Simulation Study on Optimization of Structural Parameters of Stope Based on Ground Pressure Control

Abstract

Aiming at the problem of surrounding rock instability easily induced by high ground stress in the process of deep-well mining, the optimization of stope structure parameters is studied by combining numerical simulation with theoretical analysis. Firstly, the physical and mechanical properties of rock mass are fully understood using laboratory experiments. Then, six kinds of stope structure parameter schemes are preliminarily designed using the Matthews chart method. According to the geological conditions of the Ruihai Gold Mine, a large three-dimensional numerical model is established. Based on FLAC3D, the follow-filling continuous mining method is used to simulate the six schemes. By analyzing the influence and law of different stope structures on the stress, displacement, and plastic zone evolution of surrounding rock, the most effective mining strategy to balance the safety and economic benefits of the target area is determined. In the area with good rock mass quality, the optimal stope dimensions are 20 m in height, 15 m in width, and 80 m in length. In the rock mass area with fault crossing or relatively developed joint fissures, a reduced configuration of 20 m height, 10 m width, and 70 m length is recommended to enhance stability and stress management. Finally, comparative analysis of mining methods confirms that the follow-filling continuous mining method effectively mitigates ground pressure, offering a theoretical foundation for the safe and efficient extraction of deep mineral resources.

1. Introduction

With the continuous growth in the global demand for mineral resources and the continuous depletion of shallow resources, the development of metal mines is gradually extended to deep mining; ultra-deep shaft mining has become a valuable choice for the sustainable development of the mining industry [1]. According to incomplete statistics, over 120 metal mines worldwide have reached depths exceeding 1000 m [2]. Deep ore bodies are situated in geologically complex environments characterized by high ground stress, elevated temperatures, high seepage pressure, and heightened risks of rock burst. These conditions result in systemic challenges for conventional mining methods, including instability in stopes, rising support costs, and reduced resource recovery rates [3,4,5].

Under these conditions, effective control of excavation-induced stress around the stope has emerged as a critical priority for ensuring safe mining operations [6]. In response to national initiatives emphasizing production safety and environmental protection, backfill mining methods—which counteract mining-induced stress concentrations, reduce surface subsidence, and improve recovery rates while minimizing ecological impact—have gained significant traction in the mining industry. The filling mining method has received wide attention because of its unique advantage of actively regulating the surrounding rock stress field. Through the synergistic load-sharing mechanism between backfill material and the surrounding rock, stress distribution around mined-out areas is optimized, curbing plastic zone expansion and mitigating energy accumulation risks [7,8,9,10]. Yu et al. [11] studied the influence of stope backfill on vertical stress distribution using a numerical simulation. Zhou et al. [12] used a microseismic monitoring system to prove that filling is one of the important factors for maintaining the stable distribution of underground ground pressure in mining engineering. Li et al. [13] proved that high-water material filling support can effectively guarantee the stability of stope roof through experiments. The effectiveness of ground pressure control in backfill mining is contingent upon the optimal design of stope structural parameters [14]. If parameters such as stope size, pillar position, and the strength of the filling body are not properly selected, issues such as stress concentration or the instability of the filling body may arise [15]. The selection of a mining method dictates the orebody extraction sequence, governs the formation of mined-out areas, defines the configuration of support systems, and affects the redistribution of stresses within the surrounding rock mass. A rational selection of the mining method can effectively regulate mining-induced stress, reduce surrounding rock damage, and prevent ground-pressure-related disasters such as roof falls, sidewall spalling, and rock bursts. By optimizing stope structural parameters, such as the rational arrangement of pillar size and spacing, control of stope height, and stope width, it is possible to guide the safe transfer of stress and prevent localized stress concentrations. Ground pressure manifestations exhibit spatiotemporal characteristics. The mining method used determines the extraction pace and spatial advancement pattern, while stope structural parameters regulate the rate and extent of stress release. The coordinated optimization of both factors can delay or dissipate stress accumulation, thereby enhancing the effectiveness of ground pressure control. Therefore, the dynamic balance between safety and economic cost is finally realized by optimizing the structural parameters of the stope using scientific methods [16,17,18].

Reasonable structural parameters of the stope often need to be optimized using a significant amount of research and experimental means [19,20,21,22,23]. In view of the complex geological conditions in the deep mining environment, traditional model experiments and field tests are limited in optimizing slope structural parameters [24]. With the continuous development and application of numerical calculation technology [25,26,27], the finite difference software represented by FLAC3D v3.0 has become a widely used and reliable tool for deep mining simulation due to its proven capabilities in large deformation analysis, implementation of complex constitutive models, and multi-field coupling in geotechnical engineering. This study shows that FLAC3D can well-simulate the spatial and temporal evolution of the deep mining stress field and quantitatively assess stope stability through plastic zone extension, displacement field distribution, and other indexes [28,29,30,31,32]. Zhang et al. [33] used FLAC3D to simulate and analyze the stability of high and collapse-prone stopes, and determined the optimal mining scheme suitable for the region. Wang et al. [34] used the 3Dmine-Rhino-FLAC^3D coupled modeling numerical method to analyze the stability of the stope around the subsidence area, which provided an important reference for the safe mining of mines. Wang et al. [35] studied the influence of mining disturbance on adjacent stopes on the stability of side-exposed backfill under different mining depths using FLAC3D, which improved the safety and efficiency of pillar mining.

In this study, a large-scale three-dimensional refined numerical model is constructed in the engineering background of an ultra-deep-well high-grade gold mine. The stability characteristics of rock mass under different stope structures are analyzed using FLAC3D, and the optimal stope structure scheme considering safety and efficiency is proposed. In this study, the follow-filling continuous mining method is innovatively proposed to control ground pressure, and, combined with numerical simulation analysis, reasonable stope structure parameters under ultra-deep-well mining are given, which aims to provide theoretical support for mines to choose reasonable mining schemes.

2. Introduction to Mining Methods

2.1. Geology

Ruihai Gold Mine is located in the north of Laizhou city, about 26 km away from the city. The southwest is adjacent to the Sanshandao gold mine and the newly built Laizhou port. The main ore body is hosted within the Cangshang-Sanshandao fault zone, primarily composed of pyrite sericitized granite. There is no obvious difference in lithology and structure between the surrounding rock and the ore body. Disseminated and veinlet-distributed sulfides such as pyrite can be observed within the ore body, including the significant enrichment characteristics of gold elements, showing a gradual transitional relationship with the surrounding rock, requiring boundary definition through chemical analysis.

The ore body is distributed in a large vein-like structure, with local lens-like features. Its orientation is 35°, it leans towards the southeast, and the average inclination angle is 39°. Meanwhile, the burial depth of the ore body exceeds 1000 m, and the first mining area is located at the −1480 m level. Affected by ultra-deep mining, rock burst disasters caused by high ground stress pose a serious threat to safety production, potentially leading to accidents such as roadway collapse and rock mass ejection, while also causing resource losses. To ensure the safety and efficiency of deep mining, it is necessary to optimize the structure parameters through scientific demonstration.

2.2. Mining Methods

As a typical deep metal deposit, Ruihai Gold Mine features substantial reserves, high-grade ore, and an annual design capacity of 3.96 million tons. The first mining intervals is located at the −1480 m level, with a mining depth exceeding 1000 m. The backfill mining method is adopted to address these issues under such complex geological and engineering conditions.

A mining–backfilling synchronization system is introduced, adopting a continuous mining approach with synchronized backfilling. The technology integrates extraction and backfilling, enabling the closure of excavated zones in time as mining progresses. Because the mined-out area is promptly filled, the exposed area remains minimal, theoretically removing limitations on the length of individual stopes. As the working face advances, the previously mined-out area is backfilled in time, and the fill material quickly bears the overlying rock load, preventing roof subsidence or collapse and inhibiting the development of large-scale loosening zones. The backfill material possesses a certain degree of strength and ductility, enabling it to effectively absorb and mitigate stress concentrations in the surrounding rock. This prevents the stress from transforming into a source of failure, thereby suppressing crack propagation and reducing the likelihood of rockburst occurrences. Compared to traditional methods, this process involves concurrent backfilling the mined-out area during mining, effectively mitigating issues such as surrounding rock instability and sudden ground pressure fluctuations caused by prolonged mined-out area exposure.

By promptly backfilling the mined-out area during the mining process, this technique helps mitigate the detrimental impacts of high ground stress, thereby improving operational efficiency, lowering costs, and reducing the likelihood of hazardous incidents. The methodology is illustrated in Figure 1.

• This method is suitable for very thick ore bodies with a dip angle of 20°–40° and thickness greater than 100 m.
• The ore body is divided into phases in the vertical direction and subsections within the phases, with the height of the phases being 60 m and the height of the subsections being 20 m. The mining ramp is arranged in the lower plate of the ore body to connect each section, and each section reaches the lower plate through a vein.
• The stope is aligned along the strike direction. The length of the panel is set to 200 m, and the panel is divided into two mining areas. Each panel shares an ore pass, backfill-ventilation access, and a ventilation raise. In the subsections, we consider the factors sequentially.

2.3. Rock Mechanics Experiment

To characterize the mechanical properties of the ore body and granite while supporting numerical modeling, laboratory rock mechanics experiments, including uniaxial compression, tensile strength via Brazilian splitting, and triaxial compression, were conducted. Rock samples collected from multiple depths were used for these experiments. Samples were processed into cylindrical specimens following engineering rock mechanics standard requirements by processing and grinding, as well as using the MTS-815 microcomputer-controlled rock triaxial testing system for conventional mechanical experiments, as shown in Figure 2.

As can be clearly seen in Figure 3, tensile and cleavage brittle damage are shown in rock samples, with rock dust and rock flakes ejected during the experiment. Due to the high strength and brittleness of the rock, only a small number of rock samples are monitored for post-peak deformation, despite the loading rate control of 0.0002 mm/s.

The experimental data are used to obtain the complete rock mechanical parameters through a series of experiments; the results are shown in

Table 1. Complete rock mechanical parameters.

Rock Type	Compressive Strength /MPa	Tensile Strength /MPa	Elastic Modulus /GPa	Poisson’s Ratio
Granite A	116–237	9.5	135.2–140.1	0.21–0.32
Granite B	127–211	8.2	109.1–148.5	0.20–0.36
Granite C	202–244	7.8	140.1–167.0	0.28–0.39

.

3. Design and Numerical Simulation of Structural Parameter Schemes for Large Stopes

3.1. Calculation of Mathews Stability Graph Probability Model

The improved Matthews chart method is widely used for stope structural parameters in deep metal mines [36,37]. The design process of the Mathews stability map method is based on the calculation of two factors, the stability number N and the shape factor S, which are then plotted on maps delineated into predicted stable, potentially unstable, and avalanche zones. The stability N represents the ability of the rock mass to maintain stability under a given stress condition, and the factor S reflects the size and shape of the extraction zone.

The steps for determining the structural parameters of the stope using the Mathews stability diagram method are as follows:

Step 1.

The stability index N of the rock body is calculated according to the equation.

Step 2.

Determine the mine production capacity and ore body occurrence conditions; the shape coefficient S of the exposed area of the stope is preliminarily calculated.

Step 3.

Project N and S onto Mathews stability chart in order to judge the stability of the stope preliminary.

(1)

In Mathew’s method, the rock mass stability index N is calculated by the following equation:

$$N=Q^{\prime }ABC$$

(1)

where Q′ is the modified NGI system grading index, A is the rock strength factor, B is the correction factor for the orientation of rock defects, and C is the correction factor for the orientation of the exposed surface of the design stope.

The rock mass index Q′ in Equation (2) is

$$Q^{\prime }={\displaystyle \frac{R}{J_n}}{\displaystyle \frac{J_r}{J_a}}$$

(2)

In Equation (2), R is the rock quality index, J_n is the number of joint groups, J_r is the joint roughness, and J_a is the degree of joint alteration, filling, and cementation. According to the statistics of drilling core length, R = 71–82, and the other three indexes can be obtained according to the geological survey report: J_r = 4, J_n = 2, J_a = 3.

According to the relevant data, the rock mass, ground stress, discontinuous surface, and mining method are deduced. It is inferred that the relevant parameters are Q′ = 47.4–54.6, A = 0.775, B = 0.4, C = 2, then N = 29.4–34.1, considering that, comprehensively, N takes the value of 29.4.

(2)

Calculation of shape factor S

The shape factor S can be defined as the ratio of the area to the perimeter, as shown in the following Equation (3):

$$S={\displaystyle \frac{L{L}_1}{2(L+L_1)}}$$

(3)

where L is the exposed width and L₁ is the length of the exposed surface.

When L₁/L is greater than 4:1, S remains basically unchanged. In other words, at this time, the exposed width L plays a major role in the stability of the exposed surface.

By projecting the stability N onto Figure 4, it can be obtained that the shape factor S is 6.48 for stable stopes. This indicates that when the value coefficient of the stope exceeds 6.48, it will breach the stability-failure boundary and collapse.

To achieve the annual production target of 3.96 million tons for the mine, based on the analogy analysis method and referring to the engineering experience of similar cases, the width of the stope should be controlled within the range of 10–15 m. By initially setting the maximum structural parameters of the stope as 15 m (width) × 100 m (length), and the direction of the maximum principal stress being perpendicular to the stope layout direction, the shape factor S is approximately 6.52, which exceeds the critical value of the calculation. Considering both production efficiency and on-site operational feasibility, all stope heights are uniformly set to 20 m in the simulation schemes. Stope width is set to two options (10 m and 15 m). Stope length is assigned three scenarios (90 m, 80 m, and 70 m). For each scheme, the calculated shape factor (S) and exposed surface area are both lower than the corresponding critical values. To accurately assess how stope configurations influence the stability of surrounding rock, six numerical simulation schemes are adopted in this research, as shown in

Table 2. Simulation scheme of stope structure.

Scheme	Stope Length /m	Stope Wide/m	Stope Height/m2	Exposed Surface Area/m2	Shape Coefficient S
1	90	15	20	1350	6.43
2	80	15	20	1200	6.31
3	70	15	20	1050	6.18
4	90	10	20	900	4.50
5	80	10	20	800	4.44
6	70	10	20	700	4.38

.

3.2. Model Construction and Mechanical Parameters

(1)

Model construction

In order to further determine the optimal mining structure scheme, Flac3D is used to simulate the mining filling process. According to the conditions of the gold ore body endowment, a 3D model is constructed, and it is known from the geological data that the length of the ore body is 1541 m, the endowment height ranges from −1956 m to −855 m, and the maximum thickness of the ore body is 287 m. As shown in Figure 5, the overall model consists of the quarry, the gold ore body, and the surrounding rock. Due to the large depth of the ore body, the modeling is simplified. The irregular boundary of the ore body is simplified to a more regular shape. For example, a straight line is used instead of a slight curved line, and a circular arc is used instead of a complex curve. The geometric features that have an insignificant effect on the overall mechanical behavior are removed to improve the computational efficiency. The size of the overall model in the X, Y, and Z direction is 3000 m. The middle section of the mining is located at −1480 m, and the quarry is arranged along the strike. By simulating the whole mining process of the quarry, the safety and economic indexes in it are collected and comprehensively evaluated to ensure the stability of the quarry. This analysis aims to obtain the best mining structure solution for the ultra-deep mining of Ruihai Gold Mine to ensure the safety, efficiency, and stability of the mining operation.

(2)

Analysis of grid dimensions

This simulation mainly shows the stress and deformation around the stope to analyze and study; in order to ensure that the grid division on the simulation of the impact is minimized, the grid size needs to be reasonable division.

• The stope is the focus of this study; the grid size is set at 1 m, and the minimum grid size is shown.
• At 40 m around the stope transition zone range, the grid size is set at 2 m, gradually increasing outward, and the size of the ore body is set at 8 m, as shown in Figure 6.
• The mesh generation of the surrounding rock adopts the mapping method to generate a gradient mesh, and the boundary size is set at 25 m. The mesh generated is a hybrid mesh.

(3)

Mechanical parameter selection

Based on the test data of the mechanical properties of the complete rock body, the Hoek–Brown criterion is applied to construct the rock body deterioration model in this research. The integrated strength index of the rock body is determined by the systematic parameter discounting method, and the intrinsic parameters used in the numerical simulation are derived by strict derivation [38,39]. The basic parameters required for the Hoek–Brown criterion include the uniaxial compressive strength δ_c of the intact rock mass, the Hoek–Brown constant mi of the rock mass, and the geological strength index GSI of the rock mass. According to the previous rock mechanics test and geological data, the parameters are determined as follows: δ_c = 120 MPa, m_i = 40, GSI = 70. The specific results are shown in

Table 3. Mechanical parameters of various rock masses.

Rock Type	Volume Modulus /Gpa	Shear Modulus /Gpa	Density g/cm3	Cohesion /Mpa	Internal Friction Angle/	Tensile Strength /Mpa	Poisson’s Ratio
Surrounding rock	15.79	10.84	2.61	1.97	41.53	1.83	0.23
Ore	15.11	10.33	2.71	1.43	45.94	1.24	0.19
Filling body	0.85	0.327	1.68	0.76	36.6	0.55	0.33

.

(4)

Boundary constraints and initial conditions

Combined with the actual situation, the boundary conditions are determined as follows: The mining influence range of the filling mining method is limited, and the rock mass movement value around the stope level and farther away will be very small. Displacement constraints are used at the boundary of the model (the bottom and four sides of the model), and the upper surface of the model is a free surface. According to the measured results of ground stress in Ruihai Gold Mine, it is concluded that the ground stress in the mining area can be calculated according to the following formula:

$${\sigma }_v=0.74+0.025H$$

(4)

$${\sigma }_h=1.08+0.022H$$

(5)

where σ_v is the vertical stress, MPa; σ_h is horizontal stress, MPa; and H is buried depth, m. Using the in situ stress fitting formula to apply load to the model, the actual working conditions are simulated, and the initial stress field (Figure 7) is generated. The compressive stress at the bottom of the model is 76.59 MPa, and the deviation from the set initial value is only 0.85 MPa. The results verify the accuracy of the initial in situ stress field and the rationality of the numerical model.

3.3. Results Analysis

In order to fully reflect the mechanical state of the stope and surrounding rock under different calculation conditions, the section is cut parallel to the dip angle of the ore body and at the position of the stope roof, and the section is cut perpendicular to the ore body and at the position of the middle line of the room length. The vertical section of the ore body and the slice position of the parallel stope roof are shown in Figure 8. Through the analysis of the displacement, stress, and plastic zone distribution of the profile, and combined with the selected rock mass engineering failure criterion, the stability of the stope is comprehensively judged.

(1)

Stress analysis

• Minimum Principal Stress Analysis: A vertical cross-section through the stope roof was analyzed, and the position of the section is shown in Figure 8. Overall, the distribution patterns of minimum principal stress across the six schemes are found to be similar. The stress distribution in the ore pillar exhibited an “X”-shaped pattern, while that in the backfill resembled a spindle shape, as shown in Figure 9b,e. After stope excavation, stress redistribution led to significant compressive stress concentrations in the pillars, with the highest compressive stresses observed within the pillar cores and at the corner regions. In particular, Scheme 1 and Scheme 4 exhibited large areas of compressive stress concentration in the middle of the pillars (Figure 9a,d). Two key observations can be made through comparative analysis. First, due to the influence of the mining sequence, compressive stress concentration predominantly occurred on the left side of the −1480 m sublevel. Second, when the stope width and height were kept constant, a reduction in stope length led to a corresponding decrease in the extent of compressive stress concentration within the ore pillar.
• Maximum Principal Stress Analysis: In underground mining, tensile stress is one of the primary factors contributing to roof failure. To systematically investigate tensile stress distribution characteristics, cross-sectional analysis is performed parallel to the stope roof. Based on a comparative analysis of the simulation results for all six schemes, significant tensile stress concentration is observed in each case (Figure 10). As demonstrated in Figure 10b, tensile stress concentration zones are predominantly localized in the central roof region, with magnitude progressively diminishing radially. Crucially, stress state transition is observed at the stope–backfill interface, where tensile stress transformed into compressive stress. The simulation results of the remaining schemes followed this same trend. It is noteworthy that, as the stope length decreased, the extent of the tensile stress concentration zone in the roof showed a clear tendency to shrink.

The maximum tensile and compressive stress values for each scheme are statistically analyzed, as shown in Figure 11. The simulation results indicate that, in ultra-deep mining conditions, the magnitude of tensile stress in the stope roof and floor is significantly influenced by the stope dimensions. From the simulation results, it can be discerned that the tensile stress of the roof and floor of the stope are greatly affected by the size of the stope during the mining of ultra-deep wells. When the stope height and width remain constant, the maximum tensile stress in the roof and floor increases proportionally with stope length. Numerically, the maximum tensile stress in Scheme 1 reached 1.284 MPa, which exceeds the tensile strength of the rock mass and posing instability risks. Combined with the distribution range of tensile stress shown in Figure 10, it can be observed that, as the exposed area of the stope increases, the tensile stress in the roof also increases, gradually approaching the rock’s tensile strength and eventually leading to roof failure. In contrast, the maximum tensile stresses in the remaining five schemes are all below the rock mass tensile strength of 1.24 MPa. When the stope width is 10 m, the maximum compressive stress in the pillars across different stope lengths remained around 76 MPa, indicating good overall stability. When the stope width increases to 15 m, the compressive stress in the pillar increases significantly. Among all the schemes, scheme 1 shows the highest compressive stress (84.5 MPa). Although the compressive stress value of scheme 1 is the largest, it does not exceed the compressive strength of rock mass.

(2)

Displacement analysis

In the follow-filling continuous mining method, roof and floor displacements are governed by multifactorial interactions. Stope geometry parameters significantly influence displacement field distributions, which in turn affect the stability of the backfill–pillar composite structure through stress redistribution mechanisms. Consequently, roof and floor displacements are analyzed across six schemes with varying stope geometries.

The vertical ore body orientation is made into a profile. The displacement of the top and bottom plates of the stopes in the six schemes is shown in Figure 12 below. Overall, roof subsidence predominantly occurred on the left side of the −1480 m mining level. Footwall stopes, excavated earlier due to mining sequence constraints, experienced greater stress redistribution and excavation-induced disturbances, resulting in amplified roof–floor displacements. As mining and backfilling progressed, system stability improved, with Z-axis displacements in the right-side stopes progressively diminishing.

It can be found from the right side of each subgraph that maximum roof subsidence is concentrated at the central region (Figure 12a). An equivalent arch of surrounding rock displacement is formed above the roof, with the arch span increasing and the displacement magnitude decreasing as it extended upward. When stope width is held constant, a correlative reduction in the spatial extent of the maximum subsidence contour arch is observed with decreasing stope lengths.

To investigate displacement patterns along the Z-axis in stopes, displacement and monitoring point data from the −1480 m level are analyzed. The results reveal the spatial extent and magnitude of post-excavation displacements, while displacement–time curves from roof–center monitoring points illustrate dynamic deformation trends during excavation. Cross-sectional profiles along the ore body strike are generated for the comparative analysis of displacement contour and monitoring data across the six schemes.

In scheme 1, post-excavation displacements primarily occurred in the roof and floor, forming an arched pattern. Displacement contour exhibited sparse contouring, with roof displacement ranging from 20.00 to 27.91 mm. Monitoring data (Figure 13) indicate that excavation and backfilling of the stope occurred between steps 7550 and 8240, with roof subsidence initiating immediately after excavation. Backfill reinforcement reduced the subsidence rate after step 8000, ultimately stabilizing the roof. Total roof displacement during the process ranged from 0.27 to 25.70 mm.

In scheme 2 (stope dimensions: 80 × 15 × 20 m), post-excavation displacements primarily occurred in the roof and floor, forming an arched distribution. Maximum roof subsidence localized to the right side, with displacements ranging from 15.00 to 24.3 mm. Monitoring data (Figure 14) show that stope excavation and backfilling occurred between steps 7480 and 8020, with roof subsidence initiating immediately after excavation. After step 7980, the subsidence rate decreased, indicating delayed load-bearing engagement of the backfill material. The roof stabilized progressively, with total displacement ranging from 0.18 to 23.12 mm during the process.

In scheme 3 (stope dimensions: 70 × 15 × 20 m), post-excavation displacements primarily localized to the roof and floor, exhibiting an arched distribution. Maximum roof subsidence occurred on the right side with a limited subsidence extent, ranging from 10.00 mm to 21.10 mm. Monitoring data (Figure 15) indicate that stope excavation and backfilling spanned steps 7380–7790, with roof subsidence initiating post-excavation and ultimately stabilizing. Total roof displacement during the process ranged from 0.17 mm to 19.13 mm.

In scheme 4 (stope dimensions: 90 × 10 × 20 m), post-excavation displacements are concentrated in the roof and floor, exhibiting a symmetrical arched pattern in the displacement nephograms. Roof displacement ranged from 10.00 mm to 23.32 mm. Monitoring data (Figure 16) indicate that excavation and backfilling occurred between steps 7460 and 8250. After step 8120, the backfill material began to provide structural support, markedly reducing the roof subsidence rate until stabilization is achieved. Total roof displacement during the entire process ranged from 0.19 mm to 20.80 mm.

In scheme 5 (stope dimensions: 80 × 10 × 20 m), post-excavation displacements are concentrated in the roof and floor, forming an arched distribution. Maximum subsidence localized to the stope’s right side with limited spatial extent, ranging from 10.00 mm to 21.43 mm. Monitoring data (Figure 17) indicate that excavation and backfilling occurred between steps 7380 and 8010. After step 7900, the backfill material began providing structural support, reducing the subsidence rate until stabilization. Total roof displacement during the process ranged from 0.21 mm to 18.81 mm.

In scheme 6 (stope dimensions: 70 × 10 × 20 m), post-excavation displacements are concentrated in the roof and floor, forming an arched distribution. Roof displacement ranged from 10.0 mm to 16.85 mm. Monitoring data (Figure 18) indicate that excavation and backfilling spanned steps 7330–7770, with roof subsidence initiating post-excavation and ultimately stabilizing. Total roof displacement during the process ranged from 0.20 mm to 16.33 mm.

Comparative analysis of Z-axis displacements across all designs reveals that stope exposure area significantly influences roof subsidence. When stope width is held constant, stope length emerges as a critical factor governing subsidence magnitude. Z-axis displacement results for the six schemes are summarized in Figure 19.

(3)

Plastic-zone analysis

During mining operations, the original stress equilibrium is disrupted by ground stress and mining-induced disturbances. Stress redistributes to the surrounding rock masses near excavated zones. When these rocks exceed their strength limits, elastic deformation transitions irreversibly to plastic deformation. Given the large span of stopes, post-excavation plastic zone distribution must be analyzed to evaluate rock mass failure mechanisms and assess stope stability.

In Figure 20, distinct plastic zones developed in the roof, floor, and sidewalls post-excavation. For scheme 1–3 plastic zone evolution processes are broadly similar, with spatial distributions mirroring their respective stress patterns. Plastic zones in left-side stopes exhibited larger extents due to pronounced mining-induced disturbances, with localized shear failure observed in the floor. As stope length increased, plastic zone expansion occurred proportionally. Nevertheless, global stability remained adequate, with no large-scale thorough-going failure detected.

Meanwhile, plastic region distributions in scheme 4–6 are broadly similar, primarily localized to pillars on the left side of the −1480 m level. Partial shear failure occurred in these pillars, while minor tensile failure developed in the roof and floor of the stopes. However, no thorough-going failure is observed.

To further investigate plastic zone characteristics, volumetric parameters of shear and tensile plastic zones are systematically collected and statistically analyzed in this research. Detailed results are presented in

Table 4. Calculation results regarding the plastic zone of the stope.

Scheme	1	2	3	4	5	6
Shear plastic zone volume/m3	36,631.2	27,849.2	17,157.8	79,805.1	64,363.0	36,504.9
Tensile plastic zone volume/m3	1135.2	584.3	903.6	684.5	825.1	547.6

.

4. Optimization of Structural Parameters of the Stope

Stope structural parameters are validated by using a modified Mathews stability graph method and numerical simulations. Results from displacement and stress analyses indicate that stope dimensions significantly influence stability.

For stopes with a 15 m width (scheme 1–3), the smallest maximum tensile stress and most limited tensile stress distribution are exhibited in scheme 3. Scheme 1 shows the highest tensile and compressive stresses, with its maximum tensile stress exceeding the rock mass tensile strength. Maximum displacements across all schemes remained below the 45 mm threshold [40]. The largest shear plastic zones are displayed in scheme 1, indicating extensive internal shear failure. Scheme 2 had the smallest tensile plastic zones (584.3 m³). As a consequence, when the width of the stope is 15 m, it is recommended to select the length of the stope as 80 m.

When the width of the mine room is 10 m, by comparing and analyzing the stress, displacement, and plastic zone of scheme 4–6, it can be observed that scheme 6 has the best form of stress expression, and the value of its maximum tensile stress is 0.529 MPa, which is smaller than the tensile strength of the rock body. The maximum compressive stress endured by the three schemes is around 76 MPa, and the distribution form of its maximum compressive stress is also very similar. The Z-direction displacement of the three schemes does not exceed 45 mm, and it is judged that the rock mass structure is not damaged [41,42]. Moreover, scheme 6 has the smallest Z-direction displacement. Scheme 5 has the largest volume of tensile plastic zone, and the volume of rock body subjected to tensile damage in the mining process is the largest. When the width of the mining room is 10 m, it is recommended to choose the length of the mining room to be 70 m.

On the one hand, since the influence of rock joint fissures on mining is not considered, the possibility of joint fissure slip damage on the excessively large exposed surface in actual production will be greatly increased. On the other hand, due to the large thickness of the ore column in this scheme, the horizontal displacement generated is relatively small, and the penetration ratio of the plastic zone is significantly lower than that of other schemes. Considering all of the above, scheme 2 is recommended in an area with good rock quality, and scheme 6 is more reasonable when there are faults passing through the area or a rock body with more developed joints and cracks.

5. Comparative Analysis

In a bid to investigate the effects of the following-filling mining method on ground pressure control and roof displacement of the quarry, numerical simulation analysis was carried out by using the open-field subsequent filling method for the structural parameters of the quarry of scheme 2 (20 m height × 80 m length × 15 m width) and scheme 6 (20 m height × 70 m length × 10 m width), and the results are displayed below.

(1)

Scheme 2 Results

As can be seen from Figure 21, the maximum displacement of the roof plate of scheme 2, simulated by using the open-field subsequent filling method, is 47.04 mm, which exceeds the allowable limit displacement, and the quarry is in an unstable state. The maximum tensile stress on the roof plate is 0.79 MPa, and there is a stress concentration at the roof plate. The distribution of plastic zones is similar to that of scheme 2 under the follow-fill mining method.

(2)

Scheme 6 Results

According to the simulation results Figure 22, it can be seen that the maximum settlement of the top plate of the quarry is 37.49 mm, and the maximum bulge of the bottom plate is 42.10 mm, which is close to the permissible limit displacement of the quarry; the maximum tensile stress of the quarry is 0.56 MPa, which does not exceed the tensile strength of the rock body.

Through comparative analysis, it can be seen that, in ultra-deep-well mining, the open-field subsequent filling method is prone to instability due to the large exposed area of the quarry and the long exposure time of the empty area, the significant increase in the displacement of the quarry in the Z-direction by the influence of the ground stress as well as the mining disturbances, and the larger range of stress concentration.

6. Conclusions

The complete mechanical parameters of the rock body are obtained through the preliminary rock mechanics experiments, then the size range of the quarry is preliminarily determined, and six quarry size schemes are designed by using the improved Mathews diagram method. In addition, a large-scale three-dimensional numerical model is constructed, and FLAC3D is used to simulate and analyze the mining and filling of the six designed scenarios to obtain the response characteristics of the corresponding mechanical indexes. Finally, based on the mechanical response characteristics and the instability judgment criteria, the appropriate size of the quarry structure is determined for Ruihai Gold Mine, and the conclusions are as follows:

• The modified Mathews stability graph method yielded a critical stability factor of 6.48 for the stope. Referencing analogous mining operations, a preliminary stope geometry (20 m height × 100 m length × 15 m width) is designed, achieving a stability factor of 6.52, which exceeds the critical threshold. Six alternative stope geometries with stability factors below 6.48 are subsequently developed for comparative analysis.
• Numerical analysis results across different schemes demonstrate that, during ultra-deep mining, with a stope width of 15 m, a reduction in stope length leads to a gradual decrease in both maximum tensile and compressive stresses. The maximum tensile stress of scheme 1 exceeds the tensile strength of the rock mass, so the stope has a high probability of instability and failure. When the stope width is 10 m, as the stope length decreases, the maximum tensile stress gradually decreases, while the maximum compressive stress remains basically stable at 76 MPa. In addition, with the increase in the stope exposure area, the roof settlement displacement and floor heave displacement of the stope gradually increase, but neither exceeds the allowable ultimate displacement of the stope.
• Based on the stress, displacement, and plastic zone in the numerical analysis results, it is recommended to adopt Scheme 2 in areas with good rock mass quality—that is, the stope has a height of 20 m, a length of 80 m, and a width of 15 m. In rock mass areas with fault crossings or relatively developed joint fractures, Scheme 6 is recommended as being more reasonable, which features a height of 20 m, a length of 70 m, and a width of 10 m.
• Comparing the simulation results of the open-field subsequent filling method for scheme 2 and scheme 6, it can be observed that the following filling mining method realizes the dynamic balance of the three-dimensional stress redistribution in the mining airspace through a time-sequence synergistic filling–returning process, which can better control the ground pressure and shows better enhancement of the stability of the mining field by reducing the displacement of the top and bottom plates.
• The following filling mining method introduces a transitional space before the stope is fully formed, enabling the backfilling process to be advanced and implemented simultaneously with ore extraction. This method is not only well-suited to the geological conditions of the Ruihai Gold Mine, but also demonstrates strong generalizability and potential for broader application. It is particularly applicable to deep metal deposits with steeply inclined, large-thickness ore bodies under high-in situ-stress conditions. Through integration with panelized layout, continuous operation systems, and unmanned mining technologies, this approach provides robust technical support for building a “safe, efficient, and intelligent” deep mining system. In the future, this method can be promoted in mines with similar geological and stress conditions, offering significant potential for engineering applications and widespread adoption.

7. Discussion and Limitations

In this study, a systematic numerical simulation analysis was carried out on the optimization of stope structure parameters and the adaptability of mining and filling synergistic process under high-ground-stress conditions. Meanwhile, an optimization strategy with engineering feasibility is proposed based on the practical engineering conditions/considerations. However, there are still several limitations in the following respects, which need to be further improved in follow-up studies:

• This study primarily employed static simulation methods, without considering time-dependent effects such as creep, stress relaxation, and long-term stress redistribution. In a deep high-stress environment, these effects may lead to a degradation in the mechanical performance of the surrounding rock or the failure of the supporting system, thereby increasing the risk of engineering disasters.
• The influence of instantaneous stress caused by blasting disturbance on the stability of the surrounding rock structure during roadway excavation and stope mining is not fully taken into account. In the actual blasting process, the effects of micro-crack expansion and stress superposition may appear, which will amplify the risk of surrounding rock instability.
• The surrounding rock is regarded as an ideal homogeneous isotropic medium. However, in actual engineering conditions, rock masses are typically characterized by discontinuities such as joints, fissures, bedding structures, and fault zones. These geological structures will affect the stress transfer and failure mechanisms, potentially causing deviations between simulated and actual outcomes.

Overall, this study serves as a phased achievement aimed at providing theoretical support and technical solutions for stope structure optimization and ground pressure control at the Ruihai Gold Mine. As the mine enters the production phase, the research framework will be progressively refined through the integration of field experiments, blasting simulations, and detailed geological reconstructions. These efforts will enhance the correlation between simulation outcomes and real engineering conditions, thereby improving the practical applicability of the results.