Study on Optimization of Downward Mining Schemes of Sanshandao Gold Mine

Abstract

To address the challenges associated with deep ground pressure control at the Sanshandao Gold Mine, a pre-controlled top-to-middle and deep-hole upper and lower-wall goaf subsequent filling mining method was proposed. Three distinct downward mining schemes were designed, the excavation procedure is systematically designed with 18 steps, and the temporal and spatial evolution characteristics of stress and displacement were analyzed using FLAC3D. The results revealed that stress concentration occurred during excavation steps 1–3. As excavation progressed to steps 4–9, the stress concentration area shifted primarily to the filling zones of partially excavated and filled sections. By steps 10–12, the stress concentration in these areas was alleviated. Upon completion of all excavation and filling steps, a small plastic zone was observed, accompanied by an alternating distribution of high and low stress within the backfill. Throughout the excavation process, vertical displacement ranged from 4.42 to 22.73 mm, while horizontal displacement ranged from 1.72 to 3.69 mm, indicating that vertical displacement had a more significant impact on stope stability than horizontal displacement. Furthermore, the fuzzy comprehensive evaluation method was applied to optimize the selection among the three schemes, with Scheme 2 identified as the optimal. Field industrial trials subsequently confirmed the technical rationality and practical applicability of Scheme 2 under actual mining conditions.

1. Introduction

As the first undersea bedrock mining metal mine in China, the Sanshandao Gold Mine features an outcrop on the seabed, with the ore body gradually extending landward as it descends [1,2,3]. With the ongoing deepening of the mine, the in situ stress has progressively increased, leading to more pronounced ground pressure phenomena. Stress gradient zones have formed near geological structures such as active faults and around the excavation stopes. These zones are susceptible to external dynamic disturbances, which may trigger geological disasters such as large-scale rockbursts and fault slips in the goaf [4,5,6]. Addressing the challenges of deep resource mining safety and ground pressure regulation at the Sanshandao Gold Mine, the implementation of a rational mining plan is crucial to ensure mining safety and effective ground pressure control. Consequently, selecting an appropriate deep mining scheme is of significant importance for both mine safety and efficient production [7,8].

Currently, numerous studies have been conducted by domestic and foreign experts on the optimization of different mining schemes, and good results have been achieved from the aspects of numerical simulation, theoretical analysis, and mathematical methods [9,10,11,12,13]. For example, Liu et al. [14] used the renormalization group model and numerical simulation method to analyze the retention scheme of a security pillar for seabed metal ore mining and concluded that the width of the pillar is 10 m and the spacing is 50 m. Tan et al. [15] used the DDA numerical simulation method to study the mining method of the ore body in the caving area in the southern part of Hainan Iron Mine and obtained a safe and reliable mining scheme. Wang et al. [16] used the numerical simulation method to establish three different mining schemes for the Panlong lead–zinc mine, analyzed the deformation of the strata of the three different schemes, and finally obtained the optimal scheme. Zhou et al. [17] investigated the optimal mining width of the slope of the Panzhihua #7 coal mine by the FLAC3D numerical simulation method and determined that the 6 m was the optimal mining width. Zhao et al. [18] used theoretical analysis and numerical simulation methods to analyze the effects of several downward cementation filling methods on the stability of the backfill roof and verified the rationality of the methods through experimental methods. Shi et al. [19] used numerical simulation methods to analyze three different types of support methods, including the anchor net cable support, anchor injection, and U-shaped shed support, and the results showed that the U-shaped shed support had the best effect. Liang et al. [20] used FCE and TODIM hybrid methods to optimize the optimal mining method for deep seabed gold deposits and proved the feasibility of the method through sensitivity analysis. Mijalkovski et al. [21] determined the optimal mining scheme by applying the FCE and TOPSIS methods to the mining method selection of an underground metal lead–zinc mine. Yavuz et al. [22] used the analytic hierarchy process (AHP) and Yager method to optimize the underground mining method for the Istanbul lignite mine and determined the optimal mining scheme. Bajićsanja et al. [23] used the FCE and AHP methods to optimize the mining method for the Borska Reka copper mine in Serbia to determine the optimal underground mining scheme. To solve the problem of phosphate rock mining in Dingxi mine, Hu et al. [24] used the numerical simulation method to determine the optimal mining method, applied the method to the actual field engineering, and achieved good results. Hou et al. [25] used Kunyang phosphate rock as the research object and used the entropy-weighted TOPSIS method to optimize the selection of the three mining methods for the deep phosphate ore body and determined that the open-pit mining scheme was the optimal method. Alpayi et al. [26] used the AHP and Yager methods to study the problem of underground mining method selection for different deposit shapes and ore bodies. The research methods utilized in this study primarily rely on numerical simulation and mathematical modeling. While these approaches have yielded certain insights, they are not without limitations. Although numerical simulation and mathematical methods are advantageous due to their simplicity, intuitive results, and computational efficiency, they are also prone to issues such as result variability and significant model inaccuracies. Moreover, given the inherent complexity of mining plan selection and the multitude of influencing factors, the preferred solutions identified in this study lack validation through on-site industrial trials, which are critical for assessing their reliability and practical applicability. Therefore, to optimize mining plans effectively, it is essential to integrate multiple methodologies, including numerical simulation, theoretical analysis, and mathematical modeling, complemented by field industrial trials to ensure the reliability and suitability of the proposed solution.

Therefore, to enhance the resource utilization rate of the deep ore body below −900 m in the Sanshandao Gold Mine, a pre-controlled mining method involving sub-mining and sub-filling of the upper and lower walls of deep holes in the top area is proposed based on the characteristics of deep ore body mining. Three distinct downward mining schemes were designed, and their spatial and temporal evolution characteristics of stress and displacement were analyzed using the FLAC3D method. This analysis revealed the displacement and stress evolution patterns of the three schemes, providing insights into the stress evolution laws and displacement characteristics associated with each mining approach. The fuzzy comprehensive evaluation method was then employed to optimize and identify the most suitable mining plan. Finally, the rationality of the optimal downward mining scheme was rigorously validated through field industrial trials.

2. Engineering Background

The Sanshandao Gold Mine is situated in Laizhou City, Shandong Province, and comprises three mining areas: Xinli, Xishan, and Xiling. The ore body is primarily deposited within the F1 fault zone of Sanshandao, with lithology dominated by pyrite sericite fractured rocks, pyrite sericite granitic fractured rocks, and sericite granites. The lithology of the deposit’s roof and floor consists of sericite granite, sericite granitic fractured rock, and similar materials. In the alteration zone near the main section, local rocks are more fragmented, exhibiting stronger alteration, more developed fissures, increased core fracturing, and relatively lower solidity. Currently, the Xishan mine has advanced to the middle section at a depth of −960 m. During the excavation of mining roadways near the F1 fault, varying degrees of collapse have been observed. The high-temperature and high-humidity working environment significantly hampers labor efficiency, posing a pressing need for the mine to reform its existing mining methods. Enhancing the level of automation and intelligent production operations is crucial to reducing the safety risks associated with personnel operations. To address these challenges, a pre-controlled top-to-middle and deep-hole upper and lower-wall goaf subsequent filling mining method has been proposed for implementation in the Xishan ore mine.

The deep ore body in the Xishan mining area of the Sanshandao Gold Mine has an average dip angle of 44° and a horizontal thickness of 40 m. The F1 fault is exposed in the middle of the ore body, with its occurrence nearly identical to that of the ore body. The ore rock mass within the F1 fault is highly fragmented, making it a typical inclined thick and large broken ore body.

The ore-controlling structure in the mining area is the Sanshandao Fault, with the primary fault in the zone being F1. The overall strike of the F1 fault is 40°, trending southeast, with a dip angle ranging from 35° to 45°. Both the strike and dip exhibit gentle undulations, indicative of compressional shear characteristics. The F1 fault lies within the interior of the ore body, significantly compromising the integrity of the mining field and complicating the extraction of the ore body on the fault’s upper plate, as illustrated in Figure 1. Figure 2 depicts the panel of the 945 m stope, while Figure 3 provides a schematic of the mining methods employed in the Xishan mining area.

Through on-site sampling of deep rock specimens from the Sanshandao Gold Mine, a series of static load mechanical tests were performed on the rock samples. The basic physical and mechanical parameters of the rocks obtained are shown in

Table 1. Rock mass mechanical parameters.

Rock Mass	Elastic Modulus (Pa)	Shear Modulus (Pa)	Density (g/cm3)	Internal Friction Angle (°)	Cohesion (MPa)	Tensile Strength (MPa)
Wall rock	1.096 × 1010	6.895 × 109	2.7	36.94	42.78	8.54
Ore body	32.18 × 109	2.024 × 109	2.7	32.60	21.45	4.91
1:4 backfill body	2.894 × 107	2.449 × 107	2.2	43.50	3.10	1.51
1:8 backfill body	1.234 × 107	9.71 × 106	2.1	38.70	1.71	0.42
Non-cemented backfills	6.32 × 106	3.68 × 106	1.6	32.00	0.17	0.03

.

3. Numerical Simulation of Downward Mining Schemes

3.1. Computational Model Establishment

The mine is mined by the pre-controlled top-to-middle and deep-hole upper and lower-wall goaf subsequent filling mining method, the ore body is divided into mine houses and pillars along the strike of the ore body and arranged at intervals, and the production is organized into 14 groups of ore house pillars. The height of the mining stage is 75 m, the mining section is set up in the mining stage, the mining section is 15 m or 30 m high, the segmented height used in the separated mine houses is staggered, and the trackless mining method outside the lower-wall vein is used to mine from top to bottom. For the 15 m high mine house, the cement–sand ratio is 1:4, the backfill is 5 m, the 1:4 backfill forms a preliminary condensation, and the 1:8 backfill is 10 m. For the 30 m high mine house, the cement–sand ratio is 1:4, and the backfill is 5 m; then, after the 1:4 backfill forms preliminary condensation, the 1:8 backfill is filled 12 m; then, after the 1:8 backfill is preliminarily coagulated, the non-cemented backfills are filled for 13 m.

The calculation model focuses on the deep downward mining area at an elevation of −900 to −1000 m, with a plane range spanning from lines 1700 to 1720. The model encompasses 14 stopes arranged along the strike direction of the ore body, each with a width of 8 m. The ore body is set to a thickness of 55 m and a height of 87 m, with top and bottom pillars of 6 m each. The overall model extends vertically along the strike of the ore body, centered on the ore body, with a total vertical extension of 174 m. The coordinate system is defined as follows: Z along the strike of the ore body, X perpendicular to the strike, and Y vertically upward. The model comprises six components: the upper bedrock layer, lower bedrock layer, upper-wall rock mass, lower-wall rock mass, ore body, and an artificial false roof. The mechanical parameters of the rock mass are provided in Table 1.

Additionally, the ore body model is divided into 130 groups according to the area of the mine house and the area with different filling ratios, including one group of top pillar and one group of bottom pillar, and a total of 128 groups of mine area are divided. The ore body model is meshed, and 2 m is divided into a grid. The three-dimensional numerical model is illustrated in Figure 4.

3.2. Determination of Rock Mass In Situ Stress

The determination of in situ stress in rock mass is a critical aspect of numerical simulation. Based on the test results of deep in situ stress in the Sanshandao Gold Mine, as well as past engineering experience and theoretical analysis, the vertical principal stress exhibits a linear increase with depth. The regression equations for the maximum horizontal principal stress, minimum horizontal principal stress, and vertical principal stress values as functions of depth are as follows:

$${\sigma }_{\max }=0.11+0.0539H \left(\mathrm{MPa}\right)$$

$${\sigma }_{\min }=0.13+0.0181H \left(\mathrm{MPa}\right)$$

$${\sigma }_z=0.08+0.0315H \left(\mathrm{MPa}\right)$$

where ${\sigma }_{\max }$, ${\sigma }_{\min }$, and ${\sigma }_z$ are the maximum horizontal principal stress, the minimum horizontal principal stress, and the vertical stress, respectively. H is the buried depth of the measurement point, and the unit is m.

Therefore, the model employs the Mohr–Coulomb criterion, with constraints applied to all four sides and the bottom of the model. Uniform loads are applied to the top of the orebody, and gravity loads are applied to the entire model. The model depth is set at 960 m, and the results of the in situ stress tests are converted into stresses in the X and Y directions, which are then input into the model for calculation.

3.3. Design of Downward Mining Schemes

The scheme design is primarily based on the criterion of the optimal mining method. Considering that the downward mining scheme must minimize the influence of in situ stress, the ore body is divided into stopes and pillars along the strike direction using the pre-controlled top-to-middle and deep-hole upper and lower-wall goaf subsequent filling mining method at intervals. Production is organized in units of 14 groups of stopes and pillars, with the ore body divided into three sections from top to bottom. To ensure the continuity of the ore body during the mining process, mining is conducted in a pattern of five stopes followed by one pillar. To select the best downward mining scheme, three mining schemes were established based on different mining sequences. Among them, Scheme 1 is a staggered downward mining mode from one horizontal wing to the other wing, with six vertical and two oblique intervals, and the mining sequence is shown in Figure 5. Scheme 2 is a staggered downward mining mode from the horizontal center to the two wings, with five mining and one vertical and oblique separation, and the mining sequence is shown in Figure 6. Scheme 3 is a staggered downward mining mode from the horizontal two wings to the center with five mining one, vertical interval six, and oblique separation two, and the mining sequence is shown in Figure 7.

4. Analysis of Numerical Simulation Results

4.1. Comparative Analysis of Vertical Stress Changes of Different Mining Schemes

In the stress analysis, the maximum stress concentration depends on the strength parameters. During mining steps 1–3, the stress concentration in the top and bottom pillars is not pronounced initially, but the stress concentration on both sides of the stope progressively increases. In mining steps 4–6, the stress concentration area in Scheme 2 is smaller compared to Schemes 1 and 3, although the maximum vertical stress value in Scheme 2 is significantly higher than that in Scheme 3. In mining steps 7–9, the stress concentration phenomenon in the surrounding rock on both sides of the stope becomes more pronounced, and the stress concentration area continues to expand. The stress concentration area in Scheme 2 remains smaller than in Schemes 1 and 3, but the maximum vertical stress value in Scheme 2 is slightly higher than in Scheme 1. Specifically, the maximum vertical stress in the surrounding rock of Scheme 2 is 47.0 MPa, while the maximum stress concentration values in Schemes 1 and 3 are 46.1 MPa and 48.1 MPa, respectively.

In mining steps 10–12, the stress concentration value in the surrounding rock of Scheme 2 is relatively small. The maximum stress value in Scheme 2 remains relatively low, while in mining steps 13–15, the maximum stress value exceeds 48 MPa, with the stress concentration area in Scheme 2 being smaller than in Schemes 1 and 3. In mining steps 16–18, the maximum stress concentration value in the surrounding rock on both sides of the ore body in Scheme 3 is significantly higher than in Schemes 1 and 2, reaching 55.8 MPa. The vertical stress changes for each scheme during the mining steps are illustrated in Figure 8, while the vertical stress changes for mining steps 7–9 in the three schemes are shown in Figure 9.

4.2. Comparative Analysis of Horizontal Stress Changes of Different Mining Schemes

During the initial mining steps 1–3, no significant stress concentration is observed at the top and bottom of the columns. However, the stress concentration on both sides of the stope progressively increases. In mining steps 4–6, the stress concentration area in Scheme 2 is smaller compared to Schemes 1 and 3, although the maximum vertical stress value in Scheme 2 is significantly higher than in Scheme 3. In mining steps 7–9, the stress concentration phenomenon in the surrounding rock on both sides of the stope becomes more pronounced, and the stress concentration area continues to expand. While the stress concentration area in Scheme 2 is less extensive than in Schemes 1 and 3, the maximum vertical stress value in Scheme 2 is slightly higher than in Scheme 1. Specifically, the maximum vertical stress in the surrounding rock of Scheme 2 is 47.0 MPa, compared to 46.1 MPa in Scheme 1 and 48.0 MPa in Scheme 3.

Similarly, the maximum stress value in Scheme 2 during mining steps 13–15 is also relatively low. However, in mining steps 16–18, the stress concentration area in Scheme 3 is significantly larger than in Schemes 1 and 2. The vertical stress changes for each scheme during the mining steps are illustrated in Figure 10, while the vertical stress changes for mining steps 7–9 in the three schemes are shown in Figure 11.

4.3. Analysis and Comparison of Vertical Displacement Changes of Different Mining Schemes

As excavation progresses from steps 1–3, the vertical displacement of the monitoring point increases in alignment with the calculated number of steps. This growth rate is initially rapid but subsequently slows. During excavation steps 4–6, the area exhibiting significant vertical displacement expands, and vertical displacement becomes more pronounced on both sides of the lower portion of the stope. In excavation steps 7–9, the vertical displacement in the upper half of the stope’s sides is minimal, while the displacement in the lower half is more substantial. During excavation steps 10–12, a notable increase in vertical displacement is observed, with the largest displacements concentrated in the roof, the area to be excavated, and the bottom plate.

In Scheme 1, the vertical displacement of the roof increases from 17.17 cm to 18.58 cm, and the vertical displacement of the bottom plate increases from 11.15 cm to 11.80 cm. In Scheme 2, the vertical displacement of the roof increases from 15.54 cm to 16.21 cm, while in Scheme 3, it increases from 18.96 cm to 20.67 cm. Scheme 2 demonstrates relatively effective control over vertical displacement. In subsequent mining steps 13–15, as the excavation range expands, the vertical displacement in all three schemes increases significantly. During mining steps 16–18, the vertical displacement contours of the three schemes show discernible but gradual changes. Notably, the vertical displacement of the roof in Scheme 2 remains largely unchanged. Figure 12 illustrates the vertical displacement changes associated with the mining steps for each scheme, while Figure 13 shows the vertical displacement changes during excavation steps 10–12 for the three schemes.

4.4. Analysis and Comparison of Horizontal Displacement Changes of Different Mining Schemes

During excavation steps 1–3, as the mining range expands, the horizontal stress within the model gradually increases, and horizontal deformation develops from both sides of the stope toward the excavation area. In excavation steps 4–6, the maximum horizontal displacement increases to over 2.5 cm, indicating that rock deformation becomes more pronounced with the expansion of the mining range, and energy release further intensifies. During excavation steps 7–9, the horizontal displacement of the surrounding rock exceeds 3 cm, and minor displacement also occurs in the backfill of the areas where filling has been completed. By excavation steps 10–12, the maximum horizontal displacement reaches approximately 3 cm, but the rate of increase slows, suggesting that the backfill begins to effectively inhibit the deformation of the surrounding rock. In mining steps 13–15, the horizontal displacement of the stopes on both sides increases to some extent across all three schemes, but the rate of growth slows significantly. The mechanical effect of the backfill in restraining the deformation of the surrounding rock becomes more pronounced. The maximum horizontal displacement of the surrounding rock on the left side increases from 3.42 cm, 3.36 cm, and 3.64 cm in step 13 to 3.72 cm, 3.95 cm, and 3.93 cm in step 15 for Schemes 1, 2, and 3, respectively. In mining steps 16–18, the maximum horizontal displacement of the left surrounding rock is 3.95 cm, 3.41 cm, and 4.38 cm for Schemes 1, 2, and 3, respectively. Figure 14 illustrates the horizontal displacement changes at the mining steps for each scheme, while Figure 15 shows the horizontal displacement changes during excavation steps 13–15 for the three schemes.

4.5. Evolution Analysis of Maximum and Minimum Principal Stress in Stope

During the initial excavation steps 1–3, the maximum principal stress concentration around the mining stope is not significant, with magnitudes considerably smaller than those observed in the unmined ore body and surrounding rock areas. In excavation steps 4–6, significant tensile stress concentration areas emerge on both sides of the mining stope. As excavation progresses to steps 7–12, the area of tensile stress concentration between mining chambers expands. During excavation steps 13–15, a larger area of tensile stress concentration develops in part of the backfill within the backfilling area, where tensile and compressive stresses are distributed in an alternating pattern. By excavation steps 16–18, the tensile stress concentration area reaches its maximum extent, with interconnected tensile stress zones and separated compressive stress zones in the middle. The maximum principal stresses for Schemes 1 to 3, observed during excavation steps 1 to 18, range from 44.52 to 56.77 MPa, 43.29 to 56.87 MPa, and 43.29 to 58.8 MPa, respectively. During excavation steps 1–3, compressive stress concentration becomes evident in specific filling areas, with noticeable variations in spacing between regions of low and high compressive stress. In excavation steps 4–6, certain areas of the backfill experience increased compressive stress, leading to a separation between regions of higher and lower compressive stress.

As excavation progresses to steps 7–12, the compressive stress concentration area becomes primarily localized in small sections of the surrounding rock on both sides. During excavation steps 13–15, high and low compressive stress zones alternate within the filling area, and a significant compressive stress concentration area develops in the surrounding rock on both sides of the ore body. By excavation steps 16–18, the compressive stress concentration area remains concentrated, maintaining its localized distribution. Figure 16 illustrates the relationship between the maximum principal stress and the excavation step, while Figure 17, Figure 18 and Figure 19 depict the changes in maximum and minimum principal stresses during excavation steps 16–18 for Schemes 1, 2, and 3, respectively. The numerical simulation results reveal that, following the final three stages of excavation, the stress concentration area is distributed across the stope roof and also appears within the backfill body. This is evident from the maximum principal stress contour map, which indicates that the mechanical role of the backfill body is further enhanced, playing a significant part in regulating in situ stress and ground pressure within the mining area. From the perspective of compressive stress distribution, the maximum compressive stresses for Schemes 1, 2, and 3 are 50.06 MPa, 42.56 MPa, and 58.64 MPa, respectively. A comparison of tensile stress values shows that the maximum tensile stresses for Schemes 1, 2, and 3 are 3.71 MPa, 3.43 MPa, and 4.17 MPa, respectively. The research and comparative analysis demonstrate that Scheme 2 has the most favorable effect on ground pressure regulation among the three schemes.

4.6. Stress Analysis After All Stopes Are Mined and Filled

The vertical stress distribution contour map of the stope after complete mining and filling is shown in Figure 20a. Figure 20a demonstrates that the surrounding rock in the edge area of the model is predominantly subjected to compressive stress. In contrast, within the ore body model area, the presence of the mined and filled ore body leads to the generation of both compressive and tensile stresses at different locations within the backfill. Overall, the backfill body experiences a combination of compressive and tensile stresses. The tensile stress value in the backfill of Scheme 2 is the lowest, and the maximum principal stress value in the excavation area and its vicinity is less than that in the surrounding rock at the model’s edge. After the stope is fully mined and filled, the minimum principal stress distribution map, as illustrated in Figure 20b, reveals that the surrounding rock on both sides of the filling area is subjected to significant compressive stress. Additionally, the interval distribution of high and low stress areas within the filling area exhibits distinctive characteristics. The vertical stress distribution contour map of the stope after the completion of mining and filling operations is shown in Figure 21a. Figure 21a indicates that the vertical stress in Schemes 1 and 3 is predominantly compressive, while Scheme 2 exhibits a tensile stress area, albeit with a relatively low tensile stress value of 0.027 MPa. The distribution of high and low stress intervals is evident in the filling areas of all three schemes. It is observed that regions subjected to greater compressive stress correspond to low stress areas. Additionally, a significant concentration of vertical stress is evident in the surrounding rock on both sides of the filling area, with local stress in some mining areas exceeding 50 MPa. Figure 21b presents the horizontal stress distribution contour map following the full excavation and backfilling of the stope. Analysis of the Figure 21b also reveals that the stress orientation in the majority of the backfill regions aligns with the Z-axis, with stress magnitudes ranging approximately from 2.5 to 2.6 MPa.

4.7. The Plastic Zone Analysis After All Stopes Are Mined and Filled

The plastic zone of Scheme 1, Scheme 2, and Scheme 3 after all stopes are mined and filled are shown in Figure 22. As can be seen from the Figure 22, the plastic zone area after the mining of the three schemes is small, independent of each other and not connected. It is mainly distributed in the top and bottom pillars and the edges of the backfill in each mine.

5. Optimization of Schemes for Deep Mining of Sanshandao Gold Mine

According to the analysis of the numerical simulation results of the previous three downward mining schemes, the three mining schemes have their advantages and disadvantages, and the index data are of different sizes, which is difficult to judge subjectively. Therefore, it is necessary to quantitatively analyze the evaluation indicators of each scheme by combining the AHP and FCE and optimize the three schemes, respectively [27,28,29,30,31,32,33]. In conclusion, Scheme 1, Scheme 2, and Scheme 3 are now preferred. Firstly, a comprehensive evaluation index system is established for the three mining schemes. The AHP then is used to objectively determine the weight of each factor, after which a fuzzy comprehensive evaluation can be established through FCE theory. Finally, the best downward mining scheme can be determined.

5.1. Comprehensive Evaluation Indicators

Based on the actual situation of the ore body after mining and filling, six indexes were selected from the simulation calculation results of the three mining schemes. These included the maximum compressive stress of the surrounding rock, the average vertical displacement of the top column monitoring point, the average vertical stress of the top column monitoring point, the maximum compressive stress of the backfill body, the maximum tensile stress of the backfill body, and the plastic failure degree. The comprehensive evaluation index factors for mining schemes are presented in

Table 2. Comprehensive evaluation index factors.

Index Factor	Scheme 1	Scheme 2	Scheme 3
Maximum compressive stress of surrounding rock/MPa	52.16	52.21	53.06
Average vertical displacement of top column monitoring point/cm	19.10	19.10	19.07
Average vertical stress at top column monitoring point/MPa	11.32	11.27	11.12
Maximum compressive stress of backfill/MPa	39.73	39.78	41.03
Maximum tensile stress of backfill/MPa	3.85	3.74	3.92
Plastic failure degree/%	12.35	12.40	11.83

.

5.2. Membership Degree of Quantitative Indicators

The selected quantitative indexes are as follows: the maximum compressive stress of the surrounding rock; the average vertical displacement of the top column monitoring point; the average vertical stress of the top column monitoring point; the maximum compressive stress of the backfill body; the maximum tensile stress of the backfill body; and the index of the degree of plastic failure of each scheme. The degree of membership of the quantitative indicators is determined by the membership function method, while that of the non-quantitative indicators is determined by the relative binary comparison method [34,35,36].

The target eigenvalue matrix composed of m indexes of n schemes is presented below:

$$Y=\left. [\begin{array}{cccc}{y}_{11}& y_{12}& \cdots & y_{1n}\\ y_{21}& y_{22}& \cdots & y_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ y_{m1}& y_{m2}& \cdots & y_{mn}\end{array}\right]=(y_{ij})$$

(1)

where $i=1,2,\cdots ,m$; $j=1,2,\cdots ,n$.

The following steps are to be followed in order to calculate target relative dominance [37,38]:

For larger and better indicators, the following equation is used for specification [39]:

$$r_{ij}={\displaystyle \frac{y_{ij}}{\max y_{ij}}}$$

(2)

For smaller and better indicators, the following equation is used for normalization:

$$r_{ij}={\displaystyle \frac{\min y_{ij}}{y_{ij}}}$$

(3)

The relative superiority matrix of the target is obtained:

$$R=\left. [\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ \cdots & \cdots & \cdots & \cdots \\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right]=(r_{ij})$$

(4)

where $i=1,2,\cdots ,m$; $j=1,2,\cdots ,n$.

According to Table 2 of the comprehensive evaluation index factors, the eigenvector matrix can be obtained as follows:

$$R_{1\text{–}6}=\left. [\begin{array}{ccc}52.16& 52.21& 53.06\\ 19.10& 19.10& 19.07\\ 11.32& 11.27& 11.12\\ 39.73& 39.78& 41.03\\ 3.85& 3.74& 3.92\\ 12.35& 12.40& 11.83\end{array}\right]$$

(5)

Therefore, by using Formulas (2) and (3) to normalize the above matrix, the comprehensive membership matrix is finally obtained:

$$R_{1\text{–}6}=\left. [\begin{array}{ccc}1& 0.999& 0.983\\ 1& 1& 0.998\\ 0.982& 0.987& 1\\ 1& 0.999& 0.968\\ 0.971& 1& 0.954\\ 0.996& 1& 0.954\end{array}\right]$$

(6)

5.3. Analytic Hierarchy Process

The AHP is used to determine the weighting of indicators at each level by using a multi-level analytical evaluation model [40,41].

The weight matrix of six indicators can be obtained by using AHP:

$$\left. [\begin{array}{cccccc}1& 1/3& 1& 1& 1/9& 1/7\\ 3& 1& 3& 3& 1/3& 1/2\\ 1& 1/3& 1& 1& 1/9& 1/7\\ 1& 1/3& 1& 1& 1/9& 1/7\\ 9& 3& 9& 9& 1& 3\\ 7& 2& 7& 7& 1/3& 1\end{array}\right]$$

(7)

This is a selection step based on the analytic hierarchy process as follows:

Firstly, the judgment matrix is constructed by performing pairwise comparisons among the six criteria with respect to the target layer. This matrix forms the basis for determining the relative weight of each criterion layer.

Subsequently, for each row within the judgment matrix, the geometric mean is computed. Specifically, the product of the row elements is calculated and then raised to the power of 1/n. The m-dimensional vector is obtained:

$${\varpi }_i=\sqrt[m]{{\displaystyle \prod _{j=1}^m{a}_{ij}}}$$

(8)

where $i=1,2,\cdots ,m$; $j=1,2,\cdots ,n$.

The vector is then normalized to the weight vector, and the weight vector is obtained:

$${\omega }_i={\displaystyle \frac{{\varpi }_i}{{\displaystyle {\sum }_{j=1}^m{\varpi }_j}}}$$

(9)

where $i=1,2,\cdots ,m$; $j=1,2,\cdots ,n$.

Finally, through calculation and comparison, the selection weights of mining schemes are obtained.

Finding the maximum eigenvalue ${\lambda }_{\max }=6.0774$, $CI=({\lambda }_{\max }-n)/(n-1)=0.0155$.

According to

Table 3. Average random consistency indicators.

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14
RI	0	0	0.52	0.89	1.12	1.24	1.36	1.41	1.46	1.49	1.52	1.54	1.56	1.58

, $CR=CI/RI=0.0125<0.1$ meets the consistency test.

Therefore, the weight vectors that affect the selection of mining sequence can be obtained by using the square root method as $\omega =[0.0447,0.1376,0.0447,0.0447,0.4634,0.2649]$.

5.4. Optimization of Mining Schemes in Sanshandao Gold Mine

In the deep mining process of Sanshandao gold mine, the weighted average model was used to comprehensively evaluate the above three schemes from six indicators: maximum vertical displacement of the top column, maximum vertical displacement of the bottom column, maximum compressive stress of the backfilling body, maximum tensile stress of the filling body, and the degree of damage in the plastic zone.

Based on the above calculation results, the scheme membership vector can be obtained as follows:

$$S=\omega \cdot R_{1\text{–}6}=(0.9848,0.9993,0.9642)$$

(10)

Therefore, the order priority of the three schemes is Scheme 2 > Scheme 1 > Scheme 3.

In conclusion, Scheme 2 is finally determined as the best scheme for the deep deposit of the Sanshandao gold mine.

6. Engineering Application and Limitations

The preferred Scheme 2 was implemented in an industrial trial at the mine site, with the test area selected between the 1600 and 1800 lines at the −945 m to −975 m level. Key parameters of the test area included cut-off grade: 1.00 g/t, total ore volume: 181,642 t, average grade: 2.5 g/t, and metal content: 454.105 kg. For the medium-deep hole high-section stopes in the lower wall between −945 m and −975 m, the downward drilling method was employed to extract Stopes 1#, 2#, and 3#, with subsequent analysis of economic performance metrics. The average daily production capacity in the test panel (medium-deep hole mining): 364.3 t. The total ore extracted from the three test stopes was 33,452 t, the ore recovery rate was 92.38%, and the mining dilution rate was 6.18%. Figure 23 shows the blasting effect of the 2# stope cutting patio, and Figure 24 shows the stope blasting effect. The trial achieved outstanding technical and economic performance, confirming the efficacy of the methodology. Notably, the results validated Scheme 2 as the optimal mining strategy for the given geological and operational conditions.

While the study provides valuable insights, certain limitations should be acknowledged. The optimization of mining schemes was based on numerical simulations using FLAC3D. However, numerical models inherently involve simplifications and assumptions that may not fully capture actual complexities. Future research should incorporate high-performance numerical software with enhanced computational capabilities to improve simulation accuracy and account for multi-physics interactions. Simultaneously, the fuzzy comprehensive evaluation method, while effective, introduces inherent randomness in decision-making. To strengthen the robustness of scheme selection, multi-method validation is recommended, such as theoretical analysis, physical similarity experiments, integration of machine learning algorithms, etc. Furthermore, a combination of holistic approach would better address uncertainties in geological variability, rock mass behavior, and operational constraints.

7. Conclusions

(1)

According to the characteristics of the mining method of the deep ore body of the Sanshandao gold mine, three different downward mining schemes were designed, namely, the staggered downward mining from the horizontal wing to the other wing, the vertical interval six, and the oblique interval two; the horizontal center to the two wings separated by five mining one, the vertical interval six, and the oblique interval two; and the horizontal two wings to the center of the staggered downward mining scheme.

(2)

A numerical simulation analysis was conducted on three distinct mining phases, with the objective of elucidating the evolution rules governing the maximum principal stress, minimum principal stress, equivalent strain, vertical displacement, horizontal displacement, and the distribution of the plastic zone in different mining schemes across varying mining phases. The change in vertical displacement is between 4.42 and 22.73 mm, while the change in horizontal displacement is between 1.72 and 3.69 mm. These values demonstrate that vertical displacement has a more significant impact on the stability of the stope than horizontal displacement.

(3)

As the mining range is extended, the mechanical effect of the filling body is becoming increasingly pronounced. The downward mining scheme is conducive to the effective management of deep ground pressure at the Sanshandao gold mine. Scheme 2 is conducive to the control of stress concentration, the reduction in tensile stress in the mining area, the prevention of large plastic zones and large displacements in the mining area, and the realization of ground pressure control at the Sanshandao gold mine.

(4)

Based on the characteristics of three mining technology schemes, the evolution laws of stress-strain distribution and other data for three different schemes were analyzed. The AHP and FCE method was used to optimize different mining schemes in the deep deposit of Sanshandao gold mine. Six indicators (maximum compressive stress of surrounding rock, average vertical displacement of top pillar monitoring points, average vertical stress of top pillar monitoring points, maximum compressive stress in the mining area, maximum tensile stress in the mining area, and degree of plastic failure) were selected to establish an evaluation index system, and Scheme 2 was determined as the optimal scheme. Finally, the rationality and reliability of Scheme 2 were validated through on-site industrial trials.