*2.1. Overview of Working Face*

Shenmu Dongliang Coal Mine is located 35 km to the north of Shenmu County, Shaanxi Province. It is located in the area bordering the Loess Plateau and the Maowusu Desert in northern Shaanxi Province. It has the geological characteristics of a thick loess layer load and an aeolian sand permeable layer. The Baotou Shenmu Shuozhou Railway runs through the eastern area of the mine field. The transportation is relatively convenient. According to the borehole disclosure and observation data, the Yan'an Formation coal-bearing rock series is a monoclinal structure inclined to the north or northwest, with a flat dip angle of about 1◦, aerial photo of the mine field location is shown in Figure 1:

**Figure 1.** The relationship between the location of the mine field and the stope layout.

The complexity of the structure is relatively simple. The average thickness of the 2-2 coal seam is 12.0 m, the strike longwall retreating mining method is adopted, the roof is managed by the total caving method, and a shield hydraulic support is used to support the roof of the stope. The direct roof of the 2-2 coal seam is fine-grained sandstone, followed by medium and fine sandstone with a thickness of about 4.3 m. The basic roof is 16.5 m medium-grained sandstone. The floor is dominated by siltstone, followed by mudstone with a thickness of about 2.5 m. The dip length of the working face is 303 m. At present, a 20 m wide coal pillar is reserved in this section. The roadway layout plan and the geological histogram of the working face are shown in Figure 2.

**Figure 2.** Comprehensive histogram.

#### *2.2. Establishment of a Mechanical Model of Overburden*

It can be seen from the comprehensive histogram of the rock stratum shown in Figure 2 that the overburden of the stope is mainly composed of a relatively brittle direct top of fine sandstone and a basic top of thick-, hard-, and medium-grained sandstone. The combined sandstone in the middle is thin and weak in lithology, which mainly serves as a load transfer and elastic foundation.

An elastic medium-thick plate with zero boundary displacement is separated from the basic roof rock of medium-grained sandstone overlying the stope. Its spatial stress component is shown in Figure 3.

**Figure 3.** Schematic diagram of the elastic mechanic model for the basic roof.

The balance equation of the space problem is as follows:

$$\begin{cases} \frac{\partial \tau\_{\mathbf{x}}}{\partial x} + \frac{\partial \tau\_{\mathbf{y}\mathbf{x}}}{\partial y} + \frac{\partial \tau\_{\mathbf{x}\mathbf{x}}}{\partial z} + K\_{\mathbf{x}} = 0\\ \frac{\partial \tau\_{\mathbf{x}\mathbf{y}}}{\partial x} + \frac{\partial \tau\_{\mathbf{y}}}{\partial y} + \frac{\partial \tau\_{\mathbf{z}\mathbf{y}}}{\partial z} + K\_{\mathbf{y}} = 0\\ \frac{\partial \tau\_{\mathbf{x}\mathbf{z}}}{\partial x} + \frac{\partial \tau\_{\mathbf{y}\mathbf{z}}}{\partial y} + \frac{\partial \sigma\_{\mathbf{z}}}{\partial z} + K\_{\mathbf{z}} = 0 \end{cases} . \tag{1}$$

In Equation (1), *σx*, *σy*, and *σ<sup>z</sup>* are the normal stresses in the direction, Mpa; *τyx*, *τzx*, and *τyz* are the shear stresses in the direction, MPa, and *Kx*, *Ky*, and *Kz* are the volume force per unit volume in the direction.

#### **3. Three Typical Characteristics of Basic Roof Movement on Direct Roofs with a Large Mining Height**

#### *3.1. Mechanical Model of a Beam Obtained by Dissecting a Medium-Thick Plate*

Because the mining height of fully mechanized mining and fully mechanized caving mining technology with a large mining height is multiple times that of an ordinary mining height, the size and cutting depth of the coal drum are different. The width of the front and rear scraper conveyor, the length of the top beam of the hydraulic support, and the effective support distance are also significantly increased, and the mining space is many times larger than that of general fully mechanized top-coal caving. Therefore, the space dimension of the top coal and the free face under the direct roof is also far larger than that of general fully mechanized top-coal caving and fully mechanized top-coal caving.

In view of the above reasons, since the mining disturbance range of the large-miningheight process gradually increases, and the bearing control effect of the direct roof on the transfer of load and movement results in the overlying strata being relatively weaker than that of the non-large-mining-height process, the basic roof of most large-miningheight working faces plays an absolute control role in the rock pressure behavior of the working face and the caving behavior of the top coal; for example, this occurs in Caojiatan coal mine [9], Tongxin coal mine [10], and Hanglaiwan coal mine [11]. According to microseismic event records and field investigations and analyses, it is considered that there are three typical types of the result of the fault movement of the overlying thick and hard basic roof rock after mining disturbances and its influence on the direct roof and intermediate cushion below: I. bench vertical action; II. short cantilever beam—rotary action type; and III. long cantilever beam—horizontal action type, as shown in Figure 4.

**Figure 4.** Typical state of overlying rock movement in a stope with a large mining height.

Li H's [12] discriminant theoretical formulas for mining overburden failure conditions have been clarified. Because the control effect of the direct roof strata is limited, it is not conducive to supporting working conditions and working face rock pressure control, that is, when the working face is pushed forward from the cutting position, it is assumed that the length of the free surface of the basic roof rock is the same as the pushing distance, and S is the balance judgment formula of the elastic deformation stage of the basic roof rock:

$$S = \frac{-3qI + \left[\frac{\sigma\_{\hat{\ell}}}{\sigma\_{\hat{\ell}}(1-f)} - 1 - f\right] \cdot \langle \sigma \rangle - \gamma \langle -\sigma \rangle + q}{1 - f},\tag{2}$$

where *q* is the second root of the ratio of the first and third invariants of the partial stress tensor s; *J* and the biaxial and uniaxial compressive yield stress *σ*' are about [*J* =(*σ*' − 1)/(2*σ*' − 1)]; <*σ*> is the symbol of the Macaulay matrix operation; *σ*<sup>t</sup> is the tensile stress, MPa, and *γ* is a parameter related to controlling the cross-sectional shape of the yield surface, according to Li's research results in 2018 [13], taking 2.991 as the value.

The plastic state equilibrium discrimination is combined in Equation (3):

$$G = \left[ \left( 0.1 \sigma\_t \tan \psi \right)^2 + q^2 \right] - p \tan \psi,\tag{3}$$

where *G* is the judgment formula of the plastic deformation equilibrium of the basic roof stratum; *ψ* is the shear expansion angle, ◦, and *p* is the imaginary part of the conjugate complex of the deviator stress tensor.

Based on the mechanical calculation method of calculating the I/II mixed fracture by the first-principal stress synthesis method, only singular terms are retained in the stress components, and the stress components of high-order small terms are ignored. At this time, the criterion expression of the I/II mixed-fracture tensor formula is as follows:

$$\begin{array}{l} \sigma\_{rr} = \frac{1}{2\sqrt{2\pi r}} [K\_{\mathrm{I}}(3-\cos\theta) \cdot \cos\frac{\theta}{2} + K\_{\mathrm{II}}(3\cos\theta - 1) \cdot \sin\frac{\theta}{2}] + o(r^{-1/2})\\ \sigma\_{\theta\theta} = \frac{1}{2\sqrt{2\pi r}} \cos\frac{\theta}{2} [K\_{\mathrm{I}}(1+\cos\theta) - 3K\_{\mathrm{II}}\sin\theta] + o(r^{-1/2})\\ \tau\_{r\theta} = \frac{1}{2\sqrt{2\pi r}} \cos\frac{\theta}{2} [K\_{\mathrm{I}}\sin\theta + K\_{\mathrm{II}}(3\cos\theta - 1)] + o(r^{-1/2}) \end{array} \tag{4}$$

where *K*<sup>I</sup> = *σ*<sup>∞</sup> *y* <sup>√</sup>*π<sup>a</sup>* is the stress intensity factor of a mode I crack; *<sup>K</sup>*II <sup>=</sup> *<sup>τ</sup>*∞√*π<sup>a</sup>* is the stress intensity factor of a mode II crack; r is the polar diameter around the crack in the polar coordinate system, m, and *θ* is the polar angle of the crack in the polar coordinate system, rad.

In the actual process of coal mining, due to the geological and stress conditions including too many different influencing factors [14] and due to the changes in the overburden conditions, strata, and rock mechanical properties, it is difficult to determine two stopes with the same roof structure and migration patterns in the field measurements. Therefore, in this study, we only abstractly analyzed three kinds of mechanical models that are common in the roof structure of coal mines from the perspective of rock mechanics, and these were combined with the cognitive laws of traditional research paths; on this basis, in further research, we propose the use of similar physical simulation mechanical experiments to simulate the broken movement form of the coal mine roof along the advancing direction of the working face and the shearing tendency of the coal machine.

#### *3.2. The Boundary Conditions of the Experimental Model Are Set in the Simulation of the Excavation Results*

With the continuous increase in the normal stress and stress components in the interface internal stress matrix, the possibility of plastic failure also increased. It is further concluded that with the continuous advancement of the working face, the increase in the exposed length under the basic roof will lead to different forms of failure modes and movement characteristics of the basic roof strata with different thickness-to-span ratios. When the thickness-to-span ratio is less than 0.5, when the rock stratum breaks, the masonry beam structure will be formed, that is, a type III long cantilever beam with a horizontal action structure. When the thickness-to-span ratio is greater than 0.5, the rock stratum will break and form a stepped rock beam structure, i.e., a type I stepped vertical action structure. According to the research results of Zuo et al. [15], it can be considered that the thickness-to-span ratio of a basic roof rock layer of 0.5 is the critical transformation point of the fracture form of the rock layer, and the type II short cantilever beam rotary action structure occurs from time to time as a state near the critical point. In this movement form, the deflection of the overlying rock in the vertical direction is large, and the horizontal force of the rotary lap on the top coal during the movement of the gangue fulcrum in the goaf will also promote the arch articulation of the top coal when it is released [16]. The

results of these two actions cause the cracks in the top coal to more fully develop, and cannot easily cause large displacement to the goaf direction leading to coal loss [17,18]. With the intervention of sufficient top-coal pre-cracking strategies, arch articulation can be effectively avoided. Therefore, in a fully mechanized top-coal caving face with a large mining height where the caving property of hard top coal is not ideal, the recovery rate of top coal can be improved by reasonably optimizing the roof fracture migration form to move closer to a type II structure.

Figure 5 shows the geometric model established by the working face and roadway layout and the spatial position relationship between the roof and floor of the coal seam in the numerical simulation experiment.

As shown in Figure 6, as the thickness-to-span ratio of the basic roof gradually reached 0.5 from less than 0.5 and then increased to more than 0.5, the peak displacement of the roof in the working face with a large mining height increased from 0.45 m to 0.5 m when the thickness-to-span ratio was 0.5. When the thickness-to-span ratio exceeded 0.5, the peak displacement of the roof reached 0.55 m. In addition, it is worth noting that when the thickness-to-span ratio of the basic roof rock increased, the displacement and range of the floor also increased, which indicates that the different states of loading and movement of the basic roof rock have a structural impact on the whole stope space.

**Figure 6.** Evolutionary law of displacement field of surrounding rock with different basic top thickness-to-span ratios in the advancing direction of a stope. (**a**) Thickness-to-span ratio less than 0.5. (**b**) Thickness-to-span ratio of 0.5. (**c**) Thickness-to-span ratio greater than 0.5.

Similarly, from the analysis of the effect of the overlying basic roof thickness-to-span ratio on the stress field of the stope shown in Figure 7, it can be concluded that with the increase in the thickness-to-span ratio, the leading stress peak value and range increased significantly, from 24.8 MPa to 28.62 MPa and, finally, to 32 MPa. The increase in the basic roof thickness of the same lithology led to different modes on the plate failure section of the basic roof stratum. When the rock layer is thin, the failure of the rock plate is mainly due to the normal tensile stress on the interface exceeding the tensile strength of the rock layer under the action of the roof top-coal clamping. When the rock layer is thick, the tensile stress cannot cause the thick and hard basic top rock layer to break. When the shear stress acting in the tangential direction of the breaking section reaches the shear strength of the rock layer at the fixed end edge, the rock layer will be sheared and destroyed and the step will sink. Additionally, the failure of the basic roof rock in the middle scale may only meet the two forms of mixed failure at the same time, that is, there is both vertical pressure and horizontal rotation on the top coal.

**Figure 7.** Evolutionary law of the stress field of surrounding rock with different basic top-coal thickness-to-span ratios in the advancing direction of a stope. (**a**) Thickness-to-span ratio less than 0.5. (**b**) Thickness-to-span ratio of 0.5. (**c**) Thickness-to-span ratio greater than 0.5.

Taking the upper boundary stress conditions of the top coal and the breaking results of the direct roof under the action of the basic roof movement studied above as the upper boundary loads of the coal drawing simulation experiment, it was found that when the bench vertical action occurred when the basic roof thickness-to-span ratio was greater than 0.5, as shown in Figure 8a, the top-coal drawing effect was poor, and there was more coal lost in the goaf. The result of the roof bench sinking was that the top coal fell into the goaf without fully rotating and squeezing. Under the tensile breaking mode with a thickness-to-span ratio less than 0.5, the recovery rate of the top coal was significantly improved, and gangue was observed. However, the interaction between the hinge structure of the roof and the top coal was compressed into an arch, resulting in a surplus of top coal in each round of coal drawing, which could not be released well in the simulation experiment. Obviously, there are more constraints in field applications resulting in some of the top coal being trapped by the hinge structure of the roof and left in the goaf [19]. When the thickness-to-span ratio was equal to about 0.5 in the mixed-fracture mode, the roof was characterized by short cantilever beam rotation. The rotation of the roof gave the top coal a constraint to move to the free surface, and the vertical action stage before the rotation also fractured the top coal to a certain extent, damaged the integrity of the top coal, and made the size of the released coal smaller, the degree of fragmentation higher, and the migration speed faster, so that it could fall onto the rear scraper conveyor at the top of the coal tap in time instead of being left in the goaf, improving the recovery rate of coal resources, as shown in Figure 8c. The typical characteristics of roof rotation cause the top coal to become fully pre-cracked and not obviously hinged in an arch shape during

the process of releasing and moving. Only a small amount of boundary coal loss remains behind the goaf. Therefore, when the thickness-to-span ratio reaches about 0.5 and the short cantilever rotation action characteristics appear, these conditions are the most favorable for the recovery of the top coal.

**Figure 8.** Evolutionary law of top-coal migration and release under different roof boundary conditions. (**a**) Law of top-coal release and migration of step vertical action. (**b**) Law of top-coal release and migration of short cantilever beam—rotary action type. (**c**) Law of top-coal release and migration of long cantilever beam—horizontal action type.

### **4. Discussion and Conclusions**

#### *4.1. Discussion*

Based on the established mechanical model of the top coal–direct roof–follow-up cushion–basic roof structure combined with fracture mechanics and rock mechanics, the coupling boundary conditions of the top coal–roof interface were theoretically deduced, the discrimination formulas of the elastic conditions and plastic conditions were obtained, and the critical conditions were calculated. It is considered that the basic top thickness-to-span ratio has the most significant influence on the different characteristics of rock fracture and movement. Then, numerical simulation experiments were carried out. The evolutionary laws of the stress and strain fields of surrounding rock excavation with different thicknessto-span ratios were analyzed and studied so as to verify the theoretical research results. Finally, the results were substituted into the discrete element simulation software to analyze the influence of the different characteristics of roof failure structure and critical parameters on the difficulty of top-coal caving and the recovery rate.


determines the dominant direction of fracture development during hydraulic fracturing [20–23]. Therefore, according to the application of the theoretical formula for the ideal thickness-to-span ratio of the basic roof and the boundary conditions of the top coal obtained in this paper, the roof control parameters can be optimized. By improving the geometry of the basic roof and the way in which the rock mechanical properties act on the boundary of the top-coal roof, the purpose of improving the mine pressure and the recovery rate can be achieved.
