \begin{gathered} C^{ + } = \left[ {\left( {\mathop {\max }\limits_{i} c_{ij} |j \in J_{1} } \right),\left( {\mathop {\min }\limits_{i} c_{ij} |j \in J_{2} } \right)} \right] \hfill \\ C^{ - } = \left[ {\left( {\mathop {\min }\limits_{i} c_{ij} |j \in J_{1} } \right),\left( {\mathop {\max }\limits_{i} c_{ij} |j \in J_{2} } \right)} \right] \hfill \\ \end{gathered} \right.$$
(8)

where C+ and C− are the positive and negative ideal solution matrices, respectively; J1 is a benefit index set (the higher the value of J1, the more ideal); and J2 is a cost indicator set (the lower the value of J2, the better).

Step 2 Calculate the distance between the evaluation object and the ideal solution.

$$\left\{ \begin{gathered} d_{i}^{ + } = \sqrt {\sum\limits_{j = 1}^{n} {\left( {c_{ij} - c_{j}^{ + } } \right)^{2} } } \hfill \\ d_{i}^{ - } = \sqrt {\sum\limits_{j = 1}^{n} {\left( {c_{ij} - c_{j}^{ - } } \right)^{2} } } \hfill \\ \end{gathered} \right.$$
(9)

where d+i is the distance between the object to be evaluated and the positive ideal solution, d−i is the distance between the object to be evaluated and the negative ideal solution, and c+j and c−j are the evaluation index values in the ideal solution matrix.

Step 3 Calculate the proximity of the evaluation object.

The proximity of the evaluation object can be calculated as follows:

$$E_{i}^{ + } = \frac{{d_{i}^{ - } }}{{d_{i}^{ - } + d_{i}^{ + } }}\left( {0 \le E_{i}^{ + } \le 1} \right)$$
(10)

where \(E_{i}^{ + }\) is the proximity of the object being evaluated (the greater the \(E_{i}^{ + }\), the closer the evaluated object is to the optimal solution).

4.4.3 Comparison of mining and dumping engineering coordination development schemes based on CRITIC-TOPSIS

Based on the CRITIC-TOPSIS model, the mining and dumping engineering coordination development schemes in the anticline region are comprehensively evaluated as follows:

  1. (1)

    Calculating average values of evaluation indices.

The selected key evaluation indices include the production stripping ratio (X1), weighted average transportation.

distance (X2), lifting height (X3) of the coal, weighted average transportation distance (X4), lifting height (X5) of the stripped rock, and dumping volume in the anticline region (X6). The average values of these six key indices from year 1 to year 4 of the two schemes were calculated, as shown in Table 8.

  1. (2)

    Establishing the decision matrix

Table 8 Summary of mining and dumping scheme evaluation indices in anticline region
Full size table

Based on Eq. (5) and the data listed in Table 8, the decision matrix for the mining and dumping engineering coordination development schemes is determined as follows:

$$A = \left[ {\begin{array}{*{20}c} {6.13} & {8.60} & {342.0} & {5.10} & {134.25} & {7869.25} \\ {6.74} & {8.66} & {317.5} & {5.75} & {135.50} & {7736.25} \\ \end{array} } \right]$$
  1. (3)

    Decision matrix normalization

Using Eq. (6), the normalized decision matrix A’ is determined as follows:

$$A^{^{\prime}} = \left[ {\begin{array}{*{20}c} {0.4763} & {0.4983} & {0.5186} & {0.4700} & {0.4977} & {0.5043} \\ {0.5237} & {0.5017} & {0.4814} & {0.5300} & {0.5023} & {0.4957} \\ \end{array} } \right]$$
  1. (4)

    Establishing a weighted standardized decision matrix

To establish a weighted standardized decision matrix, the objective weight of each evaluation index must first be determined. Applying the method described in (Zhang et al. [50]), the objective weight of the evaluation index is determined as follows:

$$W = \left( {\begin{array}{*{20}c} {0.2292} & {0.0169} & {0.3593} & {0.2897} & {0.0224} & {0.0824} \\ \end{array} } \right)$$

Based on the determined objective weights and Eq. (7), the weighted standardized decision matrix is determined as follows:

$$C = \left[ {\begin{array}{*{20}c} {0.1092} & {0.00838} & {0.1863} & {0.1362} & {0.0112} & {0.0416} \\ {0.1201} & {0.00844} & {0.1730} & {0.1536} & {0.0113} & {0.0409} \\ \end{array} } \right]$$
  1. (5)

    Calculating ideal proximity solution of mining and dumping coordination development schemes

The stripping ratio, weighted average transportation distance, lifting height of the coal, weighted average transportation distance, and lifting height of the stripped rock are cost-effective indices. Lower values are more ideal. The internal dumping volume in the anticline region is a benefit-oriented index. The larger the value, the better.

Applying Eq. (8), the positive and negative ideal solution matrices of the two mining and dumping engineering coordination development schemes in the anticline region are determined as follows:

$$\left\{ \begin{gathered} C^{ + } = \left[ {\begin{array}{*{20}c} {0.1092} & {0.00838} & {0.1730} & {0.1362} & {0.0112} & {0.0416} \\ \end{array} } \right] \hfill \\ C^{ - } = \left[ {\begin{array}{*{20}c} {0.1201} & {0.00844} & {0.1863} & {0.1536} & {0.0113} & {0.0409} \\ \end{array} } \right] \hfill \\ \end{gathered} \right.$$

Using Eqs. (9) and (10), the proximity values of the two mining and dumping engineering coordination development schemes in the anticline region are determined as follows:

\(E_{1}^{ + } = 0.6055\), \(E_{2}^{ + } = 0.3945\)。

The evaluation result is \(E_{1}^{ + } > E_{2}^{ + }\), which indicates that the northern priority development scheme is better than the pseudo-longitudinal mining scheme.

5 Conclusion

A steeper anticline results in drastic changes in the geological conditions of an open-pit coal mine with a nearly flat coal seam. Coal production quantity and quality, internal dumping space release and utilization, transportation distance and cost, and some other important technical and economic indicators are seriously impacted by the steeper anticline. According to the problems caused by the steeper anticline developed within the boundary of the open-pit coal mine, corresponding solutions are proposed in this paper. Among them, to fully release the internal dumping space, an innovative layout and development mode of the stripping and mining working line in the steeper anticline region is proposed; that is, the working line is arranged obliquely with the anticline axis or in the shape “Z” and develops in parallel or fan mode. In addition, to make full use of the internal dumping space, an internal dump construction and development mode combining "forward and reverse dumping" of the upper and lower dumping benches in the steeper anticline area, which is different from the traditional forward dumping mode, is designed.

The Antaibao Open-pit Coal Mine was taken as a case study to apply the relevant technical schemes for an open-pit coal mine with a nearly flat coal seam in a steeper anticline region. Two mining and dumping engineering coordination development schemes in the Luzigou anticline region of the Antaibao Open-pit Coal Mine were proposed: the northern priority development scheme and the pseudo-longitudinal mining scheme. These two schemes can effectively solve problems caused by the Luzigou anticline, such as insufficient internal dumping space, longer transportation distance, greater lifting height, and a larger production stripping ratio. The technical parameters of the two schemes are determined by using innovative theoretical calculation methods, such as the length and preceding distance of the northern priority developing working line and the horizontal advancing speed of the mining working line of the pseudo longitudinal mining scheme. Based on those parameters and the planned coal output, mining and dumping coordination plans during mining over the Luzigou anticline of the two proposed schemes were prepared. To objectively evaluate the two schemes based on the six selected indices of the mining and dumping coordination plans, a multi-index comprehensive evaluation model based on CRITIC-TOPSIS was first introduced into the evaluation of the engineering schemes of the open-pit coal mine. The evaluation results show that the pseudo-longitudinal mining scheme is better than the northern priority development scheme.

It must be pointed out that the slope stability of the internal dump in the steeper anticline region is also a problem worthy of in-depth study. We will continue to conduct our research on that, especially the issue of how to treat the basement of the internal dump in the steeper anticline region, to improve the slope stability of the internal dump, enhance the utilization rate of the internal dump space in the steeper anticline region, reduce the land occupation of the external dumping, decrease the environmental cost of open-pit mining, and achieve the goal of building an environmentally friendly green open-pit mine.