Characteristics of Stress Transfer and Progressive Fracture in Overlying Strata due to Mining-Induced Disturbances

In this study, based on the mining of the 13210 working face in the Yima coal mine of the Gengcun village, China, a simplified mechanical model for the analysis of dynamic destabilization of the overlying strata during undergroundmining was constructed. .e numerical simulation was used to analyze the stress patterns in the advanced abutments of the tunnel face and the characteristics of dynamic failures in the overlying strata. Furthermore, similitude experiments were conducted to study the process of stress release and deformation in the overlying strata, and to analyze the effects of overburden destabilization on the ground surface settlement. .e theoretical analysis indicated that if the geometric parameters of a working face are fully determined, a stiffness ratio no greater than 1 is required for dynamic destabilization to occur. .e numerical simulation results show that the stress in the overlying strata decreases with a decrease in distance from the tunnel face. .e stresses in the advanced abutments initially increase with an increase in distance from the tunnel face, followed by a decrease in stress, and an eventual stabilization of the stress levels; this corresponds to the existence of a “stress build-up zone,” “stress reduction zone,” and “native rock stress zone.” In similitude experiments, it was observed that a “pseudoplastic beam” state arises after the local stresses of the overlying strata have been completely released, and the “trapezoidal” fractures begin to form at stress concentrations. If the excavation of the working face continues to progress, the area of collapse expands upward, thereby increasing the areas of the fracture and densification zones. Owing to the nonuniform settlement of the overlying strata and the continuous development of bed-separating cracks, secondary fractures will be generated on both sides of the working face, which increase the severity of the ground surface settlement.


Introduction
In recent years, problems caused by underground mining, such as surface subsidence, rock burst failures in the working face, and overlying strata fractures, have become increasingly prominent [1].Since the inception of mining subsidence studies in the beginning of the twentieth century, a large body of research works has accumulated on mininginduced ground settlement and overlying strata failures.
ese research works generally include theoretical analyses, numerical calculations, and experimental studies.e theoretical studies on mining subsidence helped develop the masonry beam theory [2], key strata theory [3,4], and supporting plate theory [5].
e numerical approaches may be generally divided into two categories.
e first category pertains to methods based on continuum mechanics, for example, the finite element method (FEM), finite difference method (FDM), boundary element method (BEM), and element-free method (EFM).e second category of methods is based on discontinuum mechanics, which includes the discrete element method (DEM) and discontinuous deformation analysis (DDA) [6][7][8].In experimental studies, the similitude experiment is the most broadly used experimental tool for studying ground subsidence.ese experiments are straightforward to perform and provide an accurate reflection upon mining-induced ground deformations and change patterns in overburden stresses.
In this study, we briefly discuss the most important gaps in the current literature regarding stress transfers and failures in the overlying strata during underground mining processes.In the theoretical aspect, the mechanisms of rock burst failures in the overburden during underground mining remain unclear, and a consistent understanding is yet to be achieved on the overburden's deformation and failure processes, or its stress distribution patterns.In numerical simulations, the FEM and FDM are highly effective methods for simulating the properties of a material in continuum states.However, these methods are incapable of simulating the process in which a material changes from a continuous to discontinuous state, and they cannot reveal the dynamics of a material in a discontinuous state.e block-discrete element method (B-DEM) and granular DEM have certain advantages in the simulation of noncontinuum dynamics; however, it is still difficult to simulate the continuous deformation processes of a material using these methods [9].Although similitude experiments can produce patterns that are consistent with actual engineering works, these experiments lack in precision.Consequently, the similitude experiment results often have to be verified against theoretical analyses or numerical calculations.
In this study, we constructed a mechanical model for the analysis of dynamic failures in a working face, in the presence of disturbances caused by underground mining, based on the effects of working face excavation on the stress states of the overlying strata.Further, this model was used to provide the criterion for the dynamic failures in the overburden of the working face.Based on the numerical methods of the continuum-discontinuum element method (CDEM), FEM and DEM were coupled to each other to simulate the deformations and dynamics of the overburden in continuous and discontinuous states.is allows the progressive failure of the overlying strata to be analyzed as it transitions from a continuous mass to a discontinuous mass.e similitude experiments were conducted to investigate the stress relief and deformation in the overburden and to analyze the effects of overburden failure on the ground settlement.Finally, the dynamics of stress transfers and failures in the overburden during mining process were obtained via a comprehensive analysis of the results obtained from our theoretical analyses, numerical calculations, and similitude experiments.

A Dynamic Model for Underground Resource Mining
During the underground mining processes, the stress state of the overburden changes from the native state to a state with rising axial stresses and decreasing confining stresses, until failure finally occurs.e overburden failure and destabilization is triggered by the superposition of dynamic and static loading; this is already broadly recognized and accepted as a dynamic problem [10][11][12].In [13][14][15], it was observed that the excavation-induced unloading transforms the triaxial stress state of the overburden around the working face into a biaxial stress state, causing a rapid release in the stresses that were concentrated within the overburden, thereby triggering dynamic failures.Based on this analysis, we devised a simplified mechanical model for the analysis of dynamic overburden failures during the excavation of a working face using the 13210 working face in the Yima coal mine of the Gengcun village as an example, as shown in Figure 1.
Supposing that p db is the pressure acting on the roof, k db is the stiffness of the roof, u db is the deformation of the roof, p s is the load acting on the elastoplastic zone, k s is the stiffness of the elastoplastic zone, p t is the load acting on the elastic zone, k t is the stiffness of the elastic zone, a is the total sinkage of the roof, u c is the deformation of the excavation layer, and the roof may be treated as an elastic body.e conditions for equilibrium are as follows: In [16], it was observed that strain softening occurs in the elastoplastic zone of rock masses.erefore, a nonlinear constitutive equation is used here: where E is the initial elastic modulus and ε c is the peak strain.e elastoplastic zone of the excavation strata has a width of B and a thickness of H. e relationship between load and deformation under unit length conditions is as follows: where λ � EB/H is the initial stiffness and u 0 is the settlement of the roof when the roof's strain reached the peak value.e second derivative of (3) was taken to determine the inflection point of the load-versus-deformation curve for the elastoplastic zone; an inflection point occurs at u c � u 1 � 2u 0 , and the absolute gradient of the curve is λ 1 � λe −2 .Refer to [13] to determine the energy composition of the overlying strata.e system strain energy consists of the top plate and excavation layer strain energies.e total potential energy is as follows: e first derivative of (4) was set to 0 to obtain the equilibrium surface equation: e deformation at the cusp of the equilibrium surface, u c � u 1 � 2u 0 , is exactly the same as the inflection point of the elastoplastic zone's constitutive curve.e Taylor expansion was performed on (5) with u � u 1 up to the third term, which gives e point mutation theory discussed in [17] was used to obtain the standard form of the surface equation: where x (u − u 1 )/u 1 is the state variable of the system, while p and q are the control variables: where η is a dimensionless parameter that is a function of a. e bifurcation set is as follows: e substitution of ( 8), ( 9), (10), and ( 11) into (12) yields the following: Equation ( 13) is the mechanical criterion for the occurrence of rock burst failures in this system.Based on (13), it can be inferred that a sudden change occurs in the system when p ≤ 0; which implies that k ≤ 1 is a prerequisite for the occurrence of sudden destabilizations in the system.erefore, one of the conditions for the occurrence of dynamic failures in the overlying strata of this study is a sti ness ratio no greater than 1.Furthermore, a dynamic failure can occur only if soft softening has occurred in the overburden after the geometric parameters were fully determined.

Continuous-Discontinuous Deformation
Theory of Overlying Strata during Underground Mining

Basic Principle.
According to the dynamic model for underground resource mining, the continuum-based discrete element theory is adopted is this study [18].It contains two kinds of elements: blocks and contacts [19] (Figure 2).A discrete block consists of one or more FEM elements that share the same nodes and faces.A contact contains several normal and tangent springs, and each spring owns two nodes that belong to two di erent blocks.e FEM is used inside a block; while the DEM is adopted for a contact.

Governing Equation.
In the discontinuous deformation theory, the governing equation is the motion equation.e block is subjected to internal and external forces.e internal force includes the damping and deformation forces.e external force includes the external boundary force and the force between springs.As the block body is regarded as a continuous and isotropic linear elastic body, its mechanical properties can be described by the basic di erential equations of three-dimensional elastodynamics [20,21], which are as follows: equilibrium equation: geometric equation: physical equation: Boundary condition: u i u i (on the displacement boundary of Γ u ) and σ ij n j T i (on the force boundary of Γ σ ).

Advances in Civil Engineering
Here, σ ij , u i , f i , and T i are the stress, displacement, volume force, and area force, respectively; Ω and Γ denote the rock block region and its boundary, respectively; Γ � Γ u ∪ Γ σ , λ and G are the Lame constants; ρ and μ denote the mass density and damping coefficient, respectively; and δ ij is the Kronecker delta function.
Based on the elastic variational principle [20], the governing equation is as follows: where € u(t), _ u(t), and u(t) are the acceleration, speed, and displacement arrays, respectively.[M], [C], [K], and [Q] are the mass matrix, damping matrix, stiffness matrix, and nodal load array, respectively.
When we solve the governing equations, the first step is to loop each deformable block and calculate the corresponding continuous deformation.
e second step is to calculate the surface force.When we calculate the surface force, the stiffness matrix and nodal displacement are used to calculate the elastic force; the damping matrix and nodal velocity are used to calculate the damping force.Finally, the equation of motion is solved using the direct integral method.e specific equations are as follows: elastic force: damping force: Solution of the equation of motion using the direct integral method: e acceleration, velocity, and displacement of the block body nodes can be calculated by (20), where f out i includes the interface and contact forces.It is observed that the interface force is determined by the boundary conditions.

Model Boundary.
Based on the block contact theory proposed in [19], a mechanical model is proposed to describe the interaction between the two blocks.When the deformation of the material is continuous, the force between adjacent blocks is calculated based on the nodal displacement: where F n is the normal force of the spring, K n is the normal stiffness of the spring, Δu n is the normal displacement vector difference for the spring-connected blocks, F s is the tangential force of the spring, K s is the tangential stiffness of the spring, and Δu s is the tangential displacement vector difference for the spring-connected blocks.
When the deformation of the material is discontinuous, the fracture of the spring is used to simulate deformation.
e spring has two types of damage: tensile and shear failures.When the normal force of the spring is greater than the tensile strength of the material, the material suffers from tensile failure.e normal and tangential forces between the adjacent blocks are zero, that is, After the spring suffers from the shear failure, the blocks will slide relative to each other; thus, there is pressure and friction.Among them, the pressure is equal to the product of the normal stiffness of the spring and the difference of the displacement vector, and the friction is equal to the product of the normal force and the friction coefficient.Under these conditions, the direction of friction is opposite to the motion direction of the block.us, where tan φ is the friction coefficient and φ is the internal friction angle of the material.

Calculation
Steps. e dynamic relaxation method discussed in [22] is used to solve equations.
e static problem is transformed into a dynamic problem by introducing damping.Figure 3 shows the main process of this method.

Numerical Simulation and Physical Model
Test for Underground Mining e rectangular roadway section has a length of 5 m and a width of 4 m.e bottom surface of the model is fully constrained, the horizontal level of the model is surrounded, and the roof is a free surface.e working face is shown in Figure 4, and the numerical calculation model is Advances in Civil Engineering shown in Figure 5. Referring to the arrangement of the stress and displacement monitors (#1, #2, #3, and #4) shown in Figure 5, the monitor points for the numerical simulation were set.In Figure 5, the different colors represent the geologic bodies with different mechanical properties.Groups   Advances in Civil Engineering stresses of the advanced abutments and the deformational patterns of the overlying strata during mining conditions are shown in Figure 6. Figure 6(a) shows that the deformation of the overburden is relatively small during the initial stages of working face mining (advancement up to 4 m), and the deformation of the overburden increases with a decrease in distance from the tunnel face.e deformation of the overburden decreases and eventually stabilizes with an increase in distance from the tunnel face.In addition, it is observed that the stress values decrease with a decrease in distance from the tunnel face.As this distance increases, the advanced abutments of the tunnel face exhibit an increase in stress, followed by a decrease, and nally the stabilization of stress levels; this is indicative of the existence of a "stress build-up zone," "stress reduction zone," and "native rock stress zone." e stress monitoring data also indicate that the area of e ect of the working face's excavation is approximately 30 m, and the stress peak is located approximately 16 m in front of the tunnel face.
e continued excavation of the working face expands the area of the goaf and increases the deformation of the overlying strata.e stresses of the abutments gradually propagate toward the front of the working face, whereas a gradual decrease in stress occurs in the strata behind the excavation surface, accompanied by an increase in vertical displacement.is is because the strata overlying the goaf are beginning to sink under their own weight, which is because the yield strength of the strata is gradually being exceeded [23][24][25].e overburden will ultimately collapse when its deformation reaches a critical value.As shown in Figure 6(b), the displacement of the overburden in front of the working face is relatively small when the excavation of the working face has advanced up to 48 m, whereas the displacement of the strata overlying the goaf in the back has increased.At the 40 m point, the displacement of the overburden reaches its maximum at 6 m and the corresponding stress is almost 31 MPa. is indicates that the overburden will completely collapse at this point of the roof; that is, the rst weighting of the main roof occurs with a weighting interval of 40 m. e stress data also show that large stresses occur at the 50 m and 60 m points.erefore, periodic collapses will occur in the overlying strata of the roof as the working face continues to be excavated, with a periodic weighting interval of 10 m.  e processes of failure and deformation in the overlying strata during working face mining are shown in Figures 7 and 8. e calculations indicate that local failures occur in the overburden of the coal seam when the working face excavation has progressed up to 4 m; when the working face reaches 8 m, the soft and weak strata of the false roof will collapse as excavation occurs.e immediate roof collapses when the excavation of the working face has advanced up to 20 m.When the excavation of the working face advances up to 48 m, the roof will fracture at the 40 m point; thus, forming the first weighting event.erefore, the first weighting interval is approximately 40 m. e rock mass near the working face will collapse after the occurrence of bending deformations, and the caved-in rock masses will fill the goaf.e overlying strata that are far from the tunnel face will collapse on a large scale after losing their bearing capacity [26,27].When the excavation of the working face has reached 100 m, the rock masses that are far from the working face will collapse continuously.e area of collapse will expand upward, leading to an appearance of fractures and bed separations in the overburden.Further, the rock masses of the separated strata sink under their own weight.is is followed by the appearance of three distinct zones in the overburden of the goaf: the collapse zone, fracture zone, and gradual settlement zone.If the excavation of the working face progresses up to 180 m, the bed-separating cracks will develop upward and the nonuniform settlement of the overburden leads to the generation of secondary fractures.e locally developed secondary fractures will then propagate to the surface, and the area of collapse in the overburden will extend in both directions of the working face.A severe degree of surface settlement ultimately results from these processes.

4.4.
e Progressive Fracture Characteristics and Deformation Law of the Overlying Strata under the Working Face Mining.A similitude model was constructed according to the methods discussed in [28][29][30] for studying the progressive failure and deformation of the overlying strata during the mining of the working face.Based on the similarity principles, the geometric, time, and stress similarity ratios were defined as 1/250, 1/2, and 450/1, respectively.e mechanical parameters of the prototype are listed in Table 1.
e similarity materials and their mixing ratios were determined according to [31,32].e progressive fracture and deformation of the overlying strata in a variety of mining conditions are shown in Figure 9. Referring to the numerical simulation results, the model test results are analyzed, and the similarities are given.In Figure 9(a), it is shown that the overburden remained largely intact when the excavation of the working face advanced up to 4 m, without showing any significant signs of damage.Figure 9(b) shows that the softer and weaker sections of the roof began to cave-in when the excavation of the working face reached 8 m; collapses also occurred in local sections of the overburden.In Figure 9(c), it is shown that the immediate roof collapsed when the excavation of the working face reached 20 m. e area of collapse in the overlying strata was expanded and the localized fractures that were formed previously began to propagate to the rest of the overburden.e bed-separating cracks have also formed in the overburden, which indicates that the stability of the overburden has begun to deteriorate.
e settlement of the overburden also becomes quite apparent in this stage.Figure 9(d) shows that the entirety of the overburden begins to collapse when the excavation of the working face reaches 40 m, which indicates that the overlying strata exhibits "pseudoplastic beam"-like mechanical characteristics upon the relief of local stresses in the overlying strata.is manifests as a downward sag at the center of the overburden and large displacements at the center.Fractures also occurred at stress concentrations on both ends of the working face, which led to the formation of a "trapezoidal" fracture.In addition, the bed-separating cracks continued to develop until they reached the surface of the Advances in Civil Engineering overburden; thus, these cracks display a tendency to propagate upward along the overburden.Figure 9(e) indicates that in the absence of abutments, the entirety of the overburden will collapse when the excavation of the working face reaches 100 m.In this figure, it is shown that the area of collapse has expanded upward and formed a distinct "three-zone" distribution.During the formation of this "three-zone" distribution, the constraints imposed by the compression of the strata and the "trapezoidal" fracture formed around the fractures cause the boundaries of the "three-zone" distribution to take a trapezoidal form.us, a trapezoidal compacted zone was formed in the deformed strata.In addition, the continued development of bedseparating cracks leads to the formation of 35-40 m wide fractured zones on both sides of the compacted zone.e continued excavation of the working face up to 180 m, under these conditions, led to the propagation of the collapsed zone to the ground surface, as shown in Figure 9(f).As the excavation continued, stress was transferred toward both sides of the overburden, which accelerated the development of fractures in the fractured zones.Some of the fractures in the fractured zone developed up to the ground surface.Furthermore, the nonuniform settlement of the overburden induced the generation of secondary fractures in the adjacent regions.Due to the disturbances caused by the secondary fractures and the subsidence of the overlying strata, one may surmise that severe ground surface settlement will occur after rock burst failures in the overburden [33,34].Based on [35][36][37], further excavation of the working face is no longer possible, and the excavation must be stopped to allow for an appropriate level of reinforcement.e results of this similitude experiment are consistent with those of the numerical calculations, thereby indicating that the results of both the experiments are valid.is also indicates that the results of the theoretical derivations are applicable for practical applications.us, the findings of this work will provide a useful source of scientific guidance for practical engineering works in the future.Advances in Civil Engineering

Conclusions
In this study, the destabilization mechanisms and the patterns of overburden deformation and failure during underground resource mining were investigated via theoretical analyses, numerical simulations, and model experiments, based on the excavation of the 13210 working face in the Yima coal mine of the Gengcun village.e following conclusions were drawn from this study: (1) e degradation of overburden mechanical properties due to mining-induced disturbances is an important factor for the occurrence of rock burst failures in the overlying strata.If the geometric parameters of the working face are fully determined, a sti ness ratio no greater than 1 is required for the occurrence of rock burst failures in the overburden.
(2) During the excavation of a working face, the stress values of the advanced abutments decrease with a decrease in distance from the tunnel face.As the distance from the tunnel face increases, the stresses acting upon the tunnel face's advanced abutments initially increase before decreasing and stabilizing at some value; this corresponds to the existence of the "stress build-up zone," "stress reduction zone," and "native rock stress zone" in the overburden.(3) During the mining processes, the overburden exhibits a "pseudoplastic beam" stress state upon the complete release of local stresses in the overburden.Further, a "trapezoidal" fracture is formed by the cracks at stress concentrations.e continued progression of excavation expands the area of collapse in the overlying strata and increases the areas of fracture and compacted zones.More stress will then be transferred toward both ends of the working face to form high-stress zones in these areas, which ultimately leads to the formation of a "three-zone" distribution.
(4) e progression of the working face excavation is accompanied by upward expansions in the overburden's area of collapse and propagation of upward-growing bed-separating cracks; these are the key factors for the occurrence of ground settlement.Further, the nonuniform settlement of the overburden induces the generation of secondary fractures, which in turn expands the area of collapse of the overburden toward either end of the working face; this is an important factor that causes the exacerbation of surface settlement.Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

Figure 1 :
Figure 1: Simpli ed mechanical model for the analysis of underground mining.

4. 1 .
Calculation Method and Model Parameters.e CDEM was used to perform the numerical calculations in this study.e numerical model shown in Figure 4 is established according to the actual size of the 13210 working face at the YIMA Gengcun (China) coal mine.e model size is set as 300 × 150 × 83 m. e model is divided into four layers, from top to bottom, as conglomerate, roof, coal, and floor; and their thicknesses are 44 m, 15 m, 9 m, and 15 m, respectively.e horizontal and vertical stresses are 20 and 17 MPa, respectively, and the depth of each mining is 4 m.

Figure 8 :
Figure 8: e fracture characteristics and vertical displacement variation of overlying strata during the working face mining.(a) Mining to 4 m, (b) mining to 8 m, (c) mining to 20 m, (d) mining to 40 m, (e) mining to 100 m, and (f ) mining to 180 m.
c tu r e d z o n e Cracks developed to the ground O v e r l y i n g s t r a t a c o l l a p s e (f )

Figure 9 :
Figure 9: Progressive fracture and deformation of the overlying strata during the mining of the working face.(a) Mining up to 4 m, (b) mining up to 8 m, (c) mining up to 20 m, (d) mining up to 40 m, (e) mining up to 100 m, and (f ) mining up to 180 m.
1-4 represent the conglomerate, roof, coal, and floor, respectively.Groups 5-17 represent the raw coal with different mechanical properties in front of the working face.e basic mechanical parameters of groups 1-17 are shown in Table 1.4.2.Stress Transfer Law and Distribution Characteristics of Overlying Strata during the Working Face Mining.e

Table 1 :
Material parameters of the numerical model.