Mining-Induced Failure Criteria of Interactional Hard Roof Structures: A Case Study

Abstract

Due to the additional abutment stress, interactional hard roof structures (IHRS) affect the normal operation of the coal production system in underground mining. The movement of IHRS may result in security problems, such as the failure of supporting body, large deformation, and even roof caving for nearby openings. According to the physical configuration and loading conditions of IHRS in a simple two-dimensional physical model under the plane stress condition, mining-induced failure criteria were proposed and validated by the mechanical behavior of IHRS in a mechanical analysis model. The results indicate that IHRS, consisting of three interactional parts—the lower key structure, the middle soft interlayer, and the upper key structure—are governed by the additional abutment stress induced by the longwall mining working face. The fracture of the upper key structure in IHRS can be explained as follows: Due to the crushing failure, lower key structure, and middle soft interlayer yield, the action force between the upper and lower key structures vanishes, resulting in fracture of the upper key structure in IHRS. In a field case, when additional abutment stress reaches 7.37 MPa, the energy of 2.35 × 10⁵ J is generated by the fracture of the upper key structure in IHRS. Under the same geological and engineering conditions, the energy generated by IHRS is much larger than that generated by a single hard roof. The mining-induced failure criteria are successfully applied in a field case. The in-situ mechanical behavior of the openings nearby IHRS under the mining abutment stress can be clearly explained by the proposed criteria.

1. Introduction

With the development of clean utilization technologies, coal will always provide energy sources for the social development [1]. To ensure the efficient operation of coal production systems, security maintenance of entries in underground mining is extremely important, including large deformation control, rock burst forecast, and other early warnings of dynamic disaster [2,3,4]. As the development of the longwall mining, many entries are arranged along the side of a gob with a protection of coal pillar or artificial wall, so as to cope with the mining-induced movement of the hard roof structures [5,6,7]. Figure 1 schematically describes entry conditions when extracting coal from Panel 2. Tail entry provides auxiliary transportation and ventilation function for Panel 2. A coal pillar or artificial wall is built in the south of tail entry; and the coal mass of Panel 2 is located in the north of Tail entry. Gob 1 is located near the coal pillar. The spontaneous caving method was used to handle the roofs in Gob 1 [8]. To effectively control the deformation of tail entry in the strong mining pressure zone, it is important to understand the mechanical behavior of the hard roof structures above the side of Gob 1 during retreat of the mining working face of Panel 2.

Mechanical behavior of hard roof structures mainly refers to the separation, fracture, rotation, slipping, and yielding when the stress reaches the strength of structures [9,10,11,12,13,14,15,16,17]. At present, stability analyses of mechanical behavior are mainly concentrated on the single structure in one layer. Interactional effects between the hard roof structures in the different layers are rarely studied [18,19,20,21,22,23]. Shabanimashcool and Li [24] discussed the relationship between the horizontal in-situ stress and the buckling or crushing failure of the voussoir beam structures, which provide a mechanical method for the analysis of the interaction of structures in one layer. Zhang et al. [25] found that sink and rotation of the cantilever roof structure above the side of the gob generates severer pressure for the entry along the side of the gob; while the effects of this structure movement on the upper cantilever roof structure were ignored. Guo et al. [26] determined the support resistance assuming that the hard roof structures play a loading role in the lower supports together; while interactional effects between the structures were ignored. Yang and Liu et al. [27,28,29,30] demonstrated that the breakage of layered hard roof group structures led to severe concussion and determined the calculation method of the support resistance during the collapse process of multiple roofs. However, the effect of one structure caving on the other structural movement was ignored.

In-situ monitoring data in the field are widely used to predict and analyze the strong mining pressure of the entry influenced by the movement of hard roof structures [31,32,33]. Nevertheless, mechanical behaviors of hard roof structures can result in the error of the dynamic disaster early warning. Lu et al. [34] established the early warning method of the coal-rock dynamic disasters induced by the double-layer and thick igneous strata separation and fracture based on the in-situ microseismic signals. However, the horizontal and vertical positioning errors of microseismic signal sources cannot be eliminated clearly by optimizing the arrangement of the geophones. Wang et al. [35] provided a theoretical method for forecasting the location of rockburst induced by the fracture in the main roof by the in-situ microseismic monitoring results, but the positioning error of the microseismic signal sources was proved to be up to 10 m by blast experiments in the field. Bai et al. [36] proved that the lateral cantilever structure can produce supporting stress through field monitoring and numerical calculation. Under the action of the supporting stress, the entry along the side of the gob is vulnerable to large deformation and rock burst. However, the vibration signal from the structural fracture was ignored [37]. Compared with monitoring technologies in the field, mechanical behaviors of hard roof structures have a great influence on the large deformation control of entries.

To achieve pressure relief for the underground space, research on the controlling of hard roofs has been conducted recently. Zhang et al. [38] demonstrated that the hard-roof-induced face burst can be reduced effectively by preventing the roof-caving movement through solid backfilling mining method. Zhou and Li et al. [39,40] determined the reasonable backfilling ratio to control the hard roof deformation and reduce the mining abutment stress. He et al. [41] analyzed the rockburst prevention by cutting the hard roof directionally in advance under mechanical behaviors of the deep-hole directional fracturing of hard roof. To reduce the effect of the fracture failure of the overlying hard-thick sand-stone main roof on the gas permeability in the mining coal seams, Wang et al. [42] recommended shortening the hanging length of the main roof failure span using hydraulic presplitting. Zhang, et al. [43] determined the breaking form, order, step of the over roofs based on the hinge balanced cantilever beam structure model with the directional blast technology. Yu et al. [44] proposed the fracturing high-level hard rock strata using the ground hydraulic action. To achieve pressure relief of the entry nearby the side of the gob, the reasonable length and fracture location of the lateral cantilever structure were determined by mechanical analysis, but the influences of remolded structures by human on the movement of the upper structures was not considered [45,46,47].

In this work, a 2D physical model with plane-stress conditions was established to reveal the configuration and loading conditions of the interactional hard roof structures over the side of the Gob 1. After that, mining-induced failure criteria were proposed to describe the mechanical behavior of the structures, and the criteria were validated by a mechanical analytical model. Finally, the criteria were applied to analyze hard roof structures in a field case. The results contribute to understanding the strong mining pressure of the tail entry in front of the mining working face.

2. Interactional Hard Roof Structures (IHRS)

2.1. Establishment of IHRS

IHRS are established based on a simple two-dimensional physical model under the plane stress condition. The physical model is 2.5 m in length, 0.3 m in width, and 2 m in height, as shown in Figure 3. The normal displacement is fixed in the floor boundary and two-sided boundaries with the frame. The front and back boundaries of the model are in a free state. The vertical load 0.056 MPa is applied to simulate the overburden loads through 20 loading rams in the top of the model. According to the similarity theory [48], the similarity criteria must be satisfied in the physical modeling as shown in Equation (1). For this experiment, similarity ratios of geometry, density, strength, and time are determined as 160, 1.53, 244.8, and 12.65, respectively.

$$\{\begin{array}{l}\frac{C_{\sigma }}{C_{\rho }{C}_L}=1\\ C_L=\frac{L_p}{L_m}\\ C_{\sigma }=\frac{{\sigma }_p}{{\sigma }_m}\\ C_{\rho }=\frac{{\rho }_p}{{\rho }_m}\\ C_t=\frac{C_L}{\sqrt{C_L}}\end{array}$$

(1)

where C_L, C_σ, and C_t is the similarity ratio of geometry, strength, and time, respectively. C_ρ is the density similarity ratio of the prototype and the model. L_p, σ_p, and ρ_p represents the dimension, strength and density of the rock strata in the field, respectively; L_m, σ_m, and ρ_m represents the dimension, strength, and density of the rock strata in the model, respectively.

Eight materials with different deformability and strength were used to simulate the mechanical behavior of geological strata, including mudstone, coal seam 15, limestone, mudstone group 1, fine sandstone, mudstone group 2, medium sandstone, and mudstone group 3. Materials were mingled with sand, gypsum, water, calcium carbonate, and mica powder. Under the condition of the uniaxial compression test and the strength similarity ratio, the ratio of the material contents was determined based on the existing results [49]. In this work, there were eight materials, as shows in

Table 1. Materials used in the physical model.

Lithology	Sand (kg)	Calcium Carbonate	Gypsum	Amounts	Water
		(kg)	(kg)	(kg)	(L)
Mudstone group 3	70.31	7.03	7.03	84.38	9.38
Medium sandstone	158.20	15.82	36.91	210.94	23.44
Mudstone group 2	585.94	58.59	58.59	703.13	78.13
Fine sandstone	189.84	18.98	44.30	253.13	36.16
Mudstone group 1	386.72	38.67	38.67	464.06	51.56
Limestone	142.38	14.24	33.22	189.84	27.12
Coal seam 15	79.98	5.71	5.71	91.41	10.16
Mudstone	120.54	10.04	10.04	140.63	15.63

and

Table 2. Parameters of the prototype and model.

Lithology	UCS of Proto-Type	UCS of Model	Density of Proto-Type	Density of Model	Thickness of Proto-Type	Thickness of Model
	(MPa)	(kPa)	(kg/m3)	(kg/m3)	(m)	(cm)
Mudstone group 3	35.27	144.06	2265	1480	10.00	6.25
Medium sandstone	70.09	286.30	2564	1676	23.00	9.38
Mudstone group 2	35.27	144.06	2325	1520	50.00	31.25
Fine sandstone	74.61	304.81	2608	1705	18.00	11.25
Mudstone group 1	35.27	144.06	2105	1376	33.00	20.63
Limestone	71.83	293.42	2432	1590	13.50	8.44
Coal seam 15	24.83	101.41	1405	918	6.50	4.06
Mudstone	29.71	121.35	2512	1642	10.00	6.25

. In total, 1733.91 kg sand, 169.10 kg calcium carbonate, 234.49 kg gypsum, and 25 kg mica powder were used in this model.

Eight physical geological layers were modeled and compacted one by one, and every geological layer was separated with certain mica powder. After two months of the model completion, the longwall face was retreated successively from the panel center to panel boundary to simulate the mechanical behavior of hard roofs. In each stage, 50 mm long coal was excavated by using a mini shovel after 5 min. Then, the next excavation was conducted after 20 min. A universal camera was used to directly observe and record the physical configuration and loading conditions of hard roof structures. The typical results are shown in Figure 4 and Figure 5. The detailed characteristics of IHRS are described in Section 2.2.

2.2. Physical Configuration and Loading Conditions of IHRS

IHRS, consisting of a lower key structure, middle soft interlayer, and upper key structure, are governed by the mechanical behavior of the lower and upper key structures, as shown in Figure 6. The lower key structure, loaded by the middle soft interlayer, is stable with the supports of the lower structure I, the lower structure III, and the gob floor. The middle soft interlayer, supporting the upper key structure partly and loading the lower key structure entirely, is the transfer medium of the force between the upper and lower key structures. The upper key structure, loaded by the overlying strata, is stable with the supports of the upper structure II, the middle soft interlayer, and the compaction rock mass. The interactional upper structure II and upper structure III, loaded by the overlying strata, are stable with the supports of the upper key structure.

2.3. Mining-Induced Failure Criteria of IHRS

Mining-induced failure criteria are proposed based on the physical configuration and loading conditions of IHRS. As additional abutment stress loaded on the upper key structure increases, the supporting stress transferred from the middle soft interlayer to the lower key structure shows an increasing trend. The lower key structure and the middle soft interlayer fall down when crushing failure or slippage failure is generated in the contact face between the lower key structure and the lower structure I. The upper key structure is subjected to the new fracture movement when the action force between the upper and lower key structure vanishes.

The mining-induced failure criteria for IHRS can be divided into three processes, as shown in Figure 7. In Process 1, the gradual increase of additional abutment stress, which belongs to IHRS boundary condition, is the main external factor for the failure of IHRS. In process 2, the yielding at the lower key structure where crushing failure or slippage failure occurs on the contact surface is the main internal factor of IHRS failure. The fracture of the upper key structure, induced by the shear failure or tensile failure of the rock materials, is another internal factor for the failure of IHRS in Process 3. The crushing failure or slippage failure of the contact face is the result of Process 1 and the cause of Process 2. Similarly, the vanishing of the action force between the upper and lower key structures is the result of Process 2 and the cause of Process 3.

3. Validation of the Mining-Induced Failure Criteria

3.1. Process of the Increasing Additional Abutment Stress

The additional abutment stress, which is generated from overlying loads above the gob, has a loading effect on the rock around the gob [50]. With the distance from the working face to the location of minimum additional abutment stress, the additional abutment stress increases gradually. Then, it decreases gradually as the distance to the mining working face decreases from the beginning of the maximum value, as shown in Figure 8 [5]. There are four feature points on the curve of the additional abutment stress, including the points of the residual value (0, y₁), the maximum value (w, y₂), the any value (d₃, y₃), and the minimum value (∞, y₄).

$$F_a=L_I{}^{\prime }\{\begin{array}{ll}{a}_{1}d+a_2-{\gamma }^{\prime }\mathrm{H}& d<w\\ a_3{e}^{a_4(w-d)}+a_5-{\gamma }^{\prime }\mathrm{H}& d\ge w\end{array}$$

(2)

where F_a is the additional abutment stress in the front of the mining working face, kN; a₁, a₂, a₃, a₄, and a₅ are parameters of the mathematical model, which can be obtained in Equation (3); d is the distance to the mining working face, m; w is the distance between the working face and the location of the maximum value of the additional abutment stress, m; γ′ is the average volume weight of the geological strata, which can be calculated by the ratio of the cumulative sum of every strata’s volume weight, thickness, and the cumulative thickness of geological strata, kN/m³; H is the cumulative thickness of the geological strata, m.

$$\{\begin{array}{l}{a}_1=\frac{(y_2-y_1)}{w}\\ a_2=y_1\\ a_3=y_2-y_4\\ a_4=\frac{1}{w-d_3}\ln \frac{y_3-y_4}{y_2-y_4}\\ a_5=y_4\end{array}$$

(3)

3.2. Process of the Yielding for the Lower Key Structure

Since the lower structure tends to rotate around the base corner under the action of additional abutment stress, the lower key structure will lose the support of the lower structure III. The mechanical model is shown in Figure 9. The slippage failure occurs in lower key structure when the horizontal friction force R₁ and the vertical friction force R₂ are insufficient; crushing failure occurs when the crushing strength of the contact face is insufficient.

In Figure 9, F_g is the weight of the middle soft interlayer and the lower key structure, kN. F_g can be calculated by Equation (4). F_p is the the loading transferred from the upper key structure, kN; R₁ is the horizontal friction force between the lower key structure and the gob floor, kN; F_b is the vertical support force of the gob floor, kN; R₂ is the vertical friction force between the lower key structure and the lower structure I, kN; T is the horizontal support force of the lower structure I, kN; h_L is the thickness of the lower key structure, m.

$$F_g={\gamma }_L(L_{II}{h}_L+L_{II}{h}_{LS}\cos \theta )$$

(4)

where γ_L is the average volume weight of the lower key structure and the middle soft interlayer, kN/m³. γ_L can be calculated by the ratio of the cumulative sum of their volume weight and thickness and the cumulative thickness of them, kN/m³; h_LS is the thickness of the middle soft interlayer, m.

In the mechanical analysis, the equilibrium equation can be obtained in Equation (5). When the horizontal friction force R₁ reaches the ultimate value (F_btanφ_f) and the vertical friction force R₂ reaches the ultimate value (F_btanφ_b), slippage failure occurs in the lower key structure. Therefore, the first and second relationships are obtained, as shown in Equation (5). According to the static equilibrium, the resultant force along the vertical direction, the resultant force along the horizontal direction, and the resultant moment of any point all equal to zero, then the third, fourth, and fifth relationships are obtained in Equation (5). In addition, when the crushing stress (T/a) reaches the ultimate value (η_pσ_c), crushing failure of structure occurs, then the sixth relationship is obtained in Equation (5). After solving Equations (4) and (5), the criteria can be obtained in Equations (6) and (7) to protect the lower key structure from slippage failure and crushing failure.

$$\{\begin{array}{l}{R}_1\le F_b\tan {\phi }_f\\ R_2\le T\tan {\phi }_b\\ R_1=T\\ F_b=F_g+F_p-R_2\\ T{L}_{II}\sin \theta +R_2{L}_{II}\cos \theta =(F_g+F_p)(L_{II}\cos \theta -h_L\sin \theta )/2\\ T/a\le {\eta }_p{\sigma }_c\end{array}$$

(5)

$$f_1=\frac{h_L}{L_{II}}-\frac{1-2\tan \theta \tan {\phi }_f-\tan {\phi }_b\tan {\phi }_f}{\tan \theta +\tan \theta \tan {\phi }_b\tan {\phi }_f}\ge 0$$

(6)

$$F_p\le \frac{{\eta }_p{\sigma }_c(h_L-d_s)(L_{II}\sin \theta +L_{II}\cos \theta \tan {\phi }_b)}{L_{II}\cos \theta -h_L\sin \theta }-{\gamma }_L(L_{II}{h}_L+L_{II}{h}_{LS}\cos \theta )$$

(7)

where tanφ_f is the frictional coefficient of the gob floor; tanφ_b is the frictional coefficient of the lower structure I; a is the area of the contact face between the lower key structure and lower structure I as shown in Figure 7, which can be calculated by Equation (8) [51], m²; η_p is the ratio of the crushing strength and the uniaxial compressive strength for the lower key structure; σ_c is the uniaxial compressive strength of the lower key structures, kPa; f₁ is the criteria of the slippage failure of the lower key structure; L_II can be calculated by the empirical Equation (9) [52], m; θ can be calculated by Equation (10).

$$a=\frac{1}{2}(h_L-L_{II}\sin \theta )$$

(8)

$$L_{II}=\frac{2h_L}{17}\sqrt{\frac{R_T}{3q}}(\sqrt{\frac{100R_T{h}_L^2}{3sq}+102}-10\frac{h_L}{s}\sqrt{\frac{R_T}{3q}})$$

(9)

$$\theta =\arcsin (\frac{d_s}{L_{II}})$$

(10)

where R_T is the tensile strength of the lower key structure, kPa; q is the uniform stress loaded on the structures, kPa.

Once the strength exceeds the loading (see Figure 6), the hard roof can fracture into several parts. After that, the oblique part will contact with the adjacent part. This area is called the contact face, and it can be calculated by Equation (8). In addition, the oblique part is the lower key structure, whose length is related to the thickness h_L, tensile strength R_T, loading on the hard roof q, and length of the gob s. Then, the length of the lower key structure can be calculated by Equation (9). Finally, the dip angle of the lower key structure θ is established based on the mechanical model in Figure 9.

3.3. Process of the Fracture for the Upper Key Structure

The mechanical models of the upper structures are shown in Figure 10. When the vertical friction force R cannot support the overburden weight, slippage failure occurs in the upper structure II and upper structure III; when the crushing strength of the contact face cannot support the crushing force, crushing failure occurs. After the vanishing of the action force F_P′ between the upper and lower key structures, the upper key structure is subjected to the tensile failure or shear failure when the bending moment and shear force are large enough.

In Figure 10, F_gI′ is the weight of the upper soft interlayer and the upper key structure, and it can be calculated by Equation (11), kN; F_g′ is the weight of the upper soft interlayer, the upper structure II, and the upper structure III, and it can be calculated by Equation (12), kN; R is the friction force between the upper key structure and the upper structure II, kN; R′ is the shear force between the upper key structure and the upper compaction strata, kN; T′ is the horizontal crushing force of the upper structures, kN; M is the force moment of upper key structure, kN∙m. F_P′ is the support force of upper key structure by the middle soft interlayer which is the reaction of F_P, kN; h_u is the thickness of the upper key structure, m.

$$F_{gI}{}^{\prime }={\gamma }_u(h_u+h_{us})L_I{}^{\prime }$$

(11)

$$F_g{}^{\prime }={\gamma }_u(h_u+h_{us})(2L_{II}{}^{\prime }+L_{III}{}^{\prime })$$

(12)

where γ_u is the average volume weight of the upper key structure and the upper soft interlayer, which can becalculated by the ratio of the accumulated volume weight of multi-layer strata to the accumulated thickness of these strata, kN/m³; h_us is the thickness of the upper soft interlayer above the upper key structure, m.

In the mechanical analysis, the criteria are obtained in Equations (13) and (14) to protect the upper structure II and upper structure III from slippage failure and crushing failure. Similarly, the criteria are obtained in Equations (15) and (16) to protect the upper key structure from tensile failure and shear failure.

$$f_2=h_u-\frac{L_{II}{}^{\prime }(L_{II}{}^{\prime }+L_{III}{}^{\prime })}{2L_{II}{}^{\prime }+L_{III}{}^{\prime }}\tan {\phi }_b{}^{\prime }\le 0$$

(13)

$$f_3=h_u{}^2-\frac{{\gamma }_u{L}_{II}{}^{\prime }(L_{II}{}^{\prime }+L_{III}{}^{\prime })}{{\eta }_p{}^{\prime }{\sigma }_c{}^{\prime }}(h_u+h_{us})\ge 0$$

(14)

$${\sigma }_{\max }=\frac{3(F_{gI}{}^{\prime }+F_a+F_g{}^{\prime }-F_p{}^{\prime })L_I{}^{\prime }}{h_u{}^2}\le R_T{}^{\prime }$$

(15)

$${\tau }_{\max }=\frac{2F_{gI}{}^{\prime }+2F_a+F_g{}^{\prime }-F_p{}^{\prime }}{2h_u}\le [\tau ]$$

(16)

where f₂ is the criterion of the slippage failure of the upper structure II and upper structure III; f₃ is the criterion of the crushing failure of the upper structure II and upper structure III; σ_max is the maximum value of the tensile stress in the upper key structure, kPa; τ_max is the maximum value of the shear stress in the upper key structure, kPa; L_II′ can be calculated by the empirical Equation (17) [52], m. This method is similar to the calculation of Equation (9) in Section 3.2; L_III′ can be calculated by the Equation (18), m. L_III′ is related to the length of the gob, the length of the upper key structure, and the length of the upper structure II, as shown in Figure 6. L_I′ is assumed as ζ times of L_II, m; tanφ_b′ is the frictional coefficient of the upper structures; η_p′ is the ratio of the crushing strength and the uniaxial compressive strength for the upper key structure; σ_c′ is the uniaxial compressive strength of the upper key structure, kPa; F_gI′ can be calculated by the Equation (19), kN. The background of F_gI′ is explained in Equation (12); F_g′ can be calculated by the Equation (12), kN; R_T′ is the tensile strength of the upper key structure, kPa; [τ] is the shear strength of the upper key structure, kPa.

$$L_{II}{}^{\prime }=\frac{2h_u}{17}\sqrt{\frac{R_T{}^{\prime }}{3q}}(\sqrt{\frac{100R_T{}^{\prime }{h}_u^2}{3q(s-L_I{}^{\prime })}+102}-10\frac{h_u}{s-L_I{}^{\prime }}\sqrt{\frac{R_T{}^{\prime }}{3q}})$$

(17)

$$L_{III}{}^{\prime }=s-2(L_I{}^{\prime }+L_{II}{}^{\prime })$$

(18)

$$F_{gI}{}^{\prime }={\gamma }_u(h_u+h_{us})L_I{}^{\prime }$$

(19)

3.4. Limitation of the Additional Abutment Stress

When tensile failure is generated in the upper key structure, the deflection is δ times of the ultimate value, which can be used as the deformation compatibility condition. According to this condition, the limitation of the additional abutment stress can be calculated by Equation (20). The ultimate value of the deflection for the upper key structure can be calculated in Equation (21). The additional abutment stress reaches the limitation value, once the action force F_p′ between the upper and lower key structure reaches the limitation value of F_p in Equation (7). Thus, the final calculation method of the limitation of the additional abutment stress can be obtained by taking the Equation (7) and Equation (21) into Equation (20), as shown in Equation (22).

$$F_a{}^{\prime }=\frac{F_p{}^{\prime }-F_{gI}{}^{\prime }}{L_I{}^{\prime }}-\frac{4F_g{}^{\prime }}{3L_I{}^{\prime }}-\frac{8\delta {\omega }_{\max }EI}{{(L_I{}^{\prime })}^4}$$

(20)

$${\omega }_{\max }=-\frac{R_T{}^{\prime }{L^{\prime }}_I{}^2}{2E{h}_u}$$

(21)

$$F_{\max }=\frac{{\eta }_p{\sigma }_c(h_L-d_s)(L_{II}\sin \theta +L_{II}\cos \theta \tan {\phi }_b)}{\zeta L_{II}(L_{II}\cos \theta -h_L\sin \theta )}-\frac{2\delta R_T{}^{\prime }{h}_u^2+4(s-2\zeta L_{II})F_g{}^{\prime }}{3{\zeta }^2{L}_{II}^2}-\frac{F_g+F_g{}^{\prime }}{\zeta L_{II}}$$

(22)

4. Application for a Field Case

4.1. Input Parameters

The method of the in situ investigation, laboratory test, and data fitting were used to determine the input parameters of IHRS. The results in a field case of Yangquan coal mine are shown in

Table 3. Parameters of IHRS.

Lower Key Structure		Upper Key Structure		Mathematical Parameters
hL/(m)	13.5	hu/(m)	18	a1	2.66
hLS/(m)	33	hus/(m)	50	a2	5.36
γL/(kN/m3)	22,000	γu/(kN/m3)	24,000	a3	22.5
RT/(MPa)	15	RT′/(MPa)	22	a4	0.10
s/(m)	220	ζ/(1)	0.5	a5	15
ds/(m)	6.5	[τ]/(MPa)	30	w0	12.08
ηp/(1)	0.36	E/(MPa)	5 × 104	y1	5.36
σc/(MPa)	72	δ/(1)	1	y2	37.49
φb/(°)	40	ηp′/(1)	0.4	y3	25.19
φf/(°)	30	σc′/(MPa)	75	y4	15
		φb′/(°)	50	d3	20

.

4.2. Output Results

The geometrical and mechanical characteristics of the lower key structure and upper key structure are calculated in

Table 4. Characteristics of IHRS.

Lower Key Structure		Upper Key Structure
L/(m)	17.61	L/(m)	27.27
LII/(m)	19.33	LI′/(m)	9.67
LIII/(m)	181.34	LII′/(m)	28.50
ds/(m)	2.47	LIII′/(m)	143.66
θ/(°)	14.81	FgI′/(MPa)	1.63
Fg/(MPa)	1.00	Fg′/(MPa)	1.63

. IHRS are in the stable state (f₁ > 0, f₂ < 0, and f₃ > 0) when additional abutment stress equals to zero. However, failure of IHRS can occur when the additional abutment stress reaches the limitation value 7.37 MPa.

4.3. Failure Process

As shown in Figure 11a, when the additional abutment stress reaches 7.37 MPa at 23 m away from the longwall working face, yielding of the lower key structure and middle soft interlayer are induced. At the same time, as the force between the upper key structure and the lower key structure vanishes instantaneously, the shear stress is less than the shear strength, and the tensile stress is greater than the tensile strength of the upper key structure, as shown in Figure 11b,c. The fracture of upper key structure occurs due to the tensile failure.

5. Discussion

Liberating energy is an effective index to describe the interactional effects between hard roof structures. According to the method of the elastic deformation energy [53], the liberating energy from the upper key structure fracture can be calculated as 2.35 × 10⁵ J in Equation (23). If the force F_p does not exist, the upper key structure changes into a single structure and remains stable just when the additional abutment stress F_a′ changes into the upward tensile stress. Thus, the additional abutment stress F_a′ is a negative value in Equation (23). Liberating energy of 1.78 × 10⁵ J from the single upper key structure calculated by Equation (23) is clearly less than that of 2.35 × 10⁵ J from the upper key structure in IHRS.

$$V_{\epsilon }=\frac{R_T{}^{\prime }{(L_I{}^{\prime })}^2}{20E{h}_u}(4F_{gI}{}^{\prime }+4F_a{}^{\prime }+5F_g{}^{\prime })$$

(23)

The upper key structure is able to bear the additional abutment stress, when the force F_p exists, and it is subjected to tensile failure when the force F_p vanishes, as shown in Figure 11c. The tensile stress is distinctly larger than the tensile strength, even though the additional abutment stress equals zero (Figure 11a,c) when the force F_p vanishes. This result indicates that the tensile failure and liberated energy before the loading of the additional abutment stress can be generated by a single layer of the upper key structure. Besides, the greater liberating energy from the upper key structure in IHRS is also explained.

Mining-induced failure criteria can be used to effectively analyze the mechanical behavior of IHRS and determine the limitation value of the additional abutment stress. The results are helpful to protect the underground openings nearby IHRS from large deformation, such as roof sinking, floor heave, rib displacement, support failure, and even roof caving of the openings in 30 m away from the mining working face in Yangquan coal mine (Figure 12). The peak value of the deformation rate of the entry roof nearby IHRS is located between 20 m and 30 m from the mining working face. This curve shows an upward and downward trend, rather than a steady trend (Figure 13). The technologies of hydraulic fracturing to weaken hard roofs in advance have been gradually accepted in coal mines of China recently [54,55,56].

In mining engineering, there are two requirements for the application of the proposed mining-induced failure criteria: (1) There is a soft layer being sandwiched between the two interactional hard roof structures; (2) the equilibrium condition of structures should satisfy Equations (6), (13), and (14). Further, correlative parameters of IHRS need to be re-determined considering the varying geological conditions. For example, d_s, the distance between the gob floor and the contact position of the lower structures, can be changed when the immediate roof is soft. In the physical model, unexcavated zones on both sides of the coal seam is used to reduce the influence of model boundary on IHRS. The model is not a standard two-dimensional stress model since free boundaries are exposed to air and subject to atmospheric pressure.

6. Conclusions

Mechanical behavior of the interactional hard roof structures (IHRS) has a great influence on the nearby underground openings in longwall mining engineering. IHRS consist of three parts: The lower key structure, the middle soft interlayer, and the upper key structure. The lower key structure, loaded by the middle soft interlayer, is the supporting part in IHRS. The middle soft interlayer is the transfer medium of the force between the upper and lower key structures. The upper key structure, loaded by the overlying strata, mainly plays a loading role on the middle soft interlayer in IHRS.

The mining-induced failure criteria were validated by the mechanical behavior of IHRS in a mechanical analysis model. The failure of IHRS was divided into three processes: The increase in the additional abutment stress, the yielding of the lower key structure, and the fracture of the upper key structure. Yielding of the lower key structure was caused by the crushing failure on the contact face when the additional abutment stress reaches the limitation value. After that, the action force between the upper and lower key structures vanishes and the fracture of upper key structure occurs due to the tensile failure.

Under the condition of a field case, the failure of IHRS occurs at 23 m away from the mining working face with the total energy release of 2.35 × 10⁵ J when the additional abutment stress reaches the limitation value of 7.37 MPa. Meanwhile, there is strong mining pressure such as large deformation with ups and downs within a short time in the underground opening near IHRS within 30 m ahead of working face. This phenomenon proves the reliability of mining-induced failure criteria. Since IHRS may be in different environments under different engineering geological conditions, the analysis should be performed in similar ways to this paper.