# Method of Entry Layout under Synergistic Effects of Abutment Stress and Dynamic Stress

Authors: Wenlong Shen; Guocang Shi; Meng Wang; Tenglong Rong; Yungang Wang; Ruifeng Zhang; Xiangyu Wang; Jianbiao Bai
Journal: Shock and Vibration
 (2020)

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## Abstract

In underground mining engineering, rocks around the entry are always subjected to large plastic deformation disasters, such as supporting body failure, roof rock collapse, and even rock burst under abutment stress and dynamic stress. To improve the stability of these rocks, the entry layout under abutment stress and dynamic stress (ELAD) method was put forward to protect the entry from high abutment stress and dynamic stress. Dynamic disturbance intensity (DDI) was determined as the key evaluation index in ELAD, which was divided into “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type” by the dynamic disturbance threshold (DDT) and dynamic large-deformation threshold (DLT). The established servo calculation algorithm was applied into a dynamic and static numerical analysis model with FLAC3D500 software for the solving of DDT and DLT by the method of zero growth DDI of plastic failure zone and the engineering-permitted limitation deformation. This model was validated by comparing the displacement of entry with the measured results in the field. The model results validated that the entry should keep away from the dynamic stress of Violent Impact Type firstly and then be arranged in the zone where the dynamic stress belongs to Slightly Disturbed Type. DDT increases linearly and DLT decreases with a power function as the increasing of the abutment stress. ELAD method is reliable to protect this kind of underground entry and its applicability will be improved by the support resistance by comparing the results from ELAD with those from the widely used methods for field investigation discussion. The analysis procedure can be repeatable and necessary since the rock and coal materials may be different in geological and engineering conditions.


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## Body

## 1. Introduction

Underground space has become one of the widely used resources during social development in recent years, and it will provide security for human civilization for a long time in the future [1–3]. Entry is one of the underground spaces which mainly provides auxiliary transportation and ventilation function in the underground longwall mining engineering as the tail entry shown in Figure 1. Its stability is always governed by the loading stress, the mechanical behavior, and the support resistance. Influenced by the dynamic disturbance and the abutment stress, the stress will change into another state in the rock around the entry [4]. This entry will suffer from large deformation disasters, such as supporting body failure, roof rock collapse, and even rock burst when the disturbance and stress is large enough, which threatens the normal operation of mining engineering [5]. For a specific geological condition, reduction of the loading stress has been a popular way to protect this entry from large deformation disasters in longwall coal mining engineering [6].Figure 1
Geological and engineering conditions of the entry. (a) Mining engineering plan; (b) A-A cross section in (a); (c) local drilling histogram. The gob has been in consolidation before the tail entry driving begins. The tail entry with dimensions of 5.0 m in width and 4.0 m in height is arranged along the coal floor and it is going to be excavated after its location is determined.
(a)(b)(c)The loading stress mainly consists of original stress, abutment stress, and dynamic stress [7–9]. The abutment stress is the loading effect of the overburden rocks’ weight above the worked-out area on the rock around the worked-out area, which always results in the increasing of the stress in the rock [10]. The dynamic stress is the vibrational stress wave which comes from the rupture of rock, impact of caving rock, vibration of blasting, vibration of machines, and other physical motions, which always changes the strain rate of the rock [11]. The mechanical behavior of this rock has been divided into creep, static, weak dynamic, dynamic, and strong dynamic according to the strain rate [12]. The strength of the rock will increase surely with the increasing of the strain rate when the strain rate belongs to dynamic and strong dynamics. Differently, it keeps stabilization or increases slowly with the increasing of the strain rate when the strain rate belongs to static or weak dynamics. The entry will be subjected to tensile and shear fracture in brittle rock, and it will be yielded to large plastic deformation in soft rock during the coupled static-dynamic loading process [13–16]. The existing achievements, mainly concerning shallow-buried civil engineering [17–21] and underground metal mining engineering [22–26], provide precious guidance for analyzing the large deformation behavior of the entry in underground coal mining engineering [27–31]. Finding the mechanical behavior of rock around the entry under the synergistic effects of the abutment stress and dynamic stress is beneficial to the reduction of the large deformation.Loading stress relief methods can be divided into four widely used types, including solid backfilling technology, cutting roof technology, depressurizing borehole technology, and the entry layout technology [32]. The solid backfilling technology is able to protect the roofs from movement intensively and avoid the generation of abutment stress and dynamic disturbance [33–35]. However, the expensive material consumption makes the solid backfilling technology apply limitedly in the mining area where there are surface buildings, water sources, and railways. Cutting roof technology is good at reducing the abutment stress by changing the bearing structure of the roof [36–41]. However, the influences of remolded structures on the movement of the upper roof structures were not considered, and the cutting roof technology is restricted by working space, technical defects, and costs. Depressurizing the borehole technology has the ability to transfer the abutment stress from the area with a borehole to the area without borehole [42–45]. However, this borehole changes the mechanical behavior of the rock, always making the rock in reduction of strength, and it is fairly difficult to determine a reasonable borehole parameter. Relatively, entry layout technology has advantages in avoiding of high stress, reduction of costs, and increasing of resource recovery, which is the most popular method in coal mining engineering [46–48]. The famous Wilson’s equation [49] and ultimate balance theory [50, 51] can protect the entry from abutment stress but ignore the effects of dynamic disturbance. A new method needs to be found to design the location of the entry under the abutment stress and dynamic disturbance.In this work, ELAD method was put forward to design the location of the entry. Evaluation index was determined and judging criteria were established for ELAD. After that, a numerical analysis model with servo calculation algorithm was established and validated to solve the evaluation index. The result of ELAD method was compared with the results of several widely used methods. This comparison indicates that ELAD method has three advantages. In addition, a field investigation discussion also verified that ELAD method is reliable to design the location of the entry.


## 2. Method of ELAD

The amplitude of the stress wave was demonstrated as the significance influence factor of the entry deformation compared with the wave frequency and dynamic time [52]. The dynamic disturbance intensity (DDI) playing the index role in the method of ELAD was put forward to analyze the changes in stress, displacement, and plastic zone of the rocks around the entry under the influence of stress wave. For example, DDI of stress can be calculated by the ratio of the stress under the stress wave disturbance and the stress without the stress wave disturbance for any point of the rock. With the identical method, DDI of displacement, DDI of plastic failure zone, and DDI of crack can be obtained.Plastic deformation plays the principal role in elastic-plastic deformation of the rock around the entry under the stress wave and abutment stress [53]. Dynamic disturbance threshold (DDT) was proposed to prevent the rock from additional plastic deformation (APD), which can be calculated by the method of zero growth DDI of plastic failure zone. This method has the advantage of limiting the expansion of the plastic zone of the rock around the entry under the stress wave, which makes DDI of the plastic failure zone equal one. DDT equals the amplitude of this stress wave.Underground mining engineering was permitted in large deformation of entry compared with the shallow tunneling engineering [18], because of its short service life [53]. This underground entry is vulnerable to large deformation disasters (LDD) such as roof caving, rib caving, and rock burst when the deformation is large enough. Dynamic large-deformation threshold (DLT) was proposed to prevent the rock from LDD, which can be calculated by the method of engineering-permitted limitation deformation. This method has the advantage of making the deformation be in the limitation range for the entry under the stress wave which is permitted by the engineering. Additionally, DLT equals the amplitude of this stress wave.DDT and DLT will change as the static stress varies from the original stress to the abutment stress. For a specific stress condition, DDI can be divided into “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type” according to the values of DDT and DLT. Dynamic stress of Slightly Disturbed Type is determined as the dynamic stress less than DDT, that of Violent Impact Type is determined as the dynamic stress more than DLT, and that of Moderately Disturbed Type is determined as the dynamic stress between DDT and DLT.The underground entries should keep away from the dynamic stress of Violent Impact Type firstly and then be arranged in the zone where the dynamic stress belongs to Slightly Disturbed Type. By symbol description, the entries should keep away from the zone of the results ofR(x) ≥ L(x) firstly and then be arranged in the zone of the results of R(x) ≤ D(x), where R(x) is the distribution of the potential stress wave, MPa; D(x) is the distribution of DDT of the abutment stress function f(x), MPa; L(x) is the distribution of DLT of the abutment stress function f(x), MPa; and x is the location away from the side of the gob, m. The detailed solution is presented as shown in Figure 2.Figure 2
Detailed solution of the entry layout method.


## 3. Numerical Simulation Model

### 3.1. Model Establishment

#### 3.1.1. Constitutive Behavior of the Materials

Coal and rock materials are vulnerable to elastic and plastic deformation under the experimental loading test (Figure3) with the displacement loading Se (equation (1)). Mohr–Coulomb model is able to simulate the elastic deformation behavior approximatively for rock materials [54], but it is not suitable for simulating the strain softening behavior of the coal material. Taking the attenuation of the strength parameters, strain softening model has a good agreement with the plastic deformation of coal material (Figure 3(a)). The mechanical parameters of coal and rock materials are as shown in Table 1, and the attenuation rule of the cohesion parameter is as shown in Table 2. The displacement loading is Sσ as the description in equation (1).Figure 3
Relationship between stress and strain under uniaxial compression test. (a) Sample of coal. (b) Sample of mudstone. (c) Sample of sandy mudstone. (d) Sample of sandstone. (e) Sample of limestone. (f) Sample of fine sandstone.
(a)(b)(c)(d)(e)(f)(1)Se=2×10−5m/second,Sσ=2×10−8m/step.Table 1
Parameters of model material.
LithologyDensity (kg/m3)Bulk modulus (GPa)Shear modulus (GPa)Internal friction angle (°)Cohesion (MPa)Tensile strength (MPa)Mudstone24002.051.86525.801.60Sandy mudstone25802.852.28576.401.90Mudstone24002.051.86525.801.60Limestone26404.623.83657.202.20Coal14001.000.80383.601.20Sandy mudstone25802.852.28576.401.90Fine sandstone26005.854.76677.402.40Sandstone26204.964.27657.202.30Table 2
Attenuation rules of the cohesion parameter for the coal material.
Plastic strain0.000.010.01…1.00Cohesion, MPa3.602.760.14…0.14The constitutive models are all accepted by the dynamic analysis in FLAC3D, because the fully nonlinear analysis method based on the explicit finite difference scheme is used to solve the full equations of motion, using lumped grid point masses derived from the real density of surrounding zones in FLAC3D [55]. Strain softening model is determined to simulate the dynamic response of the coal material and Mohr–Coulomb model is used to simulate the dynamic response of the rock materials. For the coal sample example, its dynamic strain behaviors are as shown in Figure 4.Figure 4
Relationship between stress and strain under Dσ. (a) Dσ plays the compression-shear role in the submodel; (b) Dσ plays the tensile role in the submodel; (c) limitation dynamic stress of the submodel under different static loadings; the curves with red line describe the relationship between stress and simulation steps in Figures 4(a) and 4(b); the curves with blue line describe the relationship between stress and strain.
(a)(b)(c)The coal sample with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength) has enough capacity to bear the stress wave when the amplitude of the compression shear stress wave is less than 22.15 MPa. Within 22.15 MPa, the stress wave makes the coal sample vibrate elastically, and the vibration amplitude of the coal sample increases as the increase of the amplitude of compression shear stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. However, the stress and vertical strain cannot return to the origin state when the amplitude of the stress wave is more than 22.15 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.At the same time, this coal sample, with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength), has enough capacity to bear the stress wave when the amplitude of the tensile stress wave is less than 9.78 MPa. Within 9.78 MPa, the stress wave makes the coal sample vibrate elastically and the vibration amplitude of the coal sample increases as the increase of the amplitude of tensile stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. When the amplitude of the tensile stress wave reaches 7.38 MPa, the deformation behavior changes from compression to tensile state. However, the stress and strain cannot return to the origin state when the amplitude of the stress wave is more than 9.78 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.The limitation of the compression-shear stress wave amplitude decreases linearly and the limitation of the tensile stress wave increases linearly as the increase of the static stress loaded in the submodel, which are the damaged mechanism of the coal material. The average strain rate is 4.5 s−1 between 0.1 s−1 and 10 s−1 which belongs to the weak dynamics [12]. Therefore, the effect of the strain rate on the strength of the coal material is not considered in the numerical model.


#### 3.1.2. Model of Static Calculation

A three-dimensional numerical model was established with the geometric dimension being 65 × 65 × 65 m alongx, y, and z axial directions in FLAC3D software [55]. According to the uniform zone dimensions and the solution time in the numerical model [56], the mesh size along both x direction and y direction was determined as 1 m for every rock stratum. Those along z direction are determined as 0.94 m, 0.95 m, 0.97 m, 0.93 m, 0.96 m, 1.0 m, 1.0 m, and 1.0 m, respectively, for the eight rock strata from the bottom (sandstone) to the top (mudstone) (Figure 1(c)). The left, right, front, back, and bottom sides of the model were fixed in displacement along the normal direction. The top side of the model was loaded with a uniform vertical stress for simulating the abutment stress. After the abutment stress was initialized in the model, the entry with a dimension 5 × 4 m was developed in the center of the numerical model. Calculation of the numerical model was carried out to simulate the deformation behavior of the entry under abutment stress until the maximum unbalance force was less than 10−5 N. The in situ vertical stress, maximum horizontal principal stress, and the minimum horizontal principal stress are 15.0 MPa, 14.73 MPa, and 8.53 MPa [57]. The maximum principal horizontal stress has an orientation of N43.7°W which has an angle 46.3° with the direction of the entry driving. The horizontal principle stress resolution must be carried out to establish a geological stress as the field condition in the numerical simulation model [58]. The input maximum horizontal principle stress was calculated as 16.54 MPa perpendicular to the axial direction of the entry driving and the input minimum horizontal principle stress was calculated as 16.34 MPa towards to the axial direction of the entry driving.


#### 3.1.3. Model of Dynamic Calculation

The length of every zone edge 1 m is less than tenth of the wavelength, which agrees with the calculation requirement for the numerical model. Static viscous boundary conditions were used to improve the calculation efficiency and reduce the reflection effects of the dynamic calculation process of the numerical model. Rayleigh damping was used to simulate the friction behavior between the coal materials. By numerical simulation, the minimum critical damping ratio was determined as 0.005 and the minimum center frequency was determined as the natural vibration frequency of the model 3.8 Hz. The dynamic time was determined as 0.4 seconds to supply enough time for the balance of every zone in the model. The cosine shear stress wave was applied to the surface of the model to simulate the dynamic stress as shown in equation (2). The effective time of the dynamic stress was determined as 0.02 seconds(2)Dσ=0.51−cos2πft∗σA,where Dσ is the shear stress wave, MPa; f is the vibration frequency, Hz; t is the time of the dynamic calculation, s; and σA is the amplitude of the shear stress wave, MPa.


#### 3.1.4. Verification of Numerical Model

The displacement was determined as the analysis index to validate the numerical model consisting of the Mohr–Coulomb model for the rock material and the Strain-Softening model for the coal material during the entry development. Measuring of displacement with a steel ruler has been carried out during the development of the head entry in the field. The displacement increases quickly and then reaches a relatively stable value as shown in Figure5. The simulated results using the numerical model show great agreement with the measured results in the field, which indicates that this numerical model can be used to analyze the displacement of the entry under this kind of geological conditions.Figure 5
Comparison between the measured and simulated displacement.


### 3.2. Simulation Plans

First, five simulation cases were determined to investigate the dynamic response of the entry under the condition of the peak stress of the abutment stress (35 MPa), the original vertical stress (15 MPa), and their midvalue (25 MPa) in the field as shown in Table3. The dynamic stress σA was determined to analyze DDI, varying between 0 MPa and 20 MPa. Second, the evolutions of DDT and DLT were solved as the static stress varied from 15 MPa to 35 MPa according to the dynamic threshold algorithm as shown in Figure 6. Third, DDI was divided into three strength grades including “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type,” according to the values of DDT and DLT. Finally, L(x) and D(x) were determined to layout the entry under the condition of the abutment stress f(x) and the potential dynamic stress R(x).Table 3
Simulation plans.
Abutment stress (MPa)Dynamic stress,σA (MPa)150510152025024683502468Figure 6
Dynamic threshold algorithm. The main process includes four sections. In the first section, the calculation of static stress is carried out using the numerical simulation model until the stress keeps balance. In the second section, the judging criteria of DDT and DLT are determined using the method of zero growth DDI of plastic failure zone and the engineering-permitted limitation displacement method. In the third section, the calculation of servo stress wave is carried out using the numerical simulation model until the stress wave meets the judging criteria and the accuracy requirement. Finally, DDT and DLT are recorded.


### 3.3. Results

#### 3.3.1. Evolution of DDI

DDI presents an increasing trend as the increasing of the stress wave amplitude. For example, DDI of plastic failure zone and that of displacement increase with an increasing gradient as the increasing of the stress wave amplitude (Figure7). This kind of failure and deformation behavior will be in a state of slowdown as the input static stress increases. For example, both increasing amplitudes of DDI of plastic failure zone and DDI of displacement decrease as the increasing of the static stress. And, this kind of reduction amplitude of DDI will increase as the increasing of stress wave amplitude. However, the deformation of entry under the stress wave is larger than that without the influence of stress wave no matter how much the stress wave amplitude is.Figure 7
Evolution of DDI for the surrounding rock under different loadings. (a) DDI of plastic failure zone; (b) DDI of displacement.
(a)(b)


#### 3.3.2. Grades of DDI

DDT presents a linear increasing trend and DLT presents a reduction trend as the increasing of the abutment stress when the engineering-permitted limitation deformation is determined as 200 mm with a security coefficient of 1.5 as shown in Figure8. DLT is larger than DDT for this entry when the entry was loaded by the abutment stress between 15 MPa and 20 MPa. Using DDT and DLT, DDI was divided into three grades including “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type.” With the reduction of the range of Moderately Disturbed Type, the ranges of Slightly Disturbed Type and Violent Impact Type increase as the abutment stress increases. In addition, DDT is larger than DLT when the entry is loaded by the abutment stress between 20 MPa and 35 MPa. The deformation of the entry is larger than the engineering-permitted limitation deformation under this kind of abutment stress no matter whether DDI belongs to “Slightly Disturbed Type” or not. This kind of entry is located at the area where there exists high abutment stress. Some measures like rock support, rock consolidation, and entry layout must be taken to reduce the deformation of the entry under this kind of conditions.Figure 8
Results of the disturbing dynamic threshold and the large deformation caused dynamic threshold.


#### 3.3.3. Layout of Entry

The entry should layout at less than 4.91 m or more than 20.26 m away from the side of the gob according to the method of ELAD as shown in Figure9. The piecewise function has been proved to be a reliable function to describe the distribution of the abutment stress f(x) as shown in equation (3) [59]. By the data fitting process in MATLAB 2012b, the power function was determined to describe D(x) and L(x) as shown in Figures 10 and 11 and equations (4) and (5). The potential dynamic stress R(x) comes from the liberating energy of 2.35 × 105 J during the mining-induced fracture of the interactional hard roof structures [9, 60]. The effect of this liberating energy on the surrounding rock was replaced with a loading process of the equivalent dynamic stress, and this equivalent dynamic stress was determined as 9 MPa by using the method of elastic deformation energy [61]. The equivalent dynamic stress will propagate in the way of vibrating stress wave in sedimentary strata and its strength is in the state of attenuation when it passes through the discontinuous interface [62]. R(x) was determined as shown in Figure 12 by the displacement discontinuity method [62] and it can be described by an exponential function as shown in equation (5). Model parameters are shown in Table 4.(3)fx=a1x+a2,0≤x≤p,a3ea4x−p+a5,p≤x≤r,γH,r≤x≤∞,where f(x) is the abutment stress, MPa; a1, a2, a3, a4, and a5 are parameters of the piecewise function, which can be determined by measuring data fitting; x is the distance to the side of the gob, m; p is the distance between the side of the gob and the location of the maximum value of the abutment stress, m; r is the distance between the side of the gob and the location of the original vertical 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 stratum’s volume weight and thickness and the cumulative thickness of geological strata, kN/m3; and H is the cumulative thickness of the geological strata, m.(4)Dx=b1fxb2+b3,where b1, b2, and b3 are parameters of the power function of D(x), which can be determined by measuring data fitting.(5)Lx=c1fx2+c2fx+c3,x≤c4,0,x≥c4,where c1, c2, c3, and c4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.(6)Rx=d1ed2x+d3ed4x,where d1, d2, d3, and d4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.Figure 9
Distribution of evaluation index.Figure 10
Relationship between DDT and abutment stress.Figure 11
Relationship between DLT and abutment stress.Figure 12
Potential dynamic stressR(x).Table 4
Parameters used in the mathematical models.
ParametersValuesa12a215a320.37386a4−0.13327a514.62614b10.001379b22.449b3−0.5203P10R40c10.5463c2−24.289c3270c422.4γH15d1−0.00075d20.1257d33.437d4−0.00335


## 3.1. Model Establishment

### 3.1.1. Constitutive Behavior of the Materials

Coal and rock materials are vulnerable to elastic and plastic deformation under the experimental loading test (Figure3) with the displacement loading Se (equation (1)). Mohr–Coulomb model is able to simulate the elastic deformation behavior approximatively for rock materials [54], but it is not suitable for simulating the strain softening behavior of the coal material. Taking the attenuation of the strength parameters, strain softening model has a good agreement with the plastic deformation of coal material (Figure 3(a)). The mechanical parameters of coal and rock materials are as shown in Table 1, and the attenuation rule of the cohesion parameter is as shown in Table 2. The displacement loading is Sσ as the description in equation (1).Figure 3
Relationship between stress and strain under uniaxial compression test. (a) Sample of coal. (b) Sample of mudstone. (c) Sample of sandy mudstone. (d) Sample of sandstone. (e) Sample of limestone. (f) Sample of fine sandstone.
(a)(b)(c)(d)(e)(f)(1)Se=2×10−5m/second,Sσ=2×10−8m/step.Table 1
Parameters of model material.
LithologyDensity (kg/m3)Bulk modulus (GPa)Shear modulus (GPa)Internal friction angle (°)Cohesion (MPa)Tensile strength (MPa)Mudstone24002.051.86525.801.60Sandy mudstone25802.852.28576.401.90Mudstone24002.051.86525.801.60Limestone26404.623.83657.202.20Coal14001.000.80383.601.20Sandy mudstone25802.852.28576.401.90Fine sandstone26005.854.76677.402.40Sandstone26204.964.27657.202.30Table 2
Attenuation rules of the cohesion parameter for the coal material.
Plastic strain0.000.010.01…1.00Cohesion, MPa3.602.760.14…0.14The constitutive models are all accepted by the dynamic analysis in FLAC3D, because the fully nonlinear analysis method based on the explicit finite difference scheme is used to solve the full equations of motion, using lumped grid point masses derived from the real density of surrounding zones in FLAC3D [55]. Strain softening model is determined to simulate the dynamic response of the coal material and Mohr–Coulomb model is used to simulate the dynamic response of the rock materials. For the coal sample example, its dynamic strain behaviors are as shown in Figure 4.Figure 4
Relationship between stress and strain under Dσ. (a) Dσ plays the compression-shear role in the submodel; (b) Dσ plays the tensile role in the submodel; (c) limitation dynamic stress of the submodel under different static loadings; the curves with red line describe the relationship between stress and simulation steps in Figures 4(a) and 4(b); the curves with blue line describe the relationship between stress and strain.
(a)(b)(c)The coal sample with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength) has enough capacity to bear the stress wave when the amplitude of the compression shear stress wave is less than 22.15 MPa. Within 22.15 MPa, the stress wave makes the coal sample vibrate elastically, and the vibration amplitude of the coal sample increases as the increase of the amplitude of compression shear stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. However, the stress and vertical strain cannot return to the origin state when the amplitude of the stress wave is more than 22.15 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.At the same time, this coal sample, with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength), has enough capacity to bear the stress wave when the amplitude of the tensile stress wave is less than 9.78 MPa. Within 9.78 MPa, the stress wave makes the coal sample vibrate elastically and the vibration amplitude of the coal sample increases as the increase of the amplitude of tensile stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. When the amplitude of the tensile stress wave reaches 7.38 MPa, the deformation behavior changes from compression to tensile state. However, the stress and strain cannot return to the origin state when the amplitude of the stress wave is more than 9.78 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.The limitation of the compression-shear stress wave amplitude decreases linearly and the limitation of the tensile stress wave increases linearly as the increase of the static stress loaded in the submodel, which are the damaged mechanism of the coal material. The average strain rate is 4.5 s−1 between 0.1 s−1 and 10 s−1 which belongs to the weak dynamics [12]. Therefore, the effect of the strain rate on the strength of the coal material is not considered in the numerical model.


### 3.1.2. Model of Static Calculation

A three-dimensional numerical model was established with the geometric dimension being 65 × 65 × 65 m alongx, y, and z axial directions in FLAC3D software [55]. According to the uniform zone dimensions and the solution time in the numerical model [56], the mesh size along both x direction and y direction was determined as 1 m for every rock stratum. Those along z direction are determined as 0.94 m, 0.95 m, 0.97 m, 0.93 m, 0.96 m, 1.0 m, 1.0 m, and 1.0 m, respectively, for the eight rock strata from the bottom (sandstone) to the top (mudstone) (Figure 1(c)). The left, right, front, back, and bottom sides of the model were fixed in displacement along the normal direction. The top side of the model was loaded with a uniform vertical stress for simulating the abutment stress. After the abutment stress was initialized in the model, the entry with a dimension 5 × 4 m was developed in the center of the numerical model. Calculation of the numerical model was carried out to simulate the deformation behavior of the entry under abutment stress until the maximum unbalance force was less than 10−5 N. The in situ vertical stress, maximum horizontal principal stress, and the minimum horizontal principal stress are 15.0 MPa, 14.73 MPa, and 8.53 MPa [57]. The maximum principal horizontal stress has an orientation of N43.7°W which has an angle 46.3° with the direction of the entry driving. The horizontal principle stress resolution must be carried out to establish a geological stress as the field condition in the numerical simulation model [58]. The input maximum horizontal principle stress was calculated as 16.54 MPa perpendicular to the axial direction of the entry driving and the input minimum horizontal principle stress was calculated as 16.34 MPa towards to the axial direction of the entry driving.


### 3.1.3. Model of Dynamic Calculation

The length of every zone edge 1 m is less than tenth of the wavelength, which agrees with the calculation requirement for the numerical model. Static viscous boundary conditions were used to improve the calculation efficiency and reduce the reflection effects of the dynamic calculation process of the numerical model. Rayleigh damping was used to simulate the friction behavior between the coal materials. By numerical simulation, the minimum critical damping ratio was determined as 0.005 and the minimum center frequency was determined as the natural vibration frequency of the model 3.8 Hz. The dynamic time was determined as 0.4 seconds to supply enough time for the balance of every zone in the model. The cosine shear stress wave was applied to the surface of the model to simulate the dynamic stress as shown in equation (2). The effective time of the dynamic stress was determined as 0.02 seconds(2)Dσ=0.51−cos2πft∗σA,where Dσ is the shear stress wave, MPa; f is the vibration frequency, Hz; t is the time of the dynamic calculation, s; and σA is the amplitude of the shear stress wave, MPa.


### 3.1.4. Verification of Numerical Model

The displacement was determined as the analysis index to validate the numerical model consisting of the Mohr–Coulomb model for the rock material and the Strain-Softening model for the coal material during the entry development. Measuring of displacement with a steel ruler has been carried out during the development of the head entry in the field. The displacement increases quickly and then reaches a relatively stable value as shown in Figure5. The simulated results using the numerical model show great agreement with the measured results in the field, which indicates that this numerical model can be used to analyze the displacement of the entry under this kind of geological conditions.Figure 5
Comparison between the measured and simulated displacement.


## 3.1.1. Constitutive Behavior of the Materials

Coal and rock materials are vulnerable to elastic and plastic deformation under the experimental loading test (Figure3) with the displacement loading Se (equation (1)). Mohr–Coulomb model is able to simulate the elastic deformation behavior approximatively for rock materials [54], but it is not suitable for simulating the strain softening behavior of the coal material. Taking the attenuation of the strength parameters, strain softening model has a good agreement with the plastic deformation of coal material (Figure 3(a)). The mechanical parameters of coal and rock materials are as shown in Table 1, and the attenuation rule of the cohesion parameter is as shown in Table 2. The displacement loading is Sσ as the description in equation (1).Figure 3
Relationship between stress and strain under uniaxial compression test. (a) Sample of coal. (b) Sample of mudstone. (c) Sample of sandy mudstone. (d) Sample of sandstone. (e) Sample of limestone. (f) Sample of fine sandstone.
(a)(b)(c)(d)(e)(f)(1)Se=2×10−5m/second,Sσ=2×10−8m/step.Table 1
Parameters of model material.
LithologyDensity (kg/m3)Bulk modulus (GPa)Shear modulus (GPa)Internal friction angle (°)Cohesion (MPa)Tensile strength (MPa)Mudstone24002.051.86525.801.60Sandy mudstone25802.852.28576.401.90Mudstone24002.051.86525.801.60Limestone26404.623.83657.202.20Coal14001.000.80383.601.20Sandy mudstone25802.852.28576.401.90Fine sandstone26005.854.76677.402.40Sandstone26204.964.27657.202.30Table 2
Attenuation rules of the cohesion parameter for the coal material.
Plastic strain0.000.010.01…1.00Cohesion, MPa3.602.760.14…0.14The constitutive models are all accepted by the dynamic analysis in FLAC3D, because the fully nonlinear analysis method based on the explicit finite difference scheme is used to solve the full equations of motion, using lumped grid point masses derived from the real density of surrounding zones in FLAC3D [55]. Strain softening model is determined to simulate the dynamic response of the coal material and Mohr–Coulomb model is used to simulate the dynamic response of the rock materials. For the coal sample example, its dynamic strain behaviors are as shown in Figure 4.Figure 4
Relationship between stress and strain under Dσ. (a) Dσ plays the compression-shear role in the submodel; (b) Dσ plays the tensile role in the submodel; (c) limitation dynamic stress of the submodel under different static loadings; the curves with red line describe the relationship between stress and simulation steps in Figures 4(a) and 4(b); the curves with blue line describe the relationship between stress and strain.
(a)(b)(c)The coal sample with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength) has enough capacity to bear the stress wave when the amplitude of the compression shear stress wave is less than 22.15 MPa. Within 22.15 MPa, the stress wave makes the coal sample vibrate elastically, and the vibration amplitude of the coal sample increases as the increase of the amplitude of compression shear stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. However, the stress and vertical strain cannot return to the origin state when the amplitude of the stress wave is more than 22.15 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.At the same time, this coal sample, with the uniaxial compression stress 3.69 MPa (approximately 25 percent of the uniaxial compression strength), has enough capacity to bear the stress wave when the amplitude of the tensile stress wave is less than 9.78 MPa. Within 9.78 MPa, the stress wave makes the coal sample vibrate elastically and the vibration amplitude of the coal sample increases as the increase of the amplitude of tensile stress wave. Both the stress and the strain can return to the original value due to the fact that the stress increases linearly first and then decreases linearly along the original path as the strain varies. When the amplitude of the tensile stress wave reaches 7.38 MPa, the deformation behavior changes from compression to tensile state. However, the stress and strain cannot return to the origin state when the amplitude of the stress wave is more than 9.78 MPa. The coal sample changes in deformation behavior from small elastic state to large plastic state.The limitation of the compression-shear stress wave amplitude decreases linearly and the limitation of the tensile stress wave increases linearly as the increase of the static stress loaded in the submodel, which are the damaged mechanism of the coal material. The average strain rate is 4.5 s−1 between 0.1 s−1 and 10 s−1 which belongs to the weak dynamics [12]. Therefore, the effect of the strain rate on the strength of the coal material is not considered in the numerical model.


## 3.1.2. Model of Static Calculation

A three-dimensional numerical model was established with the geometric dimension being 65 × 65 × 65 m alongx, y, and z axial directions in FLAC3D software [55]. According to the uniform zone dimensions and the solution time in the numerical model [56], the mesh size along both x direction and y direction was determined as 1 m for every rock stratum. Those along z direction are determined as 0.94 m, 0.95 m, 0.97 m, 0.93 m, 0.96 m, 1.0 m, 1.0 m, and 1.0 m, respectively, for the eight rock strata from the bottom (sandstone) to the top (mudstone) (Figure 1(c)). The left, right, front, back, and bottom sides of the model were fixed in displacement along the normal direction. The top side of the model was loaded with a uniform vertical stress for simulating the abutment stress. After the abutment stress was initialized in the model, the entry with a dimension 5 × 4 m was developed in the center of the numerical model. Calculation of the numerical model was carried out to simulate the deformation behavior of the entry under abutment stress until the maximum unbalance force was less than 10−5 N. The in situ vertical stress, maximum horizontal principal stress, and the minimum horizontal principal stress are 15.0 MPa, 14.73 MPa, and 8.53 MPa [57]. The maximum principal horizontal stress has an orientation of N43.7°W which has an angle 46.3° with the direction of the entry driving. The horizontal principle stress resolution must be carried out to establish a geological stress as the field condition in the numerical simulation model [58]. The input maximum horizontal principle stress was calculated as 16.54 MPa perpendicular to the axial direction of the entry driving and the input minimum horizontal principle stress was calculated as 16.34 MPa towards to the axial direction of the entry driving.


## 3.1.3. Model of Dynamic Calculation

The length of every zone edge 1 m is less than tenth of the wavelength, which agrees with the calculation requirement for the numerical model. Static viscous boundary conditions were used to improve the calculation efficiency and reduce the reflection effects of the dynamic calculation process of the numerical model. Rayleigh damping was used to simulate the friction behavior between the coal materials. By numerical simulation, the minimum critical damping ratio was determined as 0.005 and the minimum center frequency was determined as the natural vibration frequency of the model 3.8 Hz. The dynamic time was determined as 0.4 seconds to supply enough time for the balance of every zone in the model. The cosine shear stress wave was applied to the surface of the model to simulate the dynamic stress as shown in equation (2). The effective time of the dynamic stress was determined as 0.02 seconds(2)Dσ=0.51−cos2πft∗σA,where Dσ is the shear stress wave, MPa; f is the vibration frequency, Hz; t is the time of the dynamic calculation, s; and σA is the amplitude of the shear stress wave, MPa.


## 3.1.4. Verification of Numerical Model

The displacement was determined as the analysis index to validate the numerical model consisting of the Mohr–Coulomb model for the rock material and the Strain-Softening model for the coal material during the entry development. Measuring of displacement with a steel ruler has been carried out during the development of the head entry in the field. The displacement increases quickly and then reaches a relatively stable value as shown in Figure5. The simulated results using the numerical model show great agreement with the measured results in the field, which indicates that this numerical model can be used to analyze the displacement of the entry under this kind of geological conditions.Figure 5
Comparison between the measured and simulated displacement.


## 3.2. Simulation Plans

First, five simulation cases were determined to investigate the dynamic response of the entry under the condition of the peak stress of the abutment stress (35 MPa), the original vertical stress (15 MPa), and their midvalue (25 MPa) in the field as shown in Table3. The dynamic stress σA was determined to analyze DDI, varying between 0 MPa and 20 MPa. Second, the evolutions of DDT and DLT were solved as the static stress varied from 15 MPa to 35 MPa according to the dynamic threshold algorithm as shown in Figure 6. Third, DDI was divided into three strength grades including “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type,” according to the values of DDT and DLT. Finally, L(x) and D(x) were determined to layout the entry under the condition of the abutment stress f(x) and the potential dynamic stress R(x).Table 3
Simulation plans.
Abutment stress (MPa)Dynamic stress,σA (MPa)150510152025024683502468Figure 6
Dynamic threshold algorithm. The main process includes four sections. In the first section, the calculation of static stress is carried out using the numerical simulation model until the stress keeps balance. In the second section, the judging criteria of DDT and DLT are determined using the method of zero growth DDI of plastic failure zone and the engineering-permitted limitation displacement method. In the third section, the calculation of servo stress wave is carried out using the numerical simulation model until the stress wave meets the judging criteria and the accuracy requirement. Finally, DDT and DLT are recorded.


## 3.3. Results

### 3.3.1. Evolution of DDI

DDI presents an increasing trend as the increasing of the stress wave amplitude. For example, DDI of plastic failure zone and that of displacement increase with an increasing gradient as the increasing of the stress wave amplitude (Figure7). This kind of failure and deformation behavior will be in a state of slowdown as the input static stress increases. For example, both increasing amplitudes of DDI of plastic failure zone and DDI of displacement decrease as the increasing of the static stress. And, this kind of reduction amplitude of DDI will increase as the increasing of stress wave amplitude. However, the deformation of entry under the stress wave is larger than that without the influence of stress wave no matter how much the stress wave amplitude is.Figure 7
Evolution of DDI for the surrounding rock under different loadings. (a) DDI of plastic failure zone; (b) DDI of displacement.
(a)(b)


### 3.3.2. Grades of DDI

DDT presents a linear increasing trend and DLT presents a reduction trend as the increasing of the abutment stress when the engineering-permitted limitation deformation is determined as 200 mm with a security coefficient of 1.5 as shown in Figure8. DLT is larger than DDT for this entry when the entry was loaded by the abutment stress between 15 MPa and 20 MPa. Using DDT and DLT, DDI was divided into three grades including “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type.” With the reduction of the range of Moderately Disturbed Type, the ranges of Slightly Disturbed Type and Violent Impact Type increase as the abutment stress increases. In addition, DDT is larger than DLT when the entry is loaded by the abutment stress between 20 MPa and 35 MPa. The deformation of the entry is larger than the engineering-permitted limitation deformation under this kind of abutment stress no matter whether DDI belongs to “Slightly Disturbed Type” or not. This kind of entry is located at the area where there exists high abutment stress. Some measures like rock support, rock consolidation, and entry layout must be taken to reduce the deformation of the entry under this kind of conditions.Figure 8
Results of the disturbing dynamic threshold and the large deformation caused dynamic threshold.


### 3.3.3. Layout of Entry

The entry should layout at less than 4.91 m or more than 20.26 m away from the side of the gob according to the method of ELAD as shown in Figure9. The piecewise function has been proved to be a reliable function to describe the distribution of the abutment stress f(x) as shown in equation (3) [59]. By the data fitting process in MATLAB 2012b, the power function was determined to describe D(x) and L(x) as shown in Figures 10 and 11 and equations (4) and (5). The potential dynamic stress R(x) comes from the liberating energy of 2.35 × 105 J during the mining-induced fracture of the interactional hard roof structures [9, 60]. The effect of this liberating energy on the surrounding rock was replaced with a loading process of the equivalent dynamic stress, and this equivalent dynamic stress was determined as 9 MPa by using the method of elastic deformation energy [61]. The equivalent dynamic stress will propagate in the way of vibrating stress wave in sedimentary strata and its strength is in the state of attenuation when it passes through the discontinuous interface [62]. R(x) was determined as shown in Figure 12 by the displacement discontinuity method [62] and it can be described by an exponential function as shown in equation (5). Model parameters are shown in Table 4.(3)fx=a1x+a2,0≤x≤p,a3ea4x−p+a5,p≤x≤r,γH,r≤x≤∞,where f(x) is the abutment stress, MPa; a1, a2, a3, a4, and a5 are parameters of the piecewise function, which can be determined by measuring data fitting; x is the distance to the side of the gob, m; p is the distance between the side of the gob and the location of the maximum value of the abutment stress, m; r is the distance between the side of the gob and the location of the original vertical 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 stratum’s volume weight and thickness and the cumulative thickness of geological strata, kN/m3; and H is the cumulative thickness of the geological strata, m.(4)Dx=b1fxb2+b3,where b1, b2, and b3 are parameters of the power function of D(x), which can be determined by measuring data fitting.(5)Lx=c1fx2+c2fx+c3,x≤c4,0,x≥c4,where c1, c2, c3, and c4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.(6)Rx=d1ed2x+d3ed4x,where d1, d2, d3, and d4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.Figure 9
Distribution of evaluation index.Figure 10
Relationship between DDT and abutment stress.Figure 11
Relationship between DLT and abutment stress.Figure 12
Potential dynamic stressR(x).Table 4
Parameters used in the mathematical models.
ParametersValuesa12a215a320.37386a4−0.13327a514.62614b10.001379b22.449b3−0.5203P10R40c10.5463c2−24.289c3270c422.4γH15d1−0.00075d20.1257d33.437d4−0.00335


## 3.3.1. Evolution of DDI

DDI presents an increasing trend as the increasing of the stress wave amplitude. For example, DDI of plastic failure zone and that of displacement increase with an increasing gradient as the increasing of the stress wave amplitude (Figure7). This kind of failure and deformation behavior will be in a state of slowdown as the input static stress increases. For example, both increasing amplitudes of DDI of plastic failure zone and DDI of displacement decrease as the increasing of the static stress. And, this kind of reduction amplitude of DDI will increase as the increasing of stress wave amplitude. However, the deformation of entry under the stress wave is larger than that without the influence of stress wave no matter how much the stress wave amplitude is.Figure 7
Evolution of DDI for the surrounding rock under different loadings. (a) DDI of plastic failure zone; (b) DDI of displacement.
(a)(b)


## 3.3.2. Grades of DDI

DDT presents a linear increasing trend and DLT presents a reduction trend as the increasing of the abutment stress when the engineering-permitted limitation deformation is determined as 200 mm with a security coefficient of 1.5 as shown in Figure8. DLT is larger than DDT for this entry when the entry was loaded by the abutment stress between 15 MPa and 20 MPa. Using DDT and DLT, DDI was divided into three grades including “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type.” With the reduction of the range of Moderately Disturbed Type, the ranges of Slightly Disturbed Type and Violent Impact Type increase as the abutment stress increases. In addition, DDT is larger than DLT when the entry is loaded by the abutment stress between 20 MPa and 35 MPa. The deformation of the entry is larger than the engineering-permitted limitation deformation under this kind of abutment stress no matter whether DDI belongs to “Slightly Disturbed Type” or not. This kind of entry is located at the area where there exists high abutment stress. Some measures like rock support, rock consolidation, and entry layout must be taken to reduce the deformation of the entry under this kind of conditions.Figure 8
Results of the disturbing dynamic threshold and the large deformation caused dynamic threshold.


## 3.3.3. Layout of Entry

The entry should layout at less than 4.91 m or more than 20.26 m away from the side of the gob according to the method of ELAD as shown in Figure9. The piecewise function has been proved to be a reliable function to describe the distribution of the abutment stress f(x) as shown in equation (3) [59]. By the data fitting process in MATLAB 2012b, the power function was determined to describe D(x) and L(x) as shown in Figures 10 and 11 and equations (4) and (5). The potential dynamic stress R(x) comes from the liberating energy of 2.35 × 105 J during the mining-induced fracture of the interactional hard roof structures [9, 60]. The effect of this liberating energy on the surrounding rock was replaced with a loading process of the equivalent dynamic stress, and this equivalent dynamic stress was determined as 9 MPa by using the method of elastic deformation energy [61]. The equivalent dynamic stress will propagate in the way of vibrating stress wave in sedimentary strata and its strength is in the state of attenuation when it passes through the discontinuous interface [62]. R(x) was determined as shown in Figure 12 by the displacement discontinuity method [62] and it can be described by an exponential function as shown in equation (5). Model parameters are shown in Table 4.(3)fx=a1x+a2,0≤x≤p,a3ea4x−p+a5,p≤x≤r,γH,r≤x≤∞,where f(x) is the abutment stress, MPa; a1, a2, a3, a4, and a5 are parameters of the piecewise function, which can be determined by measuring data fitting; x is the distance to the side of the gob, m; p is the distance between the side of the gob and the location of the maximum value of the abutment stress, m; r is the distance between the side of the gob and the location of the original vertical 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 stratum’s volume weight and thickness and the cumulative thickness of geological strata, kN/m3; and H is the cumulative thickness of the geological strata, m.(4)Dx=b1fxb2+b3,where b1, b2, and b3 are parameters of the power function of D(x), which can be determined by measuring data fitting.(5)Lx=c1fx2+c2fx+c3,x≤c4,0,x≥c4,where c1, c2, c3, and c4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.(6)Rx=d1ed2x+d3ed4x,where d1, d2, d3, and d4 are parameters of the power function of D(x) and L(x), which can be determined by measuring data fitting.Figure 9
Distribution of evaluation index.Figure 10
Relationship between DDT and abutment stress.Figure 11
Relationship between DLT and abutment stress.Figure 12
Potential dynamic stressR(x).Table 4
Parameters used in the mathematical models.
ParametersValuesa12a215a320.37386a4−0.13327a514.62614b10.001379b22.449b3−0.5203P10R40c10.5463c2−24.289c3270c422.4γH15d1−0.00075d20.1257d33.437d4−0.00335


## 4. Discussion

### 4.1. Characteristic of DDI

Plastic deformation behavior plays the main role in the reduction of the underground entry space, and the LDD will generate if the plastic deformation is large enough. The plastic deformation is mainly governed by the stress condition, the support resistance, and the material properties. For a determined geological condition, the plastic failure zone of the entry under high static stress is larger than that of the entry under low static stress, and converting the elastic zone into plastic zone needs larger dynamic stress, which are the reason for the increasing of DDT with the increasing of the static stress. Meanwhile, the deformation of the entry under high static stress is larger than that of the entry under low static stress, which is the reason for the decreasing of DLT with the increasing of the static stress. DDI was divided into “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type” by the distribution of DDT and DLT. DDI of plastic failure zone equals 1 and DDI of deformation is small when the entry is loaded by dynamic stress of the Slightly Disturbed Type. DDI of plastic failure zone is more than 1, and DDI of deformation increases clearly when the entry is loaded by the dynamic stress of Moderately Disturbed Type. DDI of plastic failure zone increases surely to more than 1 and DDI of deformation is large enough when the entry is loaded by the dynamic stress of Violent Impact Type.


### 4.2. Significance of ELAD

ELAD has three advantages in mechanical behavior, loading conditions, and deformation evaluation indexes for coal materials compared with the widely used Wilson’s equation [49], ultimate balance theory [50, 51], and the existing numerical simulation method [63]. Firstly, postpeak strain softening behavior in Strain-Softening model is able to determine reliable values of the deformation evaluation indexes compared with the post-peak strain stabilization behavior in Mohr–Coulomb model for coal materials, which is considered by ELAD. Secondly, the underground entries sometimes suffer from the abutment stress and dynamic stress at the same time. The values of the deformation evaluation indexes are full of errors if the method considers the abutment stress or the dynamic stress separately. Finally, quantitative deformation evaluation indexes are beneficial to the entry layout compared with the qualitative deformation changes. For example, underground entries will face different engineering-permitted conditions, such as the entry without APD, the entry with permitted APD, and the entry with unpermitted APD. ELAD can be used to layout these underground entries by the method of zero growth DDI of plastic failure zone and the method of engineering-permitted limitation deformation. However, Strain-Softening model just describes the deformation behavior of the coal materials, which ignores the influences of the cracks and their internal fillings. This challenging problem will be considered in the next works in the future.ELAD is compared with other widely used methods to design the underground entry layout under the same geological engineering condition in Table5. The confined core is helpful for the stabilization of the coal pillar when the entry locates at more than 6.88 m away from the side of the gob, but the deformation of the entry will exceed the engineering-permitted value and the dynamic stress disturbance is ignored. The elastic core is large enough to protect the entry from large deformation disaster when the entry locates at more than 32.32 m away from the side of the gob; however, the 32.32 m wide coal pillar generates the reduction of the coal resource recovery. The stress is less than or equals the original stress when the entry locates at less than 3.34 m or more than 40.00 m away from the side of the gob, which is beneficial to the stabilization of the entry, but 40.00 m wide coal pillar is against the improvement of the coal resource recovery. The deformation is within the engineering-permitted deformation of 200 mm when the entry locates at less than 5.84 m or more than 17.13 m away from the side of the gob, which is applicable in the zone without the disturbance of the dynamic stress. In addition, the deformation is less than the engineering-permitted deformation of 200 mm without the disturbance of the dynamic stress when the Strain-Softening model is replaced with the Mohr–Coulomb model, which is inconsistent with the deformation behavior.Table 5
Underground entry layout comparison.
MethodsEvaluation indexesSolving processResults(1) Confined core concept with Wilson’s equation [49]r0=2m/1+sinφ0/1−sinφ0tan1+sinφ0/1−sinφ0−1lnKγH/σ0x≥2r0x ≥ 6.88 m(2) Elastic core concept with ultimate balance theory [50]r0=mA/tanφ0InKγH+C0/tanφ0/C0/tanφ0+Px/Ax≥2r0+2mx ≥ 32.32 m(3) Stress relief method with stress less than original stress [63]fx≤γHx ≤ 3.34 m or x ≥ 40.00 m(4) Engineering-permitted deformation method with Strain-Softening model and without dynamic stress [47]fx≤σLx ≤ 5.84 m or x ≥ 17.13 m(5) Engineering-permitted deformation method with Mohr–Coulomb model and without dynamic stress [53]fx≤σLx ≥ 0m(6) ELAD method with Strain-Softening modelRx≤Lxx ≤ 4.91 m or x ≥ 20.26 m(7) ELAD method with Mohr–Coulomb modelRx≤Lxx ≥ 0 mwherer0 is the width of the yield zone; m is the height of the mining space, 6.5 m; K is peak stress concentration factor, 2.33; σ0 is the unconfined compressive strength, 14.76 MPa; A is lateral pressure coefficient, 1; Px is the support strength on the face of the coal wall, 0.2 MPa; φ0 is the internal friction angle of the coal material, 38°; C0 is the cohesion of the coal material, 3.6 MPa; and σL is the permitted value of the abutment stress around the entry, MPa.


### 4.3. Effects of the Support Resistance

For the field case, the underground entries are always protected by the support technologies from LDD. Figure13 presents the effects of the support resistance on the DDT and DLT. DDT and DLT increase with the increasing of support resistance, which means this entry is able to bear larger dynamic stress with the help of the support resistance. DDT is larger than DLT, because the elastic-plastic deformation of the entry reaches the engineering-permitted value before the generation of APD under the abutment stress of 22.5 MPa. However, DLT can be larger than DDT when the value of the abutment stress changes to another value, such as the loading condition that the abutment stress varies from 15 MPa to 20 MPa (see Figure 8 for details).Figure 13
Effects of the support resistance on DDT and DLT.The results of the entry layout by ELAD are different when the support resistance changes as shown in Figure14. The acceptable location is determined as less than the maximal value or more than the minimal value away from the side of the gob and the unacceptable location is between them to layout the underground entry. The range of the acceptable location increases and the range of unacceptable location decreases with the increasing of the support resistance, which is helpful to protect the underground entry from the synergistic effects of abutment stress and dynamic stress. The entry layout can be determined by Figure 14 for a determined geological, engineering, and supporting condition.Figure 14
Effects of the support resistance on entry layout with ELAD.


### 4.4. Deformation Behavior for the Field Entry

To verify the reliability of ELAD method, field investigation works have been carried out in the subordinate San coal mine in Yangquan coal field. The maximum support resistance is calculated as 0.39 MPa. There were totally 10 anchor bolts and 8 anchor cables around the entry section. The anchor bolts are 880 mm in interval, 800 mm in row space, 20 mm in diameter, 2000 mm in length, and 150 kN in tensile fracture load in the entry roof. And, they are 1900 mm in interval, 800 mm in row space, 22 mm in diameter, 2000 mm in length, and 150 kN in tensile fracture load in the entry ribs. The anchor cables are 880 mm in interval, 800 mm in row space, 21.6 mm in diameter, 5200 mm in length, and 400 kN in tensile fracture load in the entry roof. And, they are 1900 mm in interval, 800 mm in row space, 21.6 mm in diameter, 5200 mm in length, and 400 kN in tensile fracture load in the entry ribs.The entry was arranged tentatively at 10 m away from the side of the gob according to the successful case in the coal seam [64]. It suffered from large deformation in the roof during the entry driving. The roof convergence reached 265 mm, the floor convergence reached 565 mm, and the rib-to-rib convergence reached 413 mm. Anchor cables experienced body fracture failure in some areas, which threatened the stability of the entry roof. Mining engineers take some remedial measures to guarantee the system operation normally for this entry, which results in the waste of manpower and material resources. A single hydraulic prop, with an initial service load of 11 MPa, was applied to reinforce the support of the entry roof throughout the whole entry. Every failure anchor cable was replaced with a normal one. Driving heave rock in the floor was adopted several times. Representative field photos are as shown in Figure 15.Figure 15
Deformation characteristics of the entry in San coal mine in Yangquan coal field. (a) Anchor cable failure. (b) Rib deformation.
(a)(b)The maximum difference is the mechanical boundary condition of stress between the entry in San coal mine and the entry in Sijiazhuang coal mine. The geological and engineering condition shows several differences between the two coal mines, which can influence the distribution of the abutment stress [65]. For example, the average mining height, burial depth, and entry section width are 6.5 m, 600 m, and 5.0 m in San coal mine, and those are 5.5 m, 574 m, and 4.8 m in Sijiazhuang coal mine. The effect of the potential dynamic stress disturbance is not considered during determining the entry layout [6]. This result indicates that the entry can generate large deformation even though the successful case has similar geological and engineering condition and the analogy of experience has something unknown.The entry should be arranged at less than 6.77 m or more than 14.82 m away from the side of the gob in San coal mine according to the results of ELAD method in Figure14. ELAD method can protect the entry from the high static stress of abutment stress and dynamic stress of Violent Impact. Taking the resource recovery, San coal mine arranged the entry at 6 m away from the side of the gob. The deformation behavior is as shown in Figure 16, and the roof deformation is less than the engineering-permitted value of 200 mm, which verifies the reliability of ELAD method.Figure 16
Deformation behavior of the entry.


## 4.1. Characteristic of DDI

Plastic deformation behavior plays the main role in the reduction of the underground entry space, and the LDD will generate if the plastic deformation is large enough. The plastic deformation is mainly governed by the stress condition, the support resistance, and the material properties. For a determined geological condition, the plastic failure zone of the entry under high static stress is larger than that of the entry under low static stress, and converting the elastic zone into plastic zone needs larger dynamic stress, which are the reason for the increasing of DDT with the increasing of the static stress. Meanwhile, the deformation of the entry under high static stress is larger than that of the entry under low static stress, which is the reason for the decreasing of DLT with the increasing of the static stress. DDI was divided into “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type” by the distribution of DDT and DLT. DDI of plastic failure zone equals 1 and DDI of deformation is small when the entry is loaded by dynamic stress of the Slightly Disturbed Type. DDI of plastic failure zone is more than 1, and DDI of deformation increases clearly when the entry is loaded by the dynamic stress of Moderately Disturbed Type. DDI of plastic failure zone increases surely to more than 1 and DDI of deformation is large enough when the entry is loaded by the dynamic stress of Violent Impact Type.


## 4.2. Significance of ELAD

ELAD has three advantages in mechanical behavior, loading conditions, and deformation evaluation indexes for coal materials compared with the widely used Wilson’s equation [49], ultimate balance theory [50, 51], and the existing numerical simulation method [63]. Firstly, postpeak strain softening behavior in Strain-Softening model is able to determine reliable values of the deformation evaluation indexes compared with the post-peak strain stabilization behavior in Mohr–Coulomb model for coal materials, which is considered by ELAD. Secondly, the underground entries sometimes suffer from the abutment stress and dynamic stress at the same time. The values of the deformation evaluation indexes are full of errors if the method considers the abutment stress or the dynamic stress separately. Finally, quantitative deformation evaluation indexes are beneficial to the entry layout compared with the qualitative deformation changes. For example, underground entries will face different engineering-permitted conditions, such as the entry without APD, the entry with permitted APD, and the entry with unpermitted APD. ELAD can be used to layout these underground entries by the method of zero growth DDI of plastic failure zone and the method of engineering-permitted limitation deformation. However, Strain-Softening model just describes the deformation behavior of the coal materials, which ignores the influences of the cracks and their internal fillings. This challenging problem will be considered in the next works in the future.ELAD is compared with other widely used methods to design the underground entry layout under the same geological engineering condition in Table5. The confined core is helpful for the stabilization of the coal pillar when the entry locates at more than 6.88 m away from the side of the gob, but the deformation of the entry will exceed the engineering-permitted value and the dynamic stress disturbance is ignored. The elastic core is large enough to protect the entry from large deformation disaster when the entry locates at more than 32.32 m away from the side of the gob; however, the 32.32 m wide coal pillar generates the reduction of the coal resource recovery. The stress is less than or equals the original stress when the entry locates at less than 3.34 m or more than 40.00 m away from the side of the gob, which is beneficial to the stabilization of the entry, but 40.00 m wide coal pillar is against the improvement of the coal resource recovery. The deformation is within the engineering-permitted deformation of 200 mm when the entry locates at less than 5.84 m or more than 17.13 m away from the side of the gob, which is applicable in the zone without the disturbance of the dynamic stress. In addition, the deformation is less than the engineering-permitted deformation of 200 mm without the disturbance of the dynamic stress when the Strain-Softening model is replaced with the Mohr–Coulomb model, which is inconsistent with the deformation behavior.Table 5
Underground entry layout comparison.
MethodsEvaluation indexesSolving processResults(1) Confined core concept with Wilson’s equation [49]r0=2m/1+sinφ0/1−sinφ0tan1+sinφ0/1−sinφ0−1lnKγH/σ0x≥2r0x ≥ 6.88 m(2) Elastic core concept with ultimate balance theory [50]r0=mA/tanφ0InKγH+C0/tanφ0/C0/tanφ0+Px/Ax≥2r0+2mx ≥ 32.32 m(3) Stress relief method with stress less than original stress [63]fx≤γHx ≤ 3.34 m or x ≥ 40.00 m(4) Engineering-permitted deformation method with Strain-Softening model and without dynamic stress [47]fx≤σLx ≤ 5.84 m or x ≥ 17.13 m(5) Engineering-permitted deformation method with Mohr–Coulomb model and without dynamic stress [53]fx≤σLx ≥ 0m(6) ELAD method with Strain-Softening modelRx≤Lxx ≤ 4.91 m or x ≥ 20.26 m(7) ELAD method with Mohr–Coulomb modelRx≤Lxx ≥ 0 mwherer0 is the width of the yield zone; m is the height of the mining space, 6.5 m; K is peak stress concentration factor, 2.33; σ0 is the unconfined compressive strength, 14.76 MPa; A is lateral pressure coefficient, 1; Px is the support strength on the face of the coal wall, 0.2 MPa; φ0 is the internal friction angle of the coal material, 38°; C0 is the cohesion of the coal material, 3.6 MPa; and σL is the permitted value of the abutment stress around the entry, MPa.


## 4.3. Effects of the Support Resistance

For the field case, the underground entries are always protected by the support technologies from LDD. Figure13 presents the effects of the support resistance on the DDT and DLT. DDT and DLT increase with the increasing of support resistance, which means this entry is able to bear larger dynamic stress with the help of the support resistance. DDT is larger than DLT, because the elastic-plastic deformation of the entry reaches the engineering-permitted value before the generation of APD under the abutment stress of 22.5 MPa. However, DLT can be larger than DDT when the value of the abutment stress changes to another value, such as the loading condition that the abutment stress varies from 15 MPa to 20 MPa (see Figure 8 for details).Figure 13
Effects of the support resistance on DDT and DLT.The results of the entry layout by ELAD are different when the support resistance changes as shown in Figure14. The acceptable location is determined as less than the maximal value or more than the minimal value away from the side of the gob and the unacceptable location is between them to layout the underground entry. The range of the acceptable location increases and the range of unacceptable location decreases with the increasing of the support resistance, which is helpful to protect the underground entry from the synergistic effects of abutment stress and dynamic stress. The entry layout can be determined by Figure 14 for a determined geological, engineering, and supporting condition.Figure 14
Effects of the support resistance on entry layout with ELAD.


## 4.4. Deformation Behavior for the Field Entry

To verify the reliability of ELAD method, field investigation works have been carried out in the subordinate San coal mine in Yangquan coal field. The maximum support resistance is calculated as 0.39 MPa. There were totally 10 anchor bolts and 8 anchor cables around the entry section. The anchor bolts are 880 mm in interval, 800 mm in row space, 20 mm in diameter, 2000 mm in length, and 150 kN in tensile fracture load in the entry roof. And, they are 1900 mm in interval, 800 mm in row space, 22 mm in diameter, 2000 mm in length, and 150 kN in tensile fracture load in the entry ribs. The anchor cables are 880 mm in interval, 800 mm in row space, 21.6 mm in diameter, 5200 mm in length, and 400 kN in tensile fracture load in the entry roof. And, they are 1900 mm in interval, 800 mm in row space, 21.6 mm in diameter, 5200 mm in length, and 400 kN in tensile fracture load in the entry ribs.The entry was arranged tentatively at 10 m away from the side of the gob according to the successful case in the coal seam [64]. It suffered from large deformation in the roof during the entry driving. The roof convergence reached 265 mm, the floor convergence reached 565 mm, and the rib-to-rib convergence reached 413 mm. Anchor cables experienced body fracture failure in some areas, which threatened the stability of the entry roof. Mining engineers take some remedial measures to guarantee the system operation normally for this entry, which results in the waste of manpower and material resources. A single hydraulic prop, with an initial service load of 11 MPa, was applied to reinforce the support of the entry roof throughout the whole entry. Every failure anchor cable was replaced with a normal one. Driving heave rock in the floor was adopted several times. Representative field photos are as shown in Figure 15.Figure 15
Deformation characteristics of the entry in San coal mine in Yangquan coal field. (a) Anchor cable failure. (b) Rib deformation.
(a)(b)The maximum difference is the mechanical boundary condition of stress between the entry in San coal mine and the entry in Sijiazhuang coal mine. The geological and engineering condition shows several differences between the two coal mines, which can influence the distribution of the abutment stress [65]. For example, the average mining height, burial depth, and entry section width are 6.5 m, 600 m, and 5.0 m in San coal mine, and those are 5.5 m, 574 m, and 4.8 m in Sijiazhuang coal mine. The effect of the potential dynamic stress disturbance is not considered during determining the entry layout [6]. This result indicates that the entry can generate large deformation even though the successful case has similar geological and engineering condition and the analogy of experience has something unknown.The entry should be arranged at less than 6.77 m or more than 14.82 m away from the side of the gob in San coal mine according to the results of ELAD method in Figure14. ELAD method can protect the entry from the high static stress of abutment stress and dynamic stress of Violent Impact. Taking the resource recovery, San coal mine arranged the entry at 6 m away from the side of the gob. The deformation behavior is as shown in Figure 16, and the roof deformation is less than the engineering-permitted value of 200 mm, which verifies the reliability of ELAD method.Figure 16
Deformation behavior of the entry.


## 5. Conclusions

It is hard to protect the underground entry from large deformation when the entry is loaded by the abutment stress and dynamic stress simultaneously in longwall mining engineering. The new method of ELAD was put forward to layout the entry. DDI is the key technology parameter in ELAD, which is divided into three grades, “Slightly Disturbed Type,” “Moderately Disturbed Type,” and “Violent Impact Type.” The entry should keep away from the dynamic stress of Violent Impact Type firstly and then be arranged in the zone where the dynamic stress belongs to Slightly Disturbed Type. DDT and DLT were proposed to solve the grades of DDI, which can be calculated by the method of zero growth DDI of plastic failure zone and the engineering-permitted limitation deformation.A dynamic and static numerical analysis model with FLAC3D500 software was established to solve DDT and DLT. To improve the reliability of this model, the Mohr–Coulomb model and Strain-Softening model for the rock and coal material deformation behavior were validated in detail with a uniaxial compression process. The Strain-Softening model and Mohr–Coulomb model are applied to simulate the deformation behavior of the coal and rock materials, respectively. The results of the model indicate that DDI increases linearly as the increasing of the dynamic stress. DDT increases linearly and DLT decreases with a power function as the increasing of the abutment stress. DDI equals 1 in the plastic failure zone and is small enough in deformation when the dynamic stress belongs to Slightly Disturbed Type. Those increase indeed when the dynamic stress belongs to Moderately Disturbed Type and they increase to large enough values when the dynamic stress belongs to Violent Impact Type.ELAD method has advantages in mechanical behavior, loading conditions, and deformation evaluation indexes for coal materials compared with the widely used method, especially for the underground entry loaded with abutment stress and dynamic stress. The range of the acceptable location for entry layout increases indeed and the entry is able to bear larger dynamic stress with the increasing of support resistance, which improves the applicability of ELAD method. The field case discussion verified that ELAD method was reliable. The inadequacy of ELAD method is the influence of internal detailed discontinuous structures of the coal material, which will be considered in the next research project. The analysis procedure is repeatable and necessary since the coal material may differ in geological and engineering conditions.



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*Source: 6655293-2020-12-23.xml*