Study on Crushed-Stone Cementation Properties and Bottom Stope Stability of Goaf by Open Stope Mining in Inclined Ore Bodies

Abstract

The mining of the part of the inclined ore body below a goaf is crucial for improving resource extraction and safe production. In this study, the cementation properties of crushed stone during the mining of the inclined ore body were investigated by means of laboratory experiments, theoretical analysis, and numerical simulation. Additionally, orthogonal experiments were performed to assess how factors like water–cement ratio, crushed-stone particle size, and cement–sand ratio affect the strength of the grouting concretion body (GCB). Furthermore, the fluidity of the slurry under different ratios was also measured. Considering both the fluidity of the slurry and the strength of the GCB, the optimal ratios of the slurry were determined to be a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:4. This ratio was then used for crushed-stone cementing under the poorest crushed-stone particle size conditions, based on which mechanical parameters were obtained from experiments. Theoretical analysis equated the problem of the grouting range to the width of the plastic zone of surrounding rock, and a conclusion was reached that the width of the GCB should be at least 29 m. The numerical simulation results reveal that among 30 mining rooms formed below the GCB, 24 mining rooms are in a stable state and 6 mining rooms are partially damaged on a small scale. As a whole, the GCB formed by grout filling into the goaf manages to effectively support the stope below, and it is verified that the theoretical calculation method of the width of the GCB is feasible.

1. Introduction

The mining of the ore body below a goaf is of great significance for ensuring regular operation of enterprises, improving economic benefits of enterprises, achieving full utilization of resources, and promoting environmental development of mines. During mining operations, the ore body below the goaf experiences stress concentration as a result of mining disturbance. Consequently, the surrounding rock in the mining area deforms severely, which is challenging to control. In the meantime, crushed stone in the goaf is likely to enter the stope below the goaf in the mining process, thus diminishing the quality of the extracted ore and increasing operational costs [1,2,3]. Grout filling of crushed stone in the goaf is usually adopted to tackle the above challenge. The grouting concretion body (GCB) formed in the goaf can not only serve to protect the lower stope but also reduce the mixing of crushed stone into the ore body. In this way, the ore body in the stope can be mined safely and efficiently.

The method of grout filling to form a GCB in the goaf has been widely applied in engineering practices. For different engineering backgrounds, the GCB plays various roles. When the ore body is located directly below the goaf, this method contributes to forming a false roof for the mining of the ore body. Such a false roof can support the load from the overlying rock and meanwhile prevent crushed stone from entering into the mining space, thus ensuring the safety of workers below [4,5,6,7]. In the case where structures are built above the goaf, this method can effectively fill voids within the goaf and enhance the deformation resistance of crushed stone, thereby reducing the residual surface deformation and protecting the structures on the surface [8,9,10,11].

The strength of the GCB is directly related to the effect of engineering application. Scholars have extensively researched this topic for the purpose of solving problems such as the strength design of the GCB, the ratio and optimization of grouting materials, and the reduction of costs. Since different working conditions pose varying requirements for the strength of the GCB, the design of the strength of the GCB should incorporate the actual working conditions. Cai [12] proposed an empirical formula for designing half-cubic parabolic strength based on the statistical analysis on strength design values and filling heights from 31 mines all over the world. Wu et al. [13] analyzed the target strengths of the filling body in three stress states (supporting surrounding rock, laterally exposed while self-supporting, and supporting equipment), compared the vertical stress reduction ratios of the filling body before and after the introduction of the arch effect, and proposed that the transformation of the vertical stress brought by the arch effect should be taken into account in the design of the target strength of a narrow and long GCB. After determining the target strength of the GCB, another critical point is to achieve the required strength in engineering. Some scholars have successfully improved the mechanical properties of the GCB by changing the cementing materials and ratios [10,14,15,16]. Other scholars have effectively enhanced the strength of the GCB by adding fiber materials into the slurry [17,18,19]. Meanwhile, the costs should be considered on the premise of satisfying the requirement for the strength of the GCB. To reduce the cementation costs of the GCB, some scholars explored the application of solid waste, loess, and other low-cost materials to goaf filling [20,21,22,23], which realized the double goals of ensuring engineering safety and reducing engineering costs.

In summary, the method of grout filling in a goaf to form a GCB has been widely applied to the design of ore mining directly below the goaf and the protection of surface structures above the goaf, and abundant research has been carried out on problems regarding the strength of the GCB. However, studies on mining the part of the inclined ore body below the goaf are rarely reported. On the basis the previous research results, this study investigated the safe mining technology of the part of the inclined ore body below the goaf.

2. Engineering Overview

Miaoling Gold Mine is located in Songxian County, Henan Province, China. The mining area is a simple fold structure, and the strata are gently dipping northeast–southwest monoclinic tectonics. The ore body occurs in the nearly north–south fault zone, with a thickness of 0.40–13.29 m (3.43–8.02 m on average) and a dip angle of 29°–75°. The ore body is layered and mainly composed of cataclastic rock, cataclastic rhyolite, and tectonic breccia. The roof and floor surrounding rocks of the ore body are primarily rhyolites, including rhyolite, fractured rhyolite, rhyolitic tuff lava, etc. These rocks are thickly layered, blocky, widely distributed, and hard, characterized by relatively developed fractures and a quality index of generally greater than 75%.

The mining method is underground mining, and the development method is sided drift-chute. The existing mining methods include short-hole shrinkage, comprehensive shrinkage, and upward horizontal layered dry filling. In addition, some ore bodies were mined by the open-stope method in the early stage of mining. As shown in Figure 1, the overall research area is located at the PD459 level, between the two roadways CM409 and CM609. The upper ore body has been mined out by the open-stope method, resulting in the formation of a large goaf in the original ore body position.

3. Determination of the Optimal Ratio of Cemented Crushed-Stone Slurry

In this study, the method of grout filling in the broken rock body to form a GCB in the goaf is used for protecting the stope below. Therefore, it is necessary to have a comprehensive understanding of the current situation of the goaf. The field investigation results indicate that the rock inside the goaf has collapsed, and the roadway near the goaf is seriously deformed and damaged as a result of mining disturbance (Figure 2).

It can be seen from the field investigation results that the roof of the goaf has collapsed, and the interior of the goaf is full of crushed stone, which meets the basic conditions for the formation of a GCB by the grout filling method. Then, crushed stone in the goaf was sampled to study its characteristics and different factors affecting the GCB and determine the ratio of the slurry. Considering factors such as surrounding rock conditions, staff safety, and transportation difficulties, on the premise of ensuring the validity of sampling, the sampling location was finally determined to be the part of the goaf in the middle of the CM409–CM609 exploration line, specifically, the drawing funnel positioned by the original open-stope method (Figure 1).

3.1. Physical and Mechanical Properties of Crushed Stone Inside the Goaf

The crushed stone in the goaf was tuff, according to the analysis on the color, cement, structure, and other aspects of crushed stone sampled from different positions. Large rock blocks collected from the goaf were crushed into irregularly shaped specimens with a size of about 50 mm. Subsequently, no less than three specimens were taken randomly to have their density measured by the wax sealing method. The measurement results suggest that the average natural density of the crushed stone is 2.57 g/cm³.

According to the requirements of the uniaxial compressive strength (UCS) test and Brazilian splitting test specimens in the Standard for Tests Method of Engineering Rock Mass [24], large crushed rock blocks obtained from the goaf were processed into specimens, grouped, and numbered. Finally, their mechanical parameters were obtained by mechanical tests in accordance with the test requirements (Figure 3). The RMT-150B rock mechanical test system was used for the UCS test, while the YES-300 pressure testing machine (Tianshui Hong Shan Testing Machine Co., Ltd., China) was used for the Brazilian splitting test. The UCS test was performed on cylindrical specimens (height 100 mm, diameter 50 mm) at a loading speed of 0.5–1.0 MPa/s until the specimen failed, during which the longitudinal and transverse displacements under various stress levels, as well as the maximum failure load, were recorded. The Brazilian splitting test was performed on cylindrical specimens (height 30 mm, diameter 50 mm) at a loading speed of 0.3–0.5 MPa/s until specimen failure, during which the maximum failure load was recorded. The failure modes of the specimens are illustrated in Figure 3.

Mechanical parameters such as UCS, elastic modulus, and tensile strength of crushed stone from the goaf were obtained through mechanical tests, and the results are listed in

Table 1. Mechanical parameters of the crushed stone from the goaf.

Mechanical Parameter	Test Result	Average Value
UCS/MPa	80.065–124.324	101.97
Elastic modulus/GPa	22.384–34.632	29.725
Tensile strength/MPa	3.29–10.50	7.13
Poisson’s ratio	0.07–0.11	0.09

.

The average density of specimens in the UCS test is 2.59 g/cm³, and that in the Brazilian split test is 2.58 g/cm³, both resembling the results measured by the wax sealing method (2.57 g/cm³). The test results in Table 1 show that the mechanical parameters (UCS, tensile strength, elastic modulus, and Poisson’s ratio) of specimens are relatively dispersed. Still, their average values are similar to most of the values in the data. The dispersion of mechanical parameters arises from the obvious presence of cement in the crushed stone. That is, the different contents of cement in specimens promote the variability of specimens so that the group of specimens exhibits different performances.

3.2. Cementation Factors of Crushed Stone Inside the Goaf

To grasp the influences of water–cement ratio, crushed-stone particle size, and cement–sand ratio on the strength of the GCB, orthogonal experiments were performed. On the basis of the experimental results, sensitivity analysis was conducted on factors affecting the GCB specimens in the goaf, so as to obtain the final optimal ratio of the grouting materials.

1.

Orthogonal experimental design

Considering the actual situation of mining enterprises, it was decided to choose ordinary silicate cement (cement type PO42.5) and tailing sand produced by the mine as the grouting materials. With reference to the previous experience of metal mine filling [25,26], it was determined that the strength of the GCB in this experiment should range from 3 MPa to 6 MPa. Based on Equation (1) [27], the water–cement ratio is 3.5:1 when the strength of the GCB is 3 MPa and 2.5:1 when the strength is 6 MPa. Hence, the four levels of water–cement ratio in this experiment were finally set to be 2.5:1, 2.7:1, 2.9:1, and 3.1:1.

$$W/B={\displaystyle \frac{{\alpha }_a{f}_b}{f_{cu*0}+{\alpha }_a{\alpha }_b{f}_b}}$$

(1)

where W/B is the water–cement ratio of concrete; α_a and α_b are the regression coefficients; f_b is the 28 d UCS of cementing material for cemented sand, MPa; and f_cu*0 is the designed strength, MPa.

To study how the crushed-stone particle size influences the strength of the GCB, 100 × 100 × 100 mm³ cubes were selected as the specimen size. According to the Standard for Test Methods of Physical and Mechanical Properties of Concrete [28], when the cross-sectional size of the specimen is 100 × 100 mm², the maximum particle size of aggregate is 31.5 mm. Accordingly, it was determined that the particle size of aggregate in this test lies in three ranges, i.e., <10 mm, 10–20 mm, and 20–30 mm. Based on field investigation, it was found that no obvious interval exists in the crushed-stone particle size in the goaf, indicating that the distribution of crushed-stone particle size shows continuous grading. Under the condition of continuous grading, the crushed-stone particle size has an essential influence on the mechanical properties of the GCB. To reduce the adverse impact of difference in crushed-stone particle size between the engineering field and the laboratory test on the test results, photographs of crushed stone were taken at the sampling positions first. Next, the crushed-stone regions in the photographs were binarized with the aid of MATLAB (R2014b) (Figure 4) and subjected to fractal dimension identification. Eventually, according to the identification results, the mass ratios of crushed stone at the three particle size levels under different fractal dimensions were obtained in the light of Talbol’s theory [29]. With the above method, the following results were yielded: the fractal dimensions of crushed stone at the sampling positions lie between 0.62 and 0.65, mainly concentrated at 0.64, and those of crushed stone in this experiment are classified into four levels, i.e., 0.62, 0.63, 0.64, and 0.65.

The smaller the cement–sand ratio of the grouting material, the higher the proportion of sand in the slurry, which is conducive to the strength and durability of the structure. In actual construction, selecting an appropriate cement–sand ratio plays a vital role in ensuring the quality of the project. With reference to the discussion and summary of the literature [30] regarding the existing grouting materials of metal mines in China, four levels of the cement–sand ratios in this experiment were determined, i.e., 1:4, 1:6, 1:8, and 1:10.

Based on the above analysis on the factors affecting the strength of the GCB, orthogonal experiments were designed following the orthogonal experimental table in

Table 2. Table of orthogonal experiments on factors affecting the strength of the GCB.

No.	Water–Cement Ratio	Aggregate Grading	Cement–Sand Ratio	No.	Water–Cement Ratio	Aggregate Grading	Cement–Sand Ratio
1	2.5:1	1.84	1:4	9	2.9:1	1.84	1:8
2	2.5:1	1.88	1:6	10	2.9:1	1.88	1:10
3	2.5:1	1.92	1:8	11	2.9:1	1.92	1:4
4	2.5:1	1.96	1:10	12	2.9:1	1.96	1:6
5	2.7:1	1.84	1:6	13	3.1:1	1.84	1:10
6	2.7:1	1.88	1:4	14	3.1:1	1.88	1:8
7	2.7:1	1.92	1:10	15	3.1:1	1.92	1:6
8	2.7:1	1.96	1:8	16	3.1:1	1.96	1:4

.

2.

Experimental Procedure

Given that good quality of GCB specimens is a prerequisite to ensure the accuracy of the tested GCB strength, the GCB specimens were prepared in strict accordance with the operating procedure (Figure 5) [28]. First, according to the design ratio of the GCB, the required materials and test tools were prepared simultaneously. Next, water, stone, sand, and cement were taken according to the ratio and mixed evenly and fully. Afterwards, the inner wall of the mold was brushed with lubricating oil, and the mixture was placed into the mold which was then vibrated on a vibrating table. When the GCB was about to solidify, it was smoothed with a spatula. Immediately after the formation of the specimen, its surface was covered with impermeable film, and the mold was removed after the initial solidification of the specimen. Finally, the specimens were numbered and cured for 28 days by the natural curing method. It is noteworthy that they were not allowed to be moved during the curing period.

Upon the completion of curing, the specimens were tested and measured to calculate their pressure-bearing area. Specifically, a specimen was placed at the center of the test pad (Figure 6) where the load on it was continuously and uniformly raised at a rate of 0.5–1.0 MPa/s until it failed [24].

The fluidity of the slurry is a prerequisite for the pumpability of the grouting cementing material, and it also ensures better diffusion of the slurry in crushed stone in the goaf. The fluidity of the slurry was tested by the following method. First, the prepared cementing material was mixed evenly with water at the fixed water–cement ratio, and then the slurry was poured into the conical cut-off mold. With the liquid surface kept flush with the upper part, the cut-off mold was lift vertically, so that the slurry could flow freely on the glass plate. Thirty seconds later, the maximum diameter of the slurry flow was measured with the scale and regarded as its fluidity. The test procedure is presented in Figure 7.

3.

Test Results and Analysis

The results of the multifactorial orthogonal experiment on the strength of the GCB were analyzed by the intuitive analysis method. The range value indicates the degree of influence of the change in the level of a factor on the test results. The larger the range value, the more significant the impact of the change in the level of this factor on the test results, and the factor with the greatest range value is the most dominant factor. On the contrary, the factor with a smaller range value does not have a noticeable influence on the index when it changes within the chosen range [31].

①

Analysis on factors affecting UCS

The UCS test of the GCB was carried out for three specimens in each group, and the average value of the three specimens was taken as the UCS of the GCB in that group. The results of the UCS of the GCB at different ratios are given in

Table 3. UCS results of GCB specimens.

No.	UCS/MPa	No.	UCS/MPa	No.	UCS/MPa	No.	UCS/MPa
1	6.32	5	5.43	9	6.18	13	3.61
2	4.82	6	5.34	10	3.33	14	4.02
3	6.21	7	2.83	11	2.72	15	5.40
4	3.30	8	4.58	12	2.69	16	4.39

.

The average value of the test results for each factor and level was taken. Subsequently, the sensitivity analysis curves of factors influencing the UCS of the GCB were plotted with the UCS as the vertical coordinate and the levels of different influence factors as the horizontal coordinate (Figure 8).

As displayed in Figure 8, within the range of experimental design indexes, the cement–sand ratio exerts the strongest influence on the UCS of the GCB specimens, followed by aggregate grading, and water–cement ratio has the weakest influence. At the same time, the optimal ratio of the slurry to achieve a high UCS is found to be a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:8, and the second optimal ratio is a 2.5:1 water–cement ratio and 1:4 cement–sand ratio. In addition, it can be found from the range values of factors in Figure 8 that the aggregate grading notably influences the UCS of the GCB. Thus, attention should be paid to the distribution of crushed stone at the grouting location during on-site grouting, and reinforced grouting is required when possible.

②

Analysis on factors affecting slurry fluidity

Each group of fluidity experiments was repeated four times to take their average values as the fluidity of the slurry at each ratio (

Table 4. Experimental results of slurry fluidity.

No.	Slurry Fluidity/cm	No.	Slurry Fluidity/cm	No.	Slurry Fluidity/cm	No.	Slurry Fluidity/cm
1	17.0	5	18.1	9	10.0	13	6.6
2	16.0	6	27.1	10	6.4	14	13.5
3	10.4	7	5.7	11	27.6	15	21.2
4	6.8	8	7.9	12	17.4	16	29.1

).

To conduct sensitivity analysis on the two factors (cement–sand ratio and water–cement ratio) affecting slurry fluidity, the average values of the slurry fluidity test results at the four levels of the two factors were taken first, and then the sensitivity analysis curves of the two factors were plotted by taking the four levels of the two factors as the horizontal coordinate and the fluidity as the vertical coordinate (Figure 9).

As can be seen from Figure 9, cement–sand ratio is the primary factor that affects slurry fluidity, and water–cement ratio is the secondary factor. Additionally, the optimal ratio of the slurry to achieve a high slurry fluidity is a water–cement ratio of 3.1:1 and a cement–sand ratio of 1:4.

The range values of water–cement ratio and cement–sand ratio differ slightly (0.966) in Figure 8, whereas they differ hugely (13.775) in Figure 9. Such results imply that in the design of the UCS of the GCB, both cement–sand ratio and water–cement ratio need to be taken into account, while in the adjustment of the slurry fluidity, cement–sand ratio is the primary factor to be considered. Grounded in the above discussion, the optimal ratio of the slurry is analyzed by combining schemes of factors affecting the strength of the GCB (the optimal scheme is a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:8; the second most optimal scheme is a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:4) and the scheme of factors affecting the slurry fluidity (the optimal scheme is a water–cement ratio of 3.1:1 and a cement–sand ratio of 1:4). As can be observed from Figure 8 and Figure 9, in the two situations where the water–cement ratio is 2.5:1 and the cement–sand ratio is 1:8 and 1:4, respectively, the UCS of the GCB is similar, but the slurry fluidity differs remarkably. Thereby, on the premise of ensuring a fine strength, the scheme with a better slurry fluidity is selected. Ultimately, the optimal ratio of the slurry was determined to be a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:4.

4. Optimal Ratio of Cementing Slurry for Crushed Stone

To obtain the cementing width of crushed stone in the goaf, the stress state of the GCB in the goaf is theoretically analyzed. By doing so, the actual engineering situation can be simplified into a physical model, which facilitates theoretical solutions.

4.1. Mechanical Analysis on GCB in the Goaf

To achieve the dual purpose of safely mining the ore body around the goaf and preventing the crushed stone from mixing with the extracted ore, the slurry is injected into the goaf by boreholes so that the crushed stone in the goaf adjacent to the ore body is cemented into a whole and is endowed with a certain degree of support, thus increasing the stability of the surrounding rock. Based on the geological profile of the study area, a schematic diagram of grout filling of crushed stone in the goaf was drawn (Figure 10).

The ore body below the GCB in the goaf is mined using the horizontal layered dry filling method (chamber size 3.3 m × 3.3 m). The mining process can be roughly divided into four steps, namely one-step mining, one-step filling, two-step mining, and two-step filling (Figure 11).

By analyzing the position of the GCB in the goaf (between the ore body and the crushed stone in the goaf), as well as the mining method and mining room layout for the part of the ore body to be mined, the GCB to be formed can be regarded as an ore pillar on the goaf side during the mining of the ore body near the goaf. That is, the determination of the grout filling range can be transformed into the calculation of the minimum width of the ore pillar on the premise of ensuring safe mining of the ore body. As stated in previous research [32], the stress distribution in the rock mass near the goaf follows the pattern of a loose zone (goaf crushed stone), a plastic zone, and an elastic zone with the increase in distance from the goaf (Figure 12).

To ensure the safety of the mining process, the mining rooms should be located within the elastic zone, which means that the extent of the GCB should be not less than the width of the plastic zone. The literature [32] gives the following equation for calculating the width of the plastic zone:

$$x_0={\displaystyle \frac{M}{2\xi f}}\ln {\displaystyle \frac{K\gamma H+C\cot \phi }{\xi (p_1+C\cot \phi )}}$$

(2)

where M is the height of the ore body, m; H is the mining depth, m; K is the stress concentration factor, generally 1.5–3; γ is the average bulk density of the overburden, kN/m³; C is the cohesion of the GCB, MPa; φ is the internal friction angle within the GCB, °; f is the friction coefficient, tan φ; P is the resistance of the supporting equipment to the GCB, MPa; and ξ is the triaxial stress coefficient.

4.2. Determining the Width of the GCB in the Goaf

As can be known from Equation (2), the physical mechanical parameters of the GCB need to be determined in the hope of obtaining the width of the GCB. Based on the optimal ratio of the slurry (a water–cement ratio of 2.5:1 and a cement––sand ratio of 1:4), the GCB formed at the optimal ratio was subjected to a triaxial compressive strength test and a Brazilian splitting test.

Following the requirements for specimen size in triaxial compressive strength and Brazilian splitting tests [24], a cylindrical mold with a diameter of 50 mm and a height of 100 mm was used for preparing specimens in the triaxial compressive strength test, and a cylindrical mold with a diameter of 50 mm and a height of 50 mm was used for the Brazilian splitting test. According to the existing research and test standards [28], the particle size ranges of aggregate in this cementation test were determined to be <5 mm, 5–10 mm, and 10–15 mm.

As shown in Figure 8c, the strength of the GCB is the lowest when the aggregate grading is 0.65, so this aggregate grading was employed for the sake of engineering safety. Under the optimal ratio of the slurry (a water–cement ratio of 2.5:1 and a cement–sand ratio of 1:4) and the aggregate grading for the most unfavorable crushed-stone particle size distribution (0.65), GCB specimens were prepared, the process and requirements for specimen preparation being the same as those in Section 3.1. Figure 13 provides photographs of cylindrical GCB specimens that have been cemented.

Upon the completion of specimen curing, the specimens were removed from the curing site, inspected, and measured. The specimens that met the test requirements were subjected to the triaxial compressive strength test on the RMT-150B rock mechanical testing system and the Brazilian splitting test on the YES-300 pressure testing machine, and the experimental process is given in Figure 14.

Finally, the mechanical parameters of the GCB at the optimal ratio were obtained from the cementing test based on triaxial compressive strength and Brazilian splitting tests (

Table 5. Mechanical parameters of the GCB at the optimal ratio.

UCS/MPa	Elastic Modulus/GPa	Poisson’s Ratio	Cohesion/MPa	Internal Frictional Angle/°	Tensile Strength/MPa
1.09	0.081	0.25	0.21	36	0.198

).

Based on the mechanical parameters of the test grouting specimen obtained above and the stress situation of the grouting material in the goaf, the stability of the grouting material in the goaf above the stope of Miaoling Gold Mine was analyzed, and the minimum thickness at which it remained stable was calculated. The occurrence and grouting conditions of the ore body in the stope are as follows: The average thickness of the ore body within the research area is 17 m; the burial depth is 215 m; and the average bulk density of the overburden is 25 kN/m³. The cohesion and internal friction angle of the GCB are 0.21 MPa and 36°, respectively, and no support equipment generates resistance to the GCB. To ensure the safety of the project, the stress concentration coefficient was set to 3. According to the above parameters, the calculation unveils that the grouting range of the goaf along the inclined direction of the ore body should not be less than 29 m wide.

5. Stability Analysis on the Stope Below the Goaf

Based on the theoretically calculated value of the width of the GCB in the goaf, the stability of the stope below the goaf was evaluated by means of numerical simulation.

5.1. Numerical Modeling

Numerical simulation has become an indispensable research tool in the field of geotechnical engineering, successfully solving important scientific and technological problems. In this study, the stress, displacement, and failure of surrounding rock during the mining of the ore body were explored with the aid of FLAC3D 6.0. FLAC3D 6.0, an analysis program based on the three-dimensional explicit finite difference method, has become one of the most important pieces of numerical simulation software in geotechnical analysis.

The ore body model was built by stretching the ore body cross-sectional shape (Figure 1) along the strike for 60 m. Given that the ore occurrence changes insignificantly along the strike, the elevation changes in the ore body, the roof, and the floor in the stretching direction were not considered. Meanwhile, to reduce the influence of the mining-induced boundary effect, 20 m was added on both sides beyond the range of mining activities, and the finalized numerical model size was 179 m × 60 m × 80 m (Figure 15). The Mohr–Coulomb model was chosen as the constitutive model of the ore-rock body for this numerical simulation. The instability criterion used in the Mohr–Coulomb model includes the tensile intercept. As shown in Figure 16, the segment from Point A to Point B is defined based on the Mohr–Coulomb instability strength f ^s = 0, and that from Point B to Point C is defined based on the tensile instability criterion f ^t = 0 from. In addition, by introducing the function h(σ₁, σ₃) = 0, the Mohr–Coulomb model is defined as the diagonal line between f ^s = 0 and f ^t = 0 on the (σ₁, σ₃) plane. If the stress point is located within Domain 1, the point is in a shear yield state, and if the stress point falls within Domain 2, the point is in a tensile yield state. Based on the experimental results and existing studies [33,34], the mechanical parameters of the ore-rock body and the GCB in this simulation were determined (

Table 6. Mechanical parameters of rock strata and the GCB.

Name	Density/kg/m3	Elastic Modulus/GPa	Tensile Strength/MPa	Cohesion/MPa	Internal Friction Angle/°	Poisson’s Ratio
Ore body	2650	27.8	4.2	5.0	46	0.19
Surrounding rock	2680	21.0	3.5	5.3	53	0.22
GCB	2129	0.081	0.198	0.21	36	0.25
Filling body	2046	0.943	0.9	0.7	37	0.32

).

$$f^s={\sigma }_1-{\sigma }_3{\displaystyle \frac{1+\sin (\phi )}{1-\sin (\phi )}}+2c\sqrt{{\displaystyle \frac{1+\sin (\phi )}{1-\sin (\phi )}}}$$

$$f^t={\sigma }_3-{\sigma }^{\mathrm{t}}$$

$$h={\sigma }_3-\sigma \prime +{\alpha }^{\mathrm{P}}({\sigma }_1-{\sigma }^{\mathrm{P}})$$

where φ is the internal friction angle; C is the cohesion; σ^t is the tensile strength; α^p and σ^p are constants.

The boundary conditions of the numerical model are as follows: (I) horizontal displacement constraints in the Y-direction are set on the front and rear sides of the model boundary; (II) horizontal displacement constraints in the X-direction are set on the left and right sides of the model; (III) complete displacement constraints the X-, Y-, and Z-directions are set at the bottom of the model; and (IV) in view of the actual mining geologic conditions, a vertical stress with a magnitude of 3.4 MPa is applied at the top of the model.

To accurately reflect the actual engineering situation, the numerical simulation was conducted in close combination with the specific engineering background. Firstly, the ore body extracted above the 459 m level was assigned to the null model to simulate the goaf formed by open-stope mining. Subsequently, according to the theoretically calculated width of the GCB (29 m), the part of the goaf above the 459 m level was filled with slurry. The filling-induced stress distribution variation of the surrounding rock in the vertical direction is demonstrated in Figure 17.

As depicted in Figure 17, the stress becomes obviously concentrated in the surrounding rock of the goaf after the mining of the ore body above the 459 m level. The maximum stress in the surrounding rock in the vertical direction reaches approximately 20 MPa, which is about 4 times the original stress there (approximately 5 MPa). However, stress concentration in the surrounding rock is noticeably weakened after the stope is filled with the GCB. The maximum stress in the surrounding rock in the vertical direction is reduced to about 13.5 MPa, approximately 2.5 times the original stress there. This phenomenon demonstrates the important protective effect of the GCB on the stope below.

5.2. Numerical Simulation Results and Analysis

Miaoling Gold Mine adopts the upward horizontal slicing step-and-fill mining method to recover the ore body below the goaf. The ore body below the goaf is divided into four layers for mining, i.e., the first, second, third, and fourth layers from the bottom to the top, which are mined in two steps, respectively (Figure 16). In the numerical simulation, the plastic zone reflects the failure state of the rock mass, so the plastic zone distribution of the surrounding rock of the mine rooms is taken as the evaluation index of the stope stability here. During the excavation process of the mining rooms, only the current failure state of the surrounding rock is related to the stability of the mining rooms. In view of this fact, the failure of the plastic zone in the numerical simulation only considers the current failure state of the surrounding rock.

(1)

The first layer

Figure 18 displays the plastic zone distribution of the surrounding rock of the mining rooms during the mining of the ore body in the first layer. Clearly, the surrounding rock of the mining rooms in the first and second steps has not been damaged yet, indicating that the mining rooms remain in a stable state.

(2)

The second layer

Figure 19 gives the plastic zone distribution of the surrounding rock of the mining rooms during the mining of the ore body in the second layer. After the first mining step, a plastic zone emerges in the surrounding rock, but it does not affect the stability of the mining rooms because it remains far from the mining rooms. After the second mining step, a small-scale shear failure occurs on the roof of a mining room near the goaf.

(3)

The third layer

Figure 20 exhibits the plastic zone distribution of the surrounding rock of the mining rooms during the mining of the ore body in the third layer. After the first mining step, tensile failure and shear failure occur in the surrounding rock of two mining rooms near the goaf, respectively. After the second mining step, tensile failure occurs in the roof of a mining room near the goaf.

(4)

The fourth layer

Figure 21 exhibits the plastic zone distribution of the surrounding rock of the mining rooms during the mining of the ore body in the fourth layer. After the first mining step, the roof and side of a mining room near the goaf suffer shear failure. After the second mining step, the shoulder of the mining room also undergoes shear failure.

6. Discussion and Conclusions

The analysis on plastic zone distribution around the mining rooms during the mining of the ore body in the four layers reveals that the closer the mining room is to the stress concentration position, the more easily the surrounding rock is damaged. A total of 30 mining rooms are arranged in the four layers, and 6 mining rooms are partially damaged on a small scale during the mining process.

In summary, the GCB formed by grout filling in the goaf manages to support the stope below. However, affected by original mining disturbance, the surrounding rock of a few mining rooms close to the GCB is damaged. Therefore, it is suggested to strengthen the monitoring of rock pressure and displacement of the surrounding rock and take corresponding protective measures during mining activities in the mining rooms near the GCB.

In this study, the cementation performance of crushed stone in the goaf under open-stope mining of the inclined ore body and the stability of the stope below the goaf were investigated by means of laboratory experiments, theoretical analysis, and numerical simulation. The conclusions can be summarized as follows:

(1)

Through orthogonal experiments in the laboratory, the influences of different factors such as water–cement ratio, crushed-stone particle size, and cement–sand ratio on the strength of the GCB were analyzed. Meanwhile, the optimal ratio of the slurry formed by water, ordinary Portland cement PO42.5 cement, and tailings was determined to be 2.5:1:4 by taking the fluidity of the slurry as another index.

(2)

At the optimal ratio, cementing tests and mechanical tests were conducted on the crushed stone with the most unfavorable particle size distribution to obtain the mechanical parameters of the GCB under the optimal ratio conditions. Moreover, the determination of the grouting range was converted into the solution of the width of the plastic zone of the surrounding rock in the goaf by analyzing the force and action on the GCB in the goaf. Ultimately, the cementing width of the GCB was found to be not less than 29 m.

(3)

The stability of the mining room formed during the mining of the part of the inclined ore body below the goaf was explored through numerical simulation. The results suggest that among 30 mining rooms formed in the mining process, 24 mining rooms are in a stable state, and 6 mining rooms are partially damaged on a small scale. As a whole, the GCB formed by grout filling in the goaf manages to support the stope below, and it is verified that the theoretical calculation method of the width of the GCB is feasible.