Simulation of Strata Failure and Settlement in the Mining Process Using Numerical and Physical Methods

Abstract

Coal mining can cause the rupture of the overlying strata, and the energy released by large-scale fractures can therefore induce earthquake disasters, which in turn can cause more secondary disasters. In the past 50 years, countless earthquakes induced by coal mining have been reported. In this paper, the main factors relating to the mining-induced seismicity, including the mechanical properties, geometry of the space, excavation advance, and excavation rate, are investigated using both experimental and numerical methods. The sensitivity of these factors behaves differently with regard to the stress distribution and failure mode. Space geometry and excavation advances have the highest impact on the surface settlement and the failure, while the excavation rate in practical engineering projects has the least impact on the failure mode. The numerical study coincides well with the experimental observation. The result indicates that the mechanical properties given by the geological survey report can be effectively used to assess the risk of mining-induced seismicity, and the proper adjustment of the tunnel geometry can largely reduce the surface settlement and improve the safety of mining.

1. Introduction

The demand for natural resources is growing all the time worldwide, while the unexpected failure of strata and surrounding rocks has caused a great loss of lives and properties due to the misunderstanding of the underground structure safety, the complexity of geological structures, and their mechanical properties [1,2,3]. The large-scale collapse of hard roofs during coal seam mining poses enormous risks to human safety and equipment [4,5,6]. In this process, the induced-seismicity can additionally enhance the damage of the mining failure by dynamic disturbance effects of surrounding rocks, reactivating the neighboring critical geological bodies, and cyclic loading effects, which is like a chain reaction and has been extensively reported in the last decade, gaining awareness from the public and scientific community [7,8,9,10,11,12]. The data from WOS shows a notable rise in both publication numbers and citation frequencies from 2013 to 2022, with publications increasing from around 600 to over 1300 and citations growing from approximately 1000 to nearly 30,000. Here, the mining-induced seismicity is defined as the response of the rock mass to the deformation and failure of underground structures that include itself [7]. The present study focuses more on the mining-induced seismicity.

Though geological survey, supporting system, and excavation techniques have developed a lot in the past several decades, fatal and destructive accidents in mining still frequently happen and even increase due to the enormous demands for natural energy resources [13,14,15]. Tremors and induced earthquakes are two main disasters triggered by human activities, which are related but distinct phenomena that involve the shaking of the ground due to various causes. A tremor is a continuous or intermittent weak shaking of the ground, usually lasting from seconds to minutes. Tremors are typically not felt by humans unless they are very strong or close to the surface. Induced earthquakes can be caused by various activities, such as fluid injection or extraction, mining, reservoir impoundment, geothermal exploitation, or nuclear testing. Induced earthquakes can range from micro seismic events that are only detected by sensitive instruments to large and damaging events. According to the Human-Induced Earthquake Database, the factors inducing the seismicity are listed in Figure 1. As of 27 March 2023, 1294 projects have been proposed to have induced earthquakes. Earthquakes caused by mining account for no less than 24% of these projects. The earthquake at the South Stanford coalmine in 1738 was the first recorded mining-induced seismic activity [16]. Most of these mining-induced earthquakes have a magnitude below 3, and only 7.3% of them can range from 5 to 6. However, the high frequency of occurrence can still be a threat to workers.

Mining-induced seismicity is a complex phenomenon that can be influenced by a variety of factors, including both artificial factors (depth of mine, production rate, mining geometry, and excavation method) and natural factors (discontinuities, tectonic stress field, and geological structures). It is important to note that these factors can interact in complex ways, and the specific combination of factors can vary from one mining operation to another. Therefore, predicting and managing mining-induced seismicity requires a detailed understanding of both the mining operations and the geological context in which they are taking place. To simplify the analysis, this paper concentrates on the strata condition and the factors in mining techniques.

Overburden movement caused by the mining process brings about many changes in stress conditions and the internal structure of overlying strata [17]. Significant and uneven ground subsidence can also be observed when the movement is transmitted to the land surface, which has an adverse impact on the surrounding environment, such as agricultural activities and above-ground structures. The cumulative change of the stress state of the rock mass can result in new fractures or the reactivation of pre-existing faults and hence induce seismicity [18,19,20,21]. In 1996, Qian, Miao et al. [22] defined the key strata and later proposed a theory related to this concept. When there are multiple layers of hard rock in the overlying strata of the mining site, the rock layers that play a decisive role in all or partial rock activity are called key layers. The former can be called the key layer of rock movement, and the latter can be called the sub-critical layer. The breakage of key strata can control the whole or local failure of the overburden above [23]. In addition, ground stress, hydrogeological conditions, and properties of the surrounding rock have an impact on overburden behavior, as confirmed in previous research [24,25]. Therefore, studies considering multiple factors and their interactions are very necessary.

Theoretical, experimental (or field), and numerical analyses are three main tools to find the key strata and investigate the induced seismicity. (1) The theoretical method often requires a significant simplification, carrying several assumptions. Sun [26] established a roof strata model to study the relationship between mechanical properties and the stability of the covering layer. Zhang, Tu et al. [27] investigated the effects of mining height and face advance length on rock overburden failure and fracture development in the rock strata. Fault sliding is closely related to the position relationship of the stope, the mining speed, and the mechanical properties of the fault [28]. (2) The validity of the theory and the more complicated scenarios need experimental and field studies to verify. Based on physical model experiments, Zhang, Guo et al. [29] analyzed the physical and mechanical properties and microstructural characteristics of weakly cemented overburden and overburden failure and pointed out that the failure mode of ultra-thick and weakly cemented overburden cover is “beam-arch-semi-arch shell”, and the failure boundary is arch-fractured. (3) Due to the technical limitation, numerical simulation can further enrich the experimental scene and obtain more comprehensive and repeatable data [30,31,32,33,34]. Pang, Liu et al. [35] used the numerical simulation software FLAC3D to simulate the failure process of the roof overburden of the 1308 working face, and the results showed that the mining depth and the working face advance distance were the two most influential factors of the failure height of the roof cover. Ding, Wang et al. [36] determined the reasonable length of working face under similar geological conditions based on comprehensive research methods such as numerical simulation, theoretical analysis, and on-site exploration. As the distance from the top of the coal seam increases, the stress in the rock gradually shifts upward to the overlying formation, and the scale of this stress transfer gradually decreases. Building on existing research, this study addresses the limitations of prior work that often focused on isolated phenomena related to mining-induced seismicity. Previous studies have insufficiently considered the complex interactions among multiple factors, such as the combined effects of mechanical properties, excavation geometry, and mining rates, on overburden failure.

In the context of underground coal mining, mining-induced seismicity is closely linked to the failure and movement of overburden strata, particularly the key strata that control the mechanical stability of surrounding rock masses. This study investigates these failure mechanisms as the fundamental source of mining-induced seismic events, thereby directly addressing their causes and control. This research investigates the influence of overburden strata on mining-induced earthquakes during the mining process by analyzing a single factor independently and comprehensively considering multiple factors. The main factors are mining height, advancing distance, and advancing rate. Laboratory experiments and numerical modelling are applied to investigate the mining-induced seismicity of overburdened strata and the failure process. In order to further verify the accuracy of numerical simulation results, small-scale model experiments were conducted. Based on the key strata theory, a specific project case referred to in the literature [37] is used to establish a numerical model with ABAQUS. After discussing the sensitivity of single factors, the research then goes further to analyze the interaction effect between mining height and advancing rate. By analyzing both single and multiple factors, this research aims to provide a more holistic understanding of the mechanisms underlying mining-induced seismicity and to develop strategies for mitigating the associated risks.

2. Methodology

In order to investigate the influence of single factors and multiple factors on overburden failure, three research methods, including theoretical analysis, numerical simulation, and physical simulation, are applied in this research project. The key strata theory is to determine control layers in overburden, while two simulation experiments separately concentrate on numerical results and direct observations.

2.1. Theoretical Analysis

The key strata theory is an assumption model for analyzing overburden failure induced by mining. Qian et al. [22] developed this theory to investigate the law of strata movement. The key stratum is generally defined as the thick and hard rock layer. It plays a major role in controlling overlying strata behavior. This section mainly introduces how key strata theory is applied to this specific project. The position of the primary key strata (PKS) and sub key strata (SKS) is first determined and then compared with the previous judgement in the numerical model.

The application of the key strata theory in this study is essential due to its strong theoretical foundation and practical relevance in analyzing overburden failure induced by underground mining. Originally proposed by Qian et al. [22], the theory defines key strata as mechanically strong and thick rock layers that control the movement and failure of overlying strata. In this research, key strata positions are determined through a combination of stiffness criteria and breaking span calculations, allowing for a rigorous and quantifiable identification of primary and sub-key layers. This approach not only simplifies the complexity of stratigraphic modeling but also ensures that the mechanical behavior of overburden is accurately captured. Moreover, the predicted positions and failure patterns of the key strata provide the basis for numerical simulation settings and experimental validation. Given that mining-induced fractures are closely linked to the breakage and movement of these control layers, the key strata theory offers a highly suitable framework for studying the evolution of mining-induced seismicity and surface subsidence. PKS can control the behavior of the whole overburden strata above it, and SKS only controls part of the above strata. After defining the concept of key strata, the position of these special layers could be identified using a theoretical analysis method. According to the concept of key strata, the fine sandstone (PKS) has a great influence on other strata’s behavior and should be paid more attention when analyzing the overburden failure. For example, one experiment group considers the deformation modulus E of PKS as the variable.

2.2. Numerical Simulation

Numerical modelling is the major tool used in this paper to investigate the deformation and failure of the overburden. The main steps of the numerical simulation are to define the problem mathematically, select appropriate computational methods and software, establish the model and conduct tests, and visualize and interpret the results, which provide the logic to transfer engineering projects to mathematical problems and analyze the numerical results.

The numerical models are designed based on the real project reported in the literature [37]. In this case, the actual depth for the mining process is from 69 to 75 m underneath. With the application of key strata theory, the model is simplified to simulate the coal-mining process. This model is divided into ten layers along a vertical direction based on different geological conditions (Figure 2). The penultimate layer is the coal seam, and this layer is split into ten equal units so that the effect of advancing the working face can be studied. The geological parameters of ten strata from top to bottom are listed in

Table 1. Geological parameters of the model.

No	Geological Type	Thickness (m)	Young’s Modulus (×103 MPa)	Poisson’s Ratio	Cohesion (MPa)	The Angle of Internal Friction (°)
1	Mudstone	8	0.32	0.27	1.45	31.5
2	Siltstone	15	0.22	0.29	1.38	30.7
3	Interbedded mudstone	15	0.97	0.26	2.68	32.5
4	Fine sandstone (SKS)	10	4.79	0.25	7.60	33.6
5	Mudstone	8	3.16	0.24	4.42	34.8
6	Siltstone	4	2.58	0.28	2.8	32
7	Sandstone	3	2.79	0.26	2.5	31
8	Fine sandstone (PKS)	6	10.05	0.23	13.87	37.5
9	Seam	6	0.99	0.25	2.00	30.0
10	Fine sandstone	10	11.68	0.22	14.04	35.4

[37].

2.2.1. Material Properties in Numerical Simulations

To study the influence of each factor, three groups of numerical models, together with a control group X, are designed. Detailed information is shown in

Table 2. The design of the numerical models.

Group	Sub- Group	Change	Factors			Study Aim
			Young’s Modulus	Mining Height	Advancing Rate
Control group X	-	-	10,050	6	6	Comparison
Group A	A1	+10%	11,055	6	6	Sensitivity of elastic modulus
	A2	+20%	12,060	6	6
	A3	−10%	9045	6	6
	A4	−20%	8040	6	6
Group B	B1	+50%	10,050	9	6	Sensitivity of mining height
	B2	+100%	10,050	12	6
	B3	−50%	10,050	3	6
Group C	C1	+50%	10,050	6	9	Sensitivity of advancing rate
	C2	+100%	10,050	6	12
	C3	−50%	10,050	6	3

. The bold number represents the variables for each sub-group. According to the concept of key strata, the fine sandstone (PKS) has a higher influence on other strata behavior and the overburden failure. Therefore, in group A, the elastic modulus of the PKS is changed to study the sensitivity of the PKS’s elastic modulus.

2.2.2. Modeling Process

The numerical model of this case generally follows the steps: establishing a coal mining process model, meshing, model calculation, and result analysis. Geological parameters, load conditions, and boundary conditions should be determined in advance. Apart from the known values of parameters, to simulate the self-weight, the body force γ = 20 kN/m³. To simulate the lateral pressure in actual engineering, the lateral pressure coefficient K₀ = 1. Boundary conditions on two lateral sides are free in the vertical direction and zero in the horizontal displacement, i.e., u₁(x₁ = 0) = 0, u₂(x₁ = 0) = 1. The bottom layer sets as a fixed-end constraint, and the displacements in all directions are limited, i.e., u₁(z₁ = 0) = u₂ = 0. In order to simulate the mining process, four steps are set to study the variation of stress and displacement as time changes. The advancing distance is gradually increasing as the units in specific regions are gradually deactivated. Optimal meshing is a prerequisite for numerical convergence. An appropriately refined grid not only accelerates convergence but also enhances solution accuracy. In the mesh part, the element shape is set as a quadrangle due to its ability to achieve higher computational efficiency. The model is expressed as a regular rectangle, which can meet the requirements of calculation efficiency by a structured meshing technique. To enhance the computational accuracy, global seeding is implemented. During the seeding process, the approximate global element size is set to 0.5 m.

Four groups of numerical models, as listed in Table 2, are used to perform the parametric study with a control group X. These groups have a similar setup of geometry and basic properties, only being changed by some parameters, such as Young’s modulus, mining height, and advancing rate. The Mohr-Coulomb criterion is utilized as the failure model.

2.3. Physical Simulation

To verify the model’s effectiveness and accuracy in a numerical study, a physical simulation parallel to the numerical simulation is performed. It aims to investigate the influence of mining height and advancing rate in coal mining; to be specific, the fracture development process in overburdened strata. The advancing rate and mining height separately respond to the numerical group A and group B (B1, B2).

2.3.1. Experiment Preparation

The commonly used physical simulation in mining engineering is the scale model test. The scale model test is an experiment that reduces the actual size of the strata to simulate the actual mining conditions of the project. This paper applies this method to the study of the deformation and failure process in mining. In the study, the physical parameters of the scale model are as follows: the geometric scale factor is 1:200. The geological conditions are simplified from the original eight strata to five main types, and similar and contact strata are regarded as one in the physical simulation.

According to the principle of similarity, in the physical simulation model, the soil and rock layers above the tunnel are simulated by a compound of quartz sand, lime, and gypsum powder. Their proportion is determined by the mechanical properties of the simulated strata. However, the scale model still has certain limitations. We should admit that there is no perfect simulating material that can have a constant scale among different mechanical properties. The present study mainly considers the scale similarity of elastic modulus and the strength parameters, like cohesion and internal frictional angle. In the experimental model, from top to bottom, the mixing ratio of its three materials (quartz sand, lime, and gypsum powder) is 26:1:1, 26:1:2, 26:2:1, 26:2:2, and 26:2:2.5 in turn, and the weight of the added water is 1/9 of the total weight of the mortar. The curing time of the mortar mixture is controlled at 5 days at room temperature. Mica powder is sprinkled between adjacent mortar layers for observation and distinction of the interaction relationship between each stratum. The detailed parameters of each layer obtained by geotechnical testing are shown in

Table 3. The mixing ratios and mechanical properties of the simulated materials.

Layer	Simulated Material	Young’s Modulus (MPa)	Sand/Lime/Gypsum	Cohesion (kPa)	Internal Friction Angle (°)	UCS (MPa)
1	Material I	43	26:1:1	16	30	55
2	Material II	52	26:1:2	19	32	68
3	Material III	65	26:2:1	24	33	88
4	Material IV	72	26:2:2	28	35	107
5	Material V	73	26:2:2.5	29	35	111

.

2.3.2. Similar Materials

In experimental research, the different scales between the prototype and the physical model are very common. Since the size of the physical model is extremely smaller compared to the practical engineering, the similarity of the simulated material should be considered [38]. The principle of similitude was first systematically proposed by Lord Rayleigh in 1915 when discussing the dimensional analysis [39,40]. It was generally used in fluid mechanics. Recently, with the development of experimental rock mechanics, more researchers started to investigate the scale effects on the interpretation of experimental results and the validity of the small-scale tests [41,42,43]. According to the principle of similitude, we have the following ratios of the geometric and material properties between the prototype and the practical case. The geometric similarity of the model experiment can be determined by $C_L$. In the present study, the physical model is scaled at 1:200.

$$C_L={\displaystyle \frac{L_p}{L_m}}=200$$

(1)

where $L_p$ is the geometric parameter of the prototype and $L_m$ is the geometric parameter of the model.

Since the bulk density of the simulated material and the rock strata is very close, the similarity ratio of the bulk density can be seen as one:

$$C_{\gamma }={\displaystyle \frac{{\gamma }_p}{{\gamma }_m}}=1$$

(2)

where ${\gamma }_p$ is the bulk density of the prototype, and ${\gamma }_m$ is the bulk density of the model.

With the aid of the above two ratios, the similarity ratios about stress, strain, frictional coefficient, cohesion, and elastic modulus can then be determined.

$$C_{\sigma }=C_{\gamma }{C}_{\gamma }=200$$

(3)

$$C_{\epsilon }=C_f=1$$

(4)

$$C_E=C_{\sigma }=200$$

(5)

where $C_{\epsilon }$ is the similarity ratio of strain, $C_f$ is the similarity ratio of the friction coefficient, and $C_E$ is the similarity ratio of elastic modulus.

The key to the accuracy of the physical simulation in rock mechanics is the selection of similar materials [43]. The compounds of the aggregate and cement or gypsum are commonly used in rock mechanics. Due to the scale effects, the mechanical properties of the simulated material should be reduced accordingly based on the principle of similitude. For example, when the Young’s modulus of the strata is about 10 GPa, the Young’s modulus of the simulated material should be around 50 MPa. As listed in Table 3, the Young’s modulus of the simulated materials is much lower than the practical value, which ranges from 43 to 72, depending on the proportions of the three main components. The values are reasonable for the principle of similitude. However, there is a limitation about the simulated material, in that it is hard to find a perfect material with a much lower Young’s modulus but a similar strength to the prototype one. Though the internal frictional angle of the present simulated material is a little lower, fortunately, the ratios between them are not big. Therefore, they can still be used as a similar material.

2.3.3. Physical Model

The strata and the coal seam in the physical model are simulated by the above similar materials and the PMMA (polymethyl methacrylate) blocks, respectively, as shown in Figure 3. The length, width, and height of the PMMA block are 40 cm, 2 cm, and 4 cm, separately put below the simulated strata, as shown in Figure 4. Mica powder is also sprinkled between adjacent layers to simulate the interaction face of rock strata and mark the interface.

2.3.4. Experiment Process

During the experiment, the removal rate of the 16 PMMA cubes represents the advancing rate in real mining activities. The mining height is represented by the stacking number (one or two layers) of the PMMA cubes. The time interval for removing the cube is set at 20 min. The physical model A, containing only one layer of PMMA cubes, is used to study the influence of advancing rate on fracture development and ground surface settlement. Three subgroups of models (A1, A2, A3) correspond to different advancing rates in mining by changing the time interval of the removal rate of PMMA cubes in the physical model. The removal rates of models A1, A2, and A3 gradually increase from 10 min to 30 min with a 10 min increment. The physical model B is designed for investigating the influence of mining height. Two subgroups of models (B1, B2) are set in this experiment. Model B1 has one layer of PMMA cubes, while model B2 has two layers, which means the mining height in B2 is twice that of B1.

3. Results

3.1. Numerical Simulation

The numerical results of groups (A, B, C) are successively compared with the control group X to investigate the influence of Young’s modulus, mining height, and advancing rate, and their sensitivity by changing the values of these factors. The max principal stress and settlement (displacement in the vertical direction) are two main monitoring variables in the quantitative analyses. In this process, ten observation points for stress and three points for settlement are set in the computation of the simulation (Figure 5).

3.1.1. Control Group X

1.

Max principal stress

The max principal stress contour of the X group at the end of the excavation is shown in Figure 6. From the contour, the highest stress occurs at the heading surface, and there are another two obvious stress concentrations in the model. The lower is caused by the different stiffness of the stratum, and this area of concentration increases gradually from left to right. Another stress concentration occurs in the upper stratum, which is associated with the dragging of the gravity of the deep stratum and transmission from deep to this place.

To assess the stress variation with excavation progress, changes in stress belonging to the ten observation points are analyzed (Figure 7). The analysis starts from 0.5 s to 4 s with a time interval of 0.5 s, which includes three excavation steps. The data of the maximum principal stress, σ1, are plotted against time in Figure 8.

In Figure 8, each curve corresponds to the stress history of an observation point. It could be directly observed that the max principal stress starts to change when t = 1 s (1st excavation) and is transformed from compression into tensile, which is caused by the advancement of the working face. Among them, point 1 is the earliest one subjected to tensile stress and eventually reaches the peak value, which can be easily understood that the excavation process initiates from the bottom right corner. In addition, the gradual expansion of the affected area could also be read from the figure. This finding is consistent with the stress contour that excavation influences the overburden strata step-by-step, from the bottom right to the upper left.

2.

Settlement

The settlement of the surface is extremely significant for a practical project. The displacement contour after the entire excavation is shown in Figure 9. The blue area means a larger displacement, while the red area is positive due to the rebound of the floor caused by excavation, but it is close to zero. Similar to stress, the settlement also changes with time. The settlement of the three observation points is plotted in Figure 10. The settlement at three points has a similar variation tendency, rising with time.

3.1.2. Parametric Studies

Parametric analyses are conducted to understand the sensitivity of the system. Three main parameters, including elastic modulus, mining height, and advancing rate, are investigated to quantify their influence on the principal stress and surface settlement in numerical simulation.

A. Elastic modulus

1.

Max principal stress

The max principal stress against the time of group A is plotted in Figure 11. By comparing the results of four subgroups with different elastic moduli (A1—11,055 MPa, A2—12,060 MPa, A3—9045 MPa, A4—8040 MPa), it is observed that subgroups A1 and A2 generally have larger principal stress values than subgroups A3 and A4 with lower elastic modulus, indicating the positive effect of Young’s modulus on the max principal stress. Since there are two stress concentration areas, the positions of the maximum principal stress in these subgroups are found to be different. The maximum value occurs at point 1 for subgroups A1 and A2, while the maximum value appears at point 8 in subgroups A3 and A4. The result indicates that the Young’s modulus can determine the distribution of the principal stress and the maximum value.

2.

Settlement

Though the elastic modulus of PKS can effectively change the value and position of the maximum principal stress, its influence on surface settlement is not obvious. The vertical displacement against the time of group A with an interval of one second is plotted in Figure 12. With the increase in advancing time, the settlement curves at points 1, 2, and 3 for different subgroups are similar to each other. It is very hard to find out the difference. In addition, these curves also look nearly the same as that of group X.

B. Mining height

1.

Max principal stress

For group B, the mining height of the subgroups is 9 m, 12 m, and 3 m for B1, B2, and B3, respectively. The max principal stress against the time of group B is plotted in Figure 13. Most of the monitored principal stresses increase gradually with the excavation. The variation rate gently rises with time. Those at points 1, 2, 3, and 4 close at the excavation space are exceptions which has a more fluctuating curve. In other words, these points are more sensitive to the excavation. It is easy to understand. However, the differentiation of the principal stress in the whole process for different points is very close for points 5–10. The result indicates that the points with a certain distance from the excavation experience nearly the same stress variation, and the mining height has a higher influence on the working face than that at other positions.

2.

Settlement

The variation of the settlement of points 1, 2, and 3 at the surface is very similar to each other regarding the absolute value and the trend with different mining heights, as shown in Figure 14. The settlement increases with the excavation. The point on the side of the excavation start point has a higher settlement. Again, though the variation of the elastic modulus of PKS can obviously affect the distribution of the maximum principal stress, its influence on surface settlement is very limited. The result indicates that the limited change of the mining height has little influence on the settlement.

C. Advancing rate

1.

Max principal stress

The change in the advancing rate shows a distinct impact on the maximum principal stress, as shown in Figure 15. The advancing rates of the three subgroups (C1, C2, and C3) are 9, 12, and 3, respectively. This behavior is different from that in the above two cases. In the numerical simulation, the rate is controlled by adjusting the interval of the loading step. Faster excavation will produce a relatively higher undulation of the principal stress. However, such an influence on absolute value is still very limited. However, since the failure of the rock mass has a certain speed, it cannot be concluded that the influence of the advancing rate also has a limited influence on the failure.

2.

Settlement

As plotted in Figure 16, about the settlement against the time of group C, the variation rate of the settlement synchronizes with the advancing rate, and not surprisingly, point 3, at the side of the start point, has the largest settlement. However, regarding the maximum vertical displacement and the differentiation of the three subgroups, the settlement is not conspicuously affected by the excavation ratio. It is reasonable if the lag of the deformation of geological bodies is neglected. The propagation speed of the stress wave is very fast, and the stress redistribution can be seen as simultaneous compared with the size of the simulated project. But the deformation cannot be seen as instant for this size. Therefore, in order to accurately simulate the settlement, a new model considering the time lag of the deformation should be applied.

It can be known from the analysis of maximum principal stress, and the corresponding stress concentration can be adjusted if the Young’s modulus of the key strata can be changed. One way to achieve this goal is to perform the grouting to enhance the elastic modulus and the integrity of the stratum. The reduction of the principal stress can also be helpful to reduce the risk of overburden failure. If allowable, a lower excavation rate is always beneficial to the settlement and the project safety. In the excavation process, if a supporting system can be used, the stiffness of the surrounding rock can be effectively increased, and hence, the stress concentration at the far field and the settlement can be controlled.

3.2. Physical Simulation

In addition to the numerical study, physical simulation is conducted to investigate the cracking behavior of overburden strata in the excavation process. In the present FEM model, there is a shortage in that the failure process of the overlay strata is not considered. As shown in Figure 17, the cracks and collapse in the strata can be well simulated by the physical model. Vertical cracks initiate and propagate throughout the first and second layers in the vertical direction, which is like the cantilever beam failure. Then the horizontal cracks initiate and propagate in the horizontal direction for a considerable distance at the interface. The typical length of vertical cracks is about 2 cm, and the length of horizontal cracks along the interface is 10 cm. Figure 17 presents a typical crack development pattern as well as the collapse during mining. The initiation of the horizontal cracks can be well predicted by the stress concentration at the interface.

4. Discussion and Conclusions

The findings of this study have important implications for engineering practice, particularly in the design and optimization of strata control measures in response to varying mining heights and advancing rates. The sensitivity analysis demonstrates that both mining height and advancing rate significantly influence overburden behavior, including stress redistribution and surface settlement. These results suggest that excavation parameters should be closely integrated with ground control strategies to ensure safety and efficiency.

Excavation progress leads to the redistribution of in situ stress and fracture generation among overburdened strata, and a seismic event may happen during this process. In this paper, numerical modeling is conducted to investigate the sensitivity of three main parameters, including Young’s modulus, mining height, and advancing rate. The results indicate that Young’s modulus of the key strata generally has the greatest impact on the principal stress distribution but has limited influence on the settlement. In contrast, mining height has a greater influence on the total settlement of the overburden strata. The advancing rate can vary the fluctuation of the principal stress and the settlement, but has little influence on the final stress distribution and the settlement, which is reasonable due to the time effect of deformation. Physical modeling is also conducted to simulate the actual mining conditions of engineering and intuitively study the propagation of cracks. The observation from the physical experiment basically agrees with the result of the modelling simulation. Collapse occurs in the early stage of excavation, and cracks appear at the top of the model. Both vertical and horizontal cracks can be found in the excavation process. It is suggested that the grouting and shotcrete in excavation, which can increase the stiffness of the stratum or the surrounding rock, can effectively decrease the settlement in addition to the stability.

One practical engineering strategy proposed in this research is to improve the stiffness of the primary key stratum through targeted grouting reinforcement, thereby increasing its effective Young’s modulus. By enhancing the mechanical properties of this control layer, stress concentrations around the mining area can be reduced, and vertical displacement of the overburden can be effectively constrained. Grouting is particularly useful when key strata exhibit low elastic modulus and high stress concentration zones are identified. Shotcrete is recommended during early-stage excavation to enhance the stiffness of the surrounding rock mass near the working face. Numerical results show that increasing the modulus of the key stratum leads to a more uniform stress distribution and less deformation at the surface, especially under high mining height or rapid advance conditions.

In addition, the results indicate that different combinations of mining height and advance rate produce varied overburden responses, highlighting the necessity for flexible and adaptive support systems. For example, in cases with high mining heights, stronger immediate roof support and wider reinforcement zones may be required. When a faster advance rate is adopted, time-dependent deformations become more significant, and preemptive grouting or stress-relief techniques should be applied in advance.

This research primarily investigates the impact of mining technology parameters under certain conditions. However, it is limited to these specific conditions and does not encompass other possible complicated scenarios in real engineering. This simplified method is suitable for mechanism analysis and preliminary exploration of parameter sensitivity. For future research, methods such as Monte Carlo methods or random field modeling are planned to be employed to better capture the discrete and uncertain nature of geological parameters. Moreover, the long-term settlement and secondary effects of key layers involving time-dependent behavior are also an issue that cannot be ignored, which will be addressed in future work.