Relationship between Movement Laws of the Overlaying Strata and Time Space of the Mined-Out Volume

The study and accurate prediction of the movement of overburden rock mass and surface subsidence are crucial for a safe production in metal mines. This study investigates the relationship between the movement laws of overlaying strata and the time space of a mined-out volume using Rock Failure Process Analysis (RFPA) System. Furthermore, the movement, deformation, and failure laws of overlaying strata are examined in different positions when a goaf volume is certain and the failure behavior of the overlaying strata. This study analyzes the similarities and differences of the overlaying strata comparatively. Results show that, regardless of the movement range or subsidence value of the overlying rock mass, a power function relationship is observed between them and working face advancement. Setting the equation shows that the scope of the overlying rock mass is significant when the ratio of a certain position distance roof to the working face distance is small. The results provide a reference for controlling the displacement of the overlying rock mass and treating goaf.


Introduction
The 3D stress balance of surrounding rock is destroyed by underground mining and tunnel excavation [1,2], which can easily cause overburden movement, surface subsidence, and even collapse [3]. The collapse of a work-out area can seriously threaten a safe production and adversely affect the surface buildings and environment [4]. Currently, overlaying strata movement theory mainly includes "three zones," key strata, plate, and masonry beam theories [5,6]. The main methods include probability integral, numerical simulation, similar model, stochastic medium, and neural network prediction [7][8][9]. Many studies on the coal seam movement with a satisfied application are available [10,11]. The mining subsidence mechanism of a metal mine with fractured blocky rock mass is different from a coal mine with a layered rock mass. The rock mass in a metal mine has a typical inhomogeneous and discontinuous self-stressed block-hierarchical structure because the morphology of ore body, geological structure, and mining methods in metal mines differ from those in coal mines [12,13]. The subsidence of overlaying strata in a metal mine is abrupt, and its subsidence, such as collapse pit and tubular or funnel collapse, is discontinuous. However, coal mine subsidence changes quite slowly [14,15]. Thus, applying the movement theories of coal strata to metal mines is unsuitable. Consequently, investigating the overburden movement mechanism of metal mines is crucial.
At present, domestic and international scholars have created numerous theories and experience studies on overlaying strata movement from different angles and have gained certain achievements [16][17][18][19][20]. However, research on the time space of a mined-cavity volume based on the movement laws of overlaying strata is limited. On the basis of certain references [21], the stability of overlaying strata in metal mining has been analyzed systemically through a numerical simulation using rock mass failure process analysis software Rock Failure Process Analysis (RFPA) System [22,23]. From the angle of quantitative analysis, the characteristics of the metal mine strata movement are investigated, and the formula between the overlying rock mass movement and the working face propulsion in different positions of goaves is obtained. This formula offers a new method for calculating the overlying rock mass movement.

Model Building and Parameter Setting
Based on a practical engineering [21], a gold metal mining has a background of a 500 m ore body depth, a dip near the horizontal, an ore body thickness near 5 m, and a 90 m ore body length. The region is mainly composed of silty clay and detritus. The overlaying strata contain few crush zones. The occurrence is steady, and the structure is simple, that is, its roof comprises sandy clay and shale with few mudstones, and the bottom consists of sandy clay and shale. This study investigates the failure process of an overlying rock mass by using a plane strain model. The calculation model is located 150 m along the horizontal direction, 150 m in the vertical direction, has a 5 m ore body thickness, an ore body that is 35 m from the lower boundary, and 30 m far from the left and right boundaries. The model is illustrated in Figures 1 and 2. The gravity stress function in the vertical direction and the model size are considered. Therefore, a 7 MPa stress must be applied to the vertical direction. According to the measured geostress data, a 2 MPa stress is applied to the horizontal direction combined with the geological features and tectonic stress in the mine. The model parameters are randomly assigned, in which an elasticity modulus is averaged, and other physical parameters are set in accordance with the mechanical properties of rocks to simulate the complexity of the geological occurrence conditions of metal mines accurately. The parameter is illustrated in Tables 1 and 2. Research on a dynamic damage rule of overlying rock mass under the condition of the ore mining process is conducted by using a step-by-step excavation model, and each step is 10 m.

Result Analysis of Overlaying Strata Failure
A goaf roof generates microcracks and sporadic caving before the working face advances to 50 m. Evident microfissure, propagation, and partially sporadic collapses are observed on the roof when the working face advances to 50 m, which has a 5 m length and arch shape. The result is shown in Figures 3 and 4. The rupture continues to expand and cause periodic caving with the increase in the mined-out volume. After the end of mining, the overlying rock mass no longer collapses, and only sporadic caving appears above the roof. The appearance of cracks in the interior of the overburden rock does not continue its connection, thereby indicating the inexistence of a large collapse area inside the overburden rock, but the plastic zone continues to expand.
This section investigates the strata displacement and deformation in different positions through a quantitative analysis. We monitored different positions in the overlaying strata (i.e., 5, 10, 20, 30, 50, and 80 m away from the roof) to investigate the displacement and deformation in the process of mining damage in different positions of the overlying rock mass. Given the proportion relationship between the ore body trend, mining length, and average mining depth, this study investigates the laws of overburden movement and failure of metal mines under the condition of nonfull mining. Figure 5(a) illustrates the relationship among displacement changes with a 5 m distance from the roof in the overlaying strata and working face advancement. The results showed that the range of the work-out area increases with the working face length. The subsidence range of rock mass, which has a 5 m distance from the roof, is gradually increased. The subsidence process of the overlying rock mass gradually changes before the working face advances to 40 m. The overlying rock mass displacement is small. Thus, a slight mutation has occurred, thus indicating that a small amount of rupture occurs in the rock material, and the change in the overlying rock displacement is limited given the change in the volume of the rock material molecule itself. Figure 5(a) also demonstrates that the maximum subsidence value is 2.17 mm, and the sinking range is 20 mm when the working face advances to 10 m. The maximum subsidence value is 12.03 mm, and the sinking range is approximately 20 mm when the working face advances to 30 m. All of these observations indicate that no major failure and coalescence    2 Geofluids occur in the overlying rock mass. When the working face advances to 40 and 50 m, the subsidence curve shows a mutation trend, especially when the working face advances to 50 m. A "sharp point" in the curve is observed, and the maximum subsidence reaches 34.32 mm. The result shows that the overburden rock material itself has numerous molecular damages. Furthermore, crack coalescence and interaction may induce mutation. The subsidence curve has been interrupted in the working face between 60 and 90 m, thereby indicating that the collapse occurs 5 m away from the roof. The subsidence range increases with the advancement in the working face. Overall, the large subsidence and abrupt change in the overburden are caused by fissures and coalescence inside the overlying rock mass. Figure 5(b) depicts the relationship between displacement change with a 10 m distance from the roof in the overlaying strata and the working face advancement. The range value of subsidence in the 5 m overlying distance from the roof increases with the advancement in the working face. When the working face advances to 50 m, the subsidence curve is gradual, thus implying that the overlying rock has not resulted in a hole-through crack, and the failure and movement of the rock material produce a large displacement. This phenomenon denotes that no collapse occurs in the overlaying strata. The subsidence curve is interrupted when the working face advances from 60 m to 90 m, thereby signifying an occurrence of a collapse. However, the interval of interruptions is smaller than that demonstrated Figure 5(a). When the working face advances to 60 m, the caving length becomes 10 and 20 m with 10 and 5 m distance from the roof, correspondingly. When the working face advances to 90 m, the caving length becomes 11 and 22 mm with 10 and 5 mm distance from the roof, respectively. The strata subsidence is smaller at 10 m than at 5 m. Figure 5(c) exhibits that the range and value of the overlying rock mass subsidence, which are 20 m away from the roof, increase with the advancement in the working face.

Geofluids
Furthermore, the strata subsidence curve gradually changes. Thus, the internal material of the rock cover does not produce large fracture and caving before the working face advances to 80 m. The sinking curve is continuous until the working face advances to 90 m. Moreover, a polyline is produced, thereby indicating that the rock cover's internal material fracture and the longevity of a small displacement are insufficient for fracture and caving. At this time, the maximum subsidence value reaches 62.82 mm, which is the tipping point of the caving area. Figure 5(d) displays the relationship between the displacement change with a 30 m distance from the roof in the overlaying strata and the working face advancement. The range and value of subsidence in the overlaying strata with a 50 m distance from the roof gradually increase with the advancement in the working face. Although the subsidence curve, as a whole, is continuous, the curve is smoother than that with the 20 m distance from the roof. This finding shows the absence of microfissures in the overlying rock mass, but a few materials inside the damage still exist, thereby locally affecting its sinking displacement. The maximum sinking amount at this time is 58.83 mm. Figure 5(e) presents the relationship between the displacement change with a 50 m distance from the roof in the overlaying strata and the working face advancement. With the advancement in the working face, the range and value of subsidence with a 50 m distance from the roof in the overlying rock mass gradually increase. Figure 5(e) also illustrates that the subsidence curve of the overburden rock is smooth, thereby indicating no large fissure zone in the overlying rock at 50 m from the top of the roof from the beginning to the end of ore body mining. Moreover, the fracture is only found inside the material, thereby denoting that the area belongs to the plastic zone. The acoustic emission and overburden rock burst figure in this region do not exhibit a large rupture, and an acoustic emission gathers nucleation. In the end, the ore body mining subsidence is 53.46 mm. Figure 5(f) demonstrates that the subsidence curve is linear 80 m away from the roof before the working face advances to 80 m, thereby implying that this area is elastic. A minimal acoustic emission signal indicates the occurrence of a slight rupture inside the rock material. The subsidence curve has a downward bending trend, thus indicating that several material molecules have been destroyed at this time. The overlaying strata can produce a small displacement and a maximum subsidence value of 48.71 mm, which denotes a plastic region.
The aforementioned diagrams depict the following laws of overburden failure and displacement through vertical and horizontal comparison. Therefore, we can analyze and draw the following conclusions in a certain position in the overlaying strata: the subsidence value and movement range of an overlying rock mass gradually increase with the advancement in the working face. The maximum subsidence vertex curve gradually moves toward the direction of the working face advancement.
Furthermore, we can analyze and draw the following conclusions when the working face advancement is certain: the subsidence value and movement range of an overlying rock mass decrease with the increase in the distance to the roof. The slope changes in the subsidence curve vertices reflect the rate of subsidence value change at a definite localization. The subsidence value and rate of change are large when the slope variation is also considerable. The   Table 3.

Function Building and Discussion
Thus, the final curve equation can be represented as y = 10:55x 1:82 .
A small ratio of the position distance from the roof to the overlaying strata and the working face advancement indicates a large subsidence by analyzing the curves and equations in Figure 7. When the ratio tends to 0, the subsidence tends to infinity. This result is consistent with the actual monitoring data. A collapse does not produce data, and the final subsidence amount cannot be monitored. A large ratio of the distance from a certain position to the gob roof and the working face advancement implies a considerable distance from the roof or a small mined-out volume and a small subsidence in the overlaying strata. The overburden strata do not move when the position arrives at infinity or is not a goaf. Figures 8 and 9 display the relationship between the overlaying strata movement range and the working face advancement. This relationship is similar to the laws of strata subsidence. A power function relationship between these factors is observed through data analysis. The equation can be expressed as y = ax b . The parameters are shown in Table 4.
The results show that, when the ratio of the position distance roof to the working face is small, the scope of the strata movement is extensive. In particular, the overlying rock mass that is close to the roof or the relatively large gob volume can considerably influence the strata movement. The scope of the strata movement is small when the ratio of the distance to the roof and the working face is large. When infinity or no goaf is reached, the overlying rock does not move.

Conclusion
In a certain position in the overburden, the subsidence value and movement range of overburden rock gradually increase with the advancement in a working face (the volume of goaf increases gradually). The maximum subsidence vertices of a    (3) The scope of the strata movement is extensive when the ratio of the position distance to the roof and the working face advancement is small. When the ratio of the position distance to the roof and the working face is large, the strata movement demonstrates a small scope. The overburden strata do not move when infinity or no gob is reached

Data Availability
The test data used to support the findings of this study are included within the article. Readers can obtain data supporting the research results from the test data table in the paper.

Conflicts of Interest
No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publica-tion. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.    8 Geofluids