Study on Crack Penetration Induced by Fatigue Damage of Low Permeability Coal Seam under Cyclic Loading

Abstract

For low permeability coal seam permeability is weak, low degree of gas migration, prone to gas accidents and other issues. In this paper, a numerical model is established to simulate the process of hydraulic fracturing under monotonic loading and cyclic loading, and a method of increasing permeability of coal seam by cyclic loading hydraulic fracturing technology is proposed. Combined with similar experiments, the influence of cyclic load and cyclic load applied parameters on the fracturing effect of coal and rock mass was analyzed by applying a cyclic load with a pulse pump. The effect of cyclic load pressure technology on coal seam drainage was analyzed by application in 20915 gas control roadways of a coal mine in Guizhou. The results show that after fracturing, the fracture extends along the weak plane of the prefabricated fracture, the pore pressure in the fracture is high pressure, and the pore pressure around the fracture decreases step by step. Due to the compression of the crack, the energy is transferred to the two ends of the crack. The pore pressure has an irregular oval distribution, and there is stress concentration. The pressure value reaches 41.48 MPa. After the cyclic load was applied to the model, the pressure reached the maximum value of 27.64 MPa at 3.37 s. Compared with the monotonic load, the pressure value was reduced by 46.27%. Through pressure and ringing analysis, the fatigue damage of specimens can be realized under cyclic loading. In the experiment, the unconstrained initiation pressure was 2.48 MPa, but after the constraint was applied, the initiation pressure increased to 4.58 MPa, and the pressure increase reached about 55%. After multiple loading and unloading, the peak pressure of the specimen can be reduced and the number of cracks can be increased. In the experiment, the gas extraction rate of ordinary drilling was maintained at about 0.019 m³/min, and the gas extraction rate of ordinary fracturing drilling fluctuated at 0.025 m³/min after 21 days of gas extraction. The pumping capacity of 15 Hz and 20 Hz cyclic loading fracturing boreholes tended to be stable after 15 days, which were about 0.041 m³/min and 0.062 m³/min, respectively. Cyclic loading hydraulic fracturing is better than monotonic loading hydraulic fracturing, and the lower the cyclic loading frequency, the better the fracturing effect.

1. Introduction

More than 70% of coal-bearing strata in China are low-permeability coal seams, and their gas permeability is generally 0.1~10 md (2–3 orders of magnitude different from that of the Black Warriors Basin in the United States) [1,2,3,4,5]. In addition, gas is free in the coal seam fracture system, and exists in the adsorption state on the pore and fracture surface. More than 90% of the gas is adsorbed in the coal matrix block. The adsorbed methane reduces the channel of gas migration and reduces the permeability of methane in the coal seam [6,7,8,9,10,11,12]. Therefore, it is of great significance for the prevention and control of coal mine gas accidents in China to realize the efficient extraction of low-permeability coal seam gas.

At present, in increasing the permeability of coal seam, there are usually two categories: extra-layer measures and in-layer measures. Out-of-layer measures are regional measures, generally using the method of mining protective layer pressure relief and permeability enhancement [13,14,15,16]. In the case of being unable to carry out measures outside the layer, measures inside the layer are the inevitable choice. Hydraulic fracturing involves injecting high-pressure liquid into coal and rock mass, destroying the internal structure of coal and rock mass, forming a fracture network, and thereby accelerating the flow of gas. It is an effective coal seam permeability enhancement technology [17,18,19,20,21,22,23,24].

Some scholars use the finite element method [25], boundary element method [26], extended finite element method [27], and other numerical analysis methods to establish a plane model to imitate the development of coal and rock fractures in the process of hydraulic fracturing, which has been widely used.

Li [28] found that increasing the injection rate has a great influence on the vertical fracture shape of coal and rock by simulating the hydraulic fracturing process of a naturally fractured reservoir. Bi [29] used a GPD model to simulate the initiation, propagation, and combination of the fracturing process, but ignored the influence of anisotropy coefficient caused by surrounding rock stress. Liu et al. [30] found that the expansion of hydraulic fracture changes with the previous cracks, and that the effective stress is the main factor affecting the expansion of hydraulic fracturing. Zheng et al. [31] used the block discrete element method to study the viscosity and injection rate of different fracturing fluids, and found that high viscosity and high injection rate were conducive to the generation of hydraulic slotting in the penetrating layer. Yu et al. [32] studied the anisotropic angle of shale and injection rate on the fracture propagation without confining pressure, and found that the anisotropic angle was nonlinearly correlated with the breakdown pressure of shale. Patel et al. [33] proposed a new method of pre-breakdown cyclic jet hydraulic fracturing, which can increase the damage area around the hydraulic fracturing. Jia et al. [34] found that the hydraulic fractures generated by cyclic injection have high fracture curvature, which is helpful for the fatigue mechanism of rock decomposition. Liu et al. [35] also conducted triaxial hydraulic fracturing tests under different cycle durations and injection rates, determined the influence of key cycle hydraulic fracturing parameters on hydraulic fracturing causes and fracture propagation, and proposed a multistage alternate injection fracturing method for HDR.

Previous studies on hydraulic fracturing mostly consider the factors of coal and rock mass itself. Under cyclic loading, coal and rock mass not only exhibit elastic and plastic deformation, but also rheology. The damage process is extremely complex, and the damage mechanism needs to be further explored.

This paper intends to further determine the effect of anti-reflection in the process of fatigue damage by applying a cyclic load on the rock specimen and analyzing the change of frequency and amplitude. Herein, the feasibility of increasing permeability of low-permeability coal seam under a cyclic load is verified by experiments.

2. Coal Rock Fracturing Theory

2.1. Fracture Mechanics Model of Coal–Rock Mass under Monotonic Loading

Figure 1 shows the damage-cracking mechanical model of coal around a borehole under monotonic loading. The borehole is subjected to expansion force P_w, and the surrounding rock around the borehole is subjected to horizontal principal stresses σ₁ and σ₃.

According to the drilling force model, the calculation formula of coal rock burst pressure is as follows:

$${\sigma }_{\theta }=\frac{{\sigma }_1+{\sigma }_3}{2}\left(1+\frac{R_0{}^2}{r^2}\right)+\frac{{\sigma }_1-{\sigma }_3}{2}\left(1+3\frac{R_0{}^4}{r^4}\right)\cos 2\theta +T-P_w\frac{R_0{}^2}{r^2}$$

(1)

where σ_θ is tangential stress (MPa); σ₁ and σ₃ are maximum principal stress and minimum principal stress, respectively (MPa); T is tensile strength of coal and rock mass (MPa); P_w is the expansion pressure in the hole (MPa); R₀ and r represent borehole radius and distance from center, respectively (m); θ is the angle of the line between any point on the borehole wall rock and the axis relative to the horizontal direction (°).

When σ_θ = 0, the calculation formula of initiation pressure is obtained:

$$P_w=\frac{{\sigma }_1+{\sigma }_3}{2}\left(\frac{r^2}{R_0{}^2}+1\right)+\frac{{\sigma }_1-{\sigma }_3}{2}\left(\frac{r^2}{R_0{}^2}+3\frac{R_0{}^2}{r^2}\right)\cos 2\theta +T\frac{r^2}{R_0{}^2}$$

(2)

The formula for calculating the initiation pressure at the hole wall position r = R₀ is as follows:

$$P_w=\left({\sigma }_1+{\sigma }_3\right)+2\left({\sigma }_1-{\sigma }_3\right)\cos 2\theta +T$$

(3)

There is a direction θ = 90° and cos2θ = −1 around the borehole, that is, along the direction parallel to the maximum principal stress, and the initiation pressure in the loading process is minimized. Therefore, the formula for calculating the minimum initiation pressure is

$$P_w=T+3{\sigma }_3-{\sigma }_1$$

(4)

2.2. Fracture Theory of Coal under Monotonic Loading

The damage constitutive relation is established according to the damage mechanics theory:

$$\left[\sigma \right]=\left[\sigma *\right]\left[I-D\right]=\left[C\right]\left[\epsilon \right]\left[1-D\right]$$

(5)

where [C] is the material elasticity matrix, D is the damage variable under monotonic load, I is the unit matrix, [σ] is the stress matrix, [σ*] is the effective stress matrix, and [ε] is the strain matrix.

According to the damage constitutive relation (5), the functional relation between volume strain ε_v and damage degree D can be established.

Firstly, assuming that the micro-element strength follows Weibull distribution, the damage evolution equation is deduced:

$$P\left(F\right)=\frac{m}{F_0}{\left(\frac{F}{F_0}\right)}^{m-1}\exp \left[-{\left(\frac{F}{F_0}\right)}^m\right]$$

(6)

where F is a random distribution variable of the strength of the element (the strength of the element usually follows a certain strength criterion) and m and F₀ are Weibull distribution parameters (F₀ reflects the macroscopic average strength of rock and m reflects the concentration of rock element strength distribution).

It can be seen from Equation (6) that the characteristic parameters of coal damage include many physical quantities. It is necessary to test the elastic modulus E, Poisson’s ratio μ, internal friction angle φ, cohesion C, the horizontal stresses σ₁ and σ₃, and the expansion pressure P_w. At the same time, the AE signal in the crack initiation process and the phenomenological method are recorded to describe the crack development characteristics.

Secondly, the damage degree D of coal and rock mass under monotonic loading is solved.

The damage degree D is the ratio of the number of damaged micro-elements N_i to the total number of micro-elements N. In any strength interval [F, F + dF], the number of damaged micro-elements is NP (y) dy. Through integration, the function expression of damage variable D_di can be calculated:

$$D=\frac{N_f}{N}=\frac{{\displaystyle {\int }_0^{F}NP\left(y\right)dy}}{N}=1-\exp \left[-{\left(\frac{F}{F_0}\right)}^m\right]$$

(7)

2.3. Fatigue Damage Cracking Theory of Coal under Cyclic Loading

The damage evolution equation in a three-dimensional stress environment is established [36]:

$$D_i=1-{\left(1-{\left(\frac{N_i}{N_f{}_i}\right)}^{\alpha }\right)}^{\beta }$$

(8)

where D_i is the crack damage degree of level i, N_i is the number of cycles for stage i cyclic loading, N_fi is the number of cycles when the first crack reaches fatigue damage, and α and β are material parameters.

The internal damage process of coal under cyclic loading can be described by the macroscopic quantity of cumulative acoustic emission:

$$D_j=\frac{N_j}{N_{mj}}$$

(9)

where N_j is the cumulative number of acoustic emission events for level j cracking and N_mj is the total number of acoustic emission produced at stage j cracking.

According to the Formulas (8) and (9), when I = j, D_i = D_j, combined with acoustic emission data, the material parameters α and β can be solved by software calculation; that is, the damage evolution equation is established.

The total damage degree under cyclic loading is obtained by summing up the damage degree in each region:

$$D={\displaystyle {\sum }_1^N{D}_i}$$

(10)

From Formulas (8)–(10), the functional relationship between the crack damage degree of each stage and the total damage degree can be obtained, so as to reveal the crack mechanism of fatigue damage.

2.4. Mathematical Model of Fluid–Solid Coupling

2.4.1. Effective Stress of Porous Media

When the boundary of porous media is deformed by an external load, the solid skeleton will generate effective stress at the contact surface. In porous media, the pore fluid is sufficient to bear this, as well as part of the external load, so the external load will be jointly borne by the stress and the fluid force borne by the solid. The study on the interaction between pore pressure and external load is the basis of the effective stress principle, whose expression [37] is

$${\sigma }_H={\sigma }_h-[s_w{p}_w+(1-s_w)p_{nm}]I_r$$

(11)

where σ_H is effective stress (Pa), σ_h is the total stress (Pa) s_w is the wetting phase saturation (dimensionless), p_w is the pressure of the wetting phase (Pa), p_nw is the pressure of the non-wetting phase (Pa), and I_r [1, 1, 1, 0, 0, 0]^T is the unit matrix.

In order to further simplify the calculation model in the process of hydraulic fracturing, it is assumed that the non-wetting phase pressure in the whole model remains constant and is relatively much smaller than the wetting phase pressure, so p_nw can be ignored. When the reservoir is fully saturated (s_w = 0), the expression of effective stress principle is simplified as follows:

$${\sigma }_H=\sigma -p_{nm}{I}_r$$

(12)

2.4.2. Control Equation of Solid Particles in Porous Media

The process of hydraulic fracturing will change the stress field of rock in the formation. For porous media such as rock, its stress balance. The equation can be described by the principle of virtual work: the virtual work of rock within a fixed time is equal to the physical force acting on the whole rock and the superposition of virtual work generated by surface force [38].

The equilibrium equation of rock mass medium is [39]

$${\displaystyle {\int }_V({\sigma }_h-p_n{}_w{I}_r)}{\delta }_{\epsilon }dV={\displaystyle {\int }_{s}t}·{\delta }_v{\delta }_{\epsilon }dS+{{\displaystyle \int }}_{V}f·{\delta }_{v}dV$$

(13)

where δ_ε is a virtual strain rate matrix (s⁻¹), t is a surface force matrix (N/m²), δ_v is a virtual velocity matrix (m/s), f is a physical matrix (N/m³), and dV is the unit (m³).

2.4.3. Control Equation of Fluid in Porous Media

According to the principle of mass conservation, the change of fluid mass in a unit within a unit of time is equal to the difference of fluid mass flowing in and out of the unit. The classical Darcy’s law can be used for the flow relationship of fluid in rocks, whose specific expression is

$$v_w=-\frac{1}{n{\mu }_r}K·(\nabla P_w-{\rho }_{w}g)$$

(14)

where v_w is seepage velocity vector (m/s), n is porosity, μ_r is fluid viscosity (mPa), K is permeability tensor (mD), ρ_ω is fluid density (kg/m³), and g is the gravity acceleration vector (m/s²).

According to Gauss’ formula, the continuity equation of fluid medium is [40]

$${\displaystyle {\int }_V{\delta }_V\frac{1}{J}}\frac{d}{dt}(J{\rho }_{\omega }{n}_{\omega })dV+{\displaystyle {\int }_V{\delta }_v\frac{\partial }{\partial \chi }}({\rho }_{\omega }{n}_{\omega }{v}_{\omega })dV=0$$

(15)

where J is the volume change rate of the porous medium (dimensionless), n_ω is the ratio of fluid volume to total volume (dimensionless), χ is the space vector (m), dt is the time increment step (s), and ν_ω is seepage velocity (m/s).

2.4.4. Finite Element Discretization Method in ABAQUS

Define the function [41] as

$$\{\begin{array}{c}{\mu }_r=N_{\mu }\overline{\mu }\\ \epsilon =B\overline{\mu }\\ p_0=N_p{\overline{p}}_0\end{array}$$

(16)

where N_μ and B is the defined function vector matrix, $\overline{\mu }$ is element node displacement, p₀ is the pore pressure of unit node, and N_p is a shape function.

$${\displaystyle {\int }_V{a}^T\overline{A}dV+{\displaystyle {\int }_S{b}^T\overline{B}dS=0}}$$

(17)

where $\overline{A}$ is the control equation and $\overline{B}$ is the continuous boundary equation.

The solid-state finite element equation can be obtained by substituting Equation (16) into Equation (13):

$$K\frac{d\overline{u}}{dt}+C_r\frac{d{\overline{p}}_0}{dt}=\frac{df}{dt}$$

(18)

The continuity equation and boundary condition are moved to zero on the right side, and the Galerkin method is used to multiply the left side of the equation. Replace (17) with $\overline{A}$ and $\overline{B}$, replace (17) with the form function constructed by ε and p₀ in (16), and let a = −b; then, the deformation is simplified as

$$E\frac{d\overline{u}}{dt}+F{\overline{P}}_0+G\frac{d{\overline{p}}_0}{dt}=\overline{f}$$

(19)

The stress-seepage coupling Equation (20) can be obtained by simultaneous Equations (18) and (19). For the setting area, the distribution law of corresponding parameters can be obtained by solving the finite element solver in ABAQUS:

$$\left[\begin{array}{cc}K& C_r\\ E& G\end{array}\right]\frac{d}{dt}\left\{\frac{\overline{u}}{{\overline{p}}_0}\right\}+\left[\begin{array}{cc}0& 0\\ 0& F_r\end{array}\right]\left\{\frac{\overline{u}}{{\overline{p}}_0}\right\}=\left\{\begin{array}{c}\frac{d}{dt}\\ \overline{f}\end{array}\right\}$$

(20)

with

$$K={\displaystyle {\int }_V{B}^T{D}_{ep}B}dV$$

(21)

$$C_r={\displaystyle {\int }_V{B}^T{D}_{ep}m\frac{\left(s_0+\xi p_0\right)}{3K_s}{N}_p}dV-{\displaystyle {\int }_V{B}^T\left(s_0+\xi p_0\right)m{N}_p}dV$$

(22)

$$E={\displaystyle {\int }_V{N}_p{}^T\left[s_0\left(m^T-\frac{m^T{D}_{ep}}{3K_s}\right)B\right]}dV$$

(23)

$$F_r={{\displaystyle \int }}_V{\left(\nabla N_p\right)}^{T}k{k}_r\nabla N_{p}dV$$

(24)

$$G={\displaystyle {\int }_V{N}_p^T\left\{s_0\left[\left(\frac{1-n}{K_s}-\frac{m^T{D}_{ep}m}{{\left(3K_s\right)}^2}\right)\right]·\left(s_0+\xi p_0\right)+\xi n+n\frac{s_0}{K_0}\right\}}{N}_{p}dV$$

(25)

$$df={\displaystyle {\int }_V{N}_u{}^{T}dfdV}+{\displaystyle {\int }_S{N}_u{}^{T}d\tau dS}$$

(26)

$$\overline{f}={\displaystyle {\int }_s{N}_u{}^T{q}_{0b}dS}-{{\displaystyle {\int }_V\left(\nabla N_p\right)}}^{T}k{k}_{r}gdv$$

(27)

where q_0b is the fluid flow on the boundary and k is the permeability coefficient tensor.

3. Numerical Simulations

3.1. Fundamental Model

Based on the ABAQUS extended finite element method, combined with the basic parameters of the model, (see

Table 1. Model parameter table.

Parameter	Poisson’s Ratio	Young’s Modulus E (Gpa)	Permeability (m·s−1)	Viscosity (Pa·s)
Taking values	0.03	15	0.0000001	0.001

), a two-dimensional numerical model of 200 × 200 mm fracturing was established. There are 27,565 units in the model, and drilling is carried out in the middle of the model. The diameter of the drilling is 20 mm, as shown in Figure 2. The 8 MPa vertical stress and 4 MPa horizontal stress were applied around the initial model, and the fixed boundary was set to prevent the movement of the model during fracturing, so as to simulate the propagation and development law of prefabricated cracks in the model during fracturing. The material parameters of numerical simulation were measured by experiments, and the external stress was simply calculated by the burial depth of the engineering test site.

3.2. The Initiation Change of Monotonic Load on Prefabricated Cracks

By establishing a numerical model, the calculation time of the design model is 100 s, and the increment is 10,000 steps [42]. The pore pressure distribution and fracture width cloud map of each time period were obtained.

Figure 3a shows that after fracturing, the fracture extends along the direction of the prefabricated fracture, the pore pressure in the fracture presents a high pressure state, and the pore pressure around the fracture decreases step by step. At both ends of the crack, the pore pressure has an irregular oval distribution, and stress concentration occurs; the pressure value reaches 41.48 MPa. This is due to the formation of fluid pressure transmission in the fracture, which makes the pressure around the fracture generally increase. When the crack extends to the boundary of the model, the pressure in the crack tip decreases obviously and eventually tends to balance. There is no obvious downward trend of pressure in the borehole center, and the state of high stress is maintained due to the propagation of injected high-pressure fluid in the borehole center, as shown in Figure 3b.

It can be seen from Figure 4 that the central part of the crack is the widest, and the crack tip crack width decreases gradually in the direction of crack development. This is consistent with the pore pressure distribution in Figure 3, mainly due to the permeability difference and tensile strength difference between the reservoir and the interlayer. The fracturing fluid enters the reservoir from the injection point, and then gradually penetrates into the interlayer. At this time, the permeability difference of the interlayer hinders the seepage of the fracturing fluid. At the same time, the tensile strength of the interlayer is greater than that of the reservoir, the crack initiation is more difficult, and the crack will extend along the direction of the fracture length. When the water pressure in the borehole continues to increase, the crack further turns to the direction of the maximum principal stress. At this time, the deflection of the crack is mostly affected by the shear stress, and the crack presents a symmetrical distribution in the ideal state. With an increase in time, the length and width of the crack increase significantly, and the maximum compressive stress still appears in the crack initiation part. In Figure 4b, the direction given by the upper left corner crack is below the end-biased model, which may be caused by the boundary size of the square model.

3.3. The Influence of Cyclic Load on Fracture Morphology

In order to further understand the influence of cyclic loading on the fracturing effect of the model, the simulated water pressure loading mode was modified. The load was selected by a sawtooth wave function and the cycle period was set to 10 steps [43]. By applying cyclic load to the model and monitoring the same position, the pore pressure distribution and fracture width variation diagram of the drilling center are obtained, as shown in Figure 5.

It can be seen from Figure 5a that after the cyclic loading is applied to the model, the change trend of the pore pressure curve is similar to that of the monotonic loading, but the pore pressure curve after the cyclic loading exhibited five obvious small-range amplitudes compared with the monotonic loading. The pressure reached the maximum value of 27.64 MPa at 3.37 s. Compared with the monotonic load, the pressure value was reduced by 46.27%, and the crack initiation time of the model was also about 3 s earlier, indicating that multiple loading and unloading of the pressure at the injection point of the model can reduce the pressure at the crack initiation of the model. After the pore pressure reached the peak value, it rapidly decreased to about 21.48 MPa, and then the pressure continued to fluctuate downward, gradually decreasing and eventually tended to be flat. The development of cracks is basically consistent with the monotonic load. At the crack initiation time, the crack width increases rapidly to about 0.0021 m, and then the change of crack width is not obvious.

3.4. The Influence of Different Confining Pressures on Pore Pressure

Under the action of surrounding rock stress, the pores and fissures of coal and rock mass will be compacted. The peak strength and elastic modulus of coal and rock mass increase with the increase in confining pressure, which enhances the ability of coal and rock mass to resist damage, and changes the pore pressure of coal and rock mass during fracturing, thus affecting the initiation pressure of coal and rock mass. In order to explore the influence of surrounding rock stress on the pore pressure of the model, six groups of surrounding rock stress of 0, 2, 4, 6, 8, and 10 MPa were applied to the model; the simulation results are shown in Figure 6.

By observing the effect distribution of pore pressure under different confining pressures, the peak value of pore pressure increased from 14 MPa to 39 MPa when the confining pressure increased from 0 MPa to 10 MPa. The time to reach the peak stress was different. With the increase in confining pressure, it takes a longer time to reach the peak pore pressure. However, with the increase in confining pressure, the time increment decreases and shows an exponential function as a whole, as shown in Figure 7a. Through peak value and time analysis, it can be concluded that confining pressure has an obvious influence on pore pressure, and the larger the confining pressure, the larger the pore pressure is in the model. This is because when there is no confining pressure, the fracturing pressure interacts with the compressive strength of coal rock itself, and when the confining pressure is greater than the compressive strength, cracks will occur. When confining pressure is applied outside the coal rock, the action direction of confining pressure is opposite to the fracturing pressure. At this time, the fracturing pressure needs to be greater than the sum of the compressive strength and confining pressure of coal rock to produce cracks.

The peak value of pore pressure under different confining pressures has been linearly fitted, and the variation diagram of pore pressure with confining pressure is shown in Figure 7b. With the increasing confining pressure, the pore pressure increases linearly. It can be shown that under the same conditions, the greater the confining pressure, the greater the pore pressure in coal and rock mass.

4. Hydraulic Fracturing Experiment

The numerical simulation analysis shows that the cyclic load can significantly reduce the fracturing pressure, and the functional relationship between the fracture generation time and the fracture pressure under different confining pressures can be obtained. However, the simulation process cannot monitor the micro-cracks before the failure of the specimen. Therefore, we monitored the micro-fracture generation time and number of parameters through ordinary fracturing and cyclic loading fracturing experiments. Based on numerical simulation and laboratory experiments, hydraulic fracturing under cyclic loading can be better studied.

4.1. Experimental System

Constrained cracking experiments take into account the acoustic emission instrument measurement range limit using 1200 mm diameter circular steel barrel as the coal rock cracking chamber, with a steel barrel wall of thickness 15~20 mm and height of 500 mm. The specimens of cube shape were used in the monotonic loading test. The length of the section edge is 800–850 mm and the height is 500 mm. The expansion tube was inserted into the center of the cube at the same time as pouring the specimen. The inner diameter of the fracturing borehole is 30~50 mm [44]. The coal rock fracturing platform is shown in Figure 8, and the stress microstructure is shown in Figure 9.

4.2. Fracturing Experiment and Process

The hydraulic pump station was started to exert monotonic and cyclic loads on the cube specimen, and the acoustic emission instrument and high-speed camera were started to collect information. The cyclic loading cracking experiment adopted two-stage cracking. First, the initial cracking was carried out, and then the cracking was expanded. The schematic diagram of the cracking process is shown in Figure 10. The number of crack propagation events and the variation law of propagation energy with time were monitored with an acoustic emission instrument, and the dynamic change law of crack from initiation, to propagation, to arrest was observed. When the crack extends to the constraint boundary of the steel barrel, the pressure was stopped and the experiment was completed.

4.3. Experimental Results

4.3.1. The Law of Crack Expansion Energy under Monotonic Loading

By applying a monotonic load, the change rule of crack AE signal was monitored, and the crack initiation pressure and crack development characteristics of concrete specimens under monotonic load were analyzed. The monotonic load cracking diagram is shown in Figure 11.

At the beginning of the fracturing experiment, the pressure increased continuously; the acoustic emission event occurred at 17 s, and the concrete specimen exhibited fine cracks. With the increase of pressure, the fracturing continued. At 45 s, the number of acoustic emission events in the concrete specimens increased sharply, reaching the maximum, and then decreased rapidly. It can be judged that the concrete specimen cracked rapidly at 45 s and formed two macroscopic cracks. At the same time, the monotonic load reached the peak value, and the crack initiation pressure of the concrete specimen was 21 MPa. There was no obvious change in the direction of crack development, and the fracture ring profile was single. It is speculated that the initial fracturing plays a leading role in the whole fracturing process. After 45 s, due to the damage of concrete specimens, the internal pressure was released and the number of acoustic emission events decreased. The experimental results show that the monotonic loading on concrete specimens by expansion tube can achieve rapid cracking and produce a few cracks, but the number is relatively small.

4.3.2. Change Rule of Crack Expansion Energy Induced by Cyclic Loading

In order to further explore the fracture development characteristics of concrete specimens under different load fracturing, through the fracturing conditions of two groups of different cyclic loads (unconstrained fracturing and constrained fracturing), the fracturing effect was analyzed from the number of loading and unloading and the corresponding peak combined with AE signal change.

Unconstrained Cracking

The crack development characteristics of concrete specimens under cyclic loading were analyzed by applying cyclic loading on unconstrained concrete specimens and monitoring the change law of crack AE signals. The cyclic load cracking diagram is shown in Figure 12.

From Figure 12, it can be seen that the concrete specimens were loaded and unloaded three times; the three loading peaks are 2.19 MPa, 2.84 MPa, and 2.04 MPa, respectively. Compared with the monotonic loading, the ringing reaction occurred in the cyclic loading test for about 12 s, while the first ringing event occurred in the monotonic loading test for about 17 s, and the ringing number of monotonic loading was less than 600 times. In the cyclic loading test, the number and energy of acoustic emission events were the most concentrated near the third loading peak, and the number of ringing events was nearly 800 times. At this time, the concrete specimen broke and three penetrating cracks were cracked, as shown in Figure 13 and Figure 14. Experiments show that multiple loading and unloading can significantly reduce the peak fracturing pressure. From the perspective of overlooking, the angle between the three cracks is about 120°, and the crack propagated along the minimum resistance line. A sketch is shown in Figure 14b. During the propagation process, the crack always tends to develop in the direction of small resistance and deviates from the direction of large resistance.

Constrained Cracking

The concrete specimen was restrained by a steel tube, and the change rule of crack AE signal was monitored by applying a cyclic load on the concrete specimen, as shown in Figure 15.

As shown in Figure 15, after several loading and unloading, the loading peak of the concrete specimen was 4.58 MPa, and finally, tensile failure occurred under tensile stress. Once a limited number of macroscopic cracks are formed, it is difficult to crack by applying expansion force, which is determined by the way it is applied. At 199 s, the pressure is only 1 MPa, but the ring count is the highest. This shows that under the action of a cyclic load, the fatigue damage of concrete can be realized by using a low-amplitude cyclic load.

Compared with the unconstrained experiment, it can be found that the unconstrained initiation pressure was 2.48 MPa, but after the constraint is applied, the initiation pressure increased to 4.58 MPa, and the pressure increase reached about 55%. Due to the external constraint of the specimen, when the water injection pressure increases, the micro-cracks near the borehole are subjected to force, and the cracks are subjected to external stress. In order to unload the external stress applied, the energy is transferred to the weak surface of the crack, so that the stress at the crack tip is concentrated. When the specimen strength is lower than the peak stress at the crack tip, the crack will expand. When the constraint exists, if the crack wants to continue to expand, it needs to resist the specimen strength and external constraint at the same time. Therefore, the crack initiation pressure of the constrained experiment is significantly greater than that of the unconstrained experiment, and the number of cracks is also more than the latter. However, the two groups of experiments are carried out under the condition of no surrounding rock stress. If there is surrounding rock stress, the initiation pressure calculated according to Formulas (2) can generally reach more than 10 MPa. As the range increases, the fracturing pressure increases.

5. Engineering Verification

5.1. Drilling Arrangement

The test mine is located in the northwest wing of the Jinsha–Qianxi syncline. The mine field is generally a syncline structure and has a secondary fold [45]. The Jinsha–Qianxi syncline is located on the east side of the well field, and its axis is ‘S’-shaped in plane. The dip angle of northwest wing is relatively slow, and secondary folds have developed. The Xinhua syncline is located in the middle of the well field, which is a secondary fold of the northwest wing of the Jinsha–Qianxi syncline, and its axis tends to northwest. The test was carried out for nine coal seams; for the coal seam located in the middle of the Longtan coal group, the horizon is stable and the coal thickness is 1.27~5.79 m (average of 2.77 m). The direct roof is silty mudstone, upward is siltstone or fine sandstone, the direct floor is argillaceous siltstone, and the local area is silty mudstone and siltstone. The permeability coefficient of the coal seam is 0.05~7.17 m²/(MPa²·d), and the gas content is 20.82~23.42 m³/t. The drilling position is 20915 on the gas control roadway. The inclined length of the test face is 172 m, and the strike length is 610 m. The buried depth of the coal seam in the test area is 393~421 m. The test site diagram is shown in Figure 16.

Four boreholes were drilled in the test. One common borehole was used, the other was used for monotonic loading fracturing, and the two were used for cyclic loading fracturing. The common emulsified water pump was used in the monotonic loading hydraulic fracturing drilling, and the pulse water pump was used in the cyclic loading hydraulic fracturing drilling. The peak water injection pressure was 25 MPa and the frequency was 25 Hz. The start-up pressure of the pump was set to 5 MPa and the pump was pressurized at a rate of 0.2 MPa/min for about 180 min. If the water injection pressure of the pump drops off a cliff without rebounding, or the fracture is completed when the gas concentration of the observation hole increases, the water injection is stopped; the fracture parameters of the borehole are shown in

Table 2. Drilling parameters.

Drilling Type	Drilling Number	Maximum Fracturing Pressure (Mpa)	Fracturing Time (min)	Cyclic Loading Frequency (Hz)
Common borehole	1#	-	-	-
Monotonic loading hydraulic fracturing	2#	23	80	-
Cyclic loading hydraulic fracturing	3#	15	140	20
	4#	11	100	15

Note: - represents that there is no such parameter.

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5.2. Extraction Effect Analysis

The boreholes were treated with the predetermined process; four boreholes were sealed for 20 m, and the extraction pipes were connected for continuous extraction. We recorded and compared the change of gas flow of each borehole, obtaining the curve of gas emission and gas concentration with time, as shown in Figure 17 and Figure 18.

According to Figure 17, the gas extraction rate of ordinary boreholes was maintained at about 0.019 m³/min, and the gas extraction rate decreased by 0.007 m³/min after 21 days of extraction. The maximum pressure of monotonic hydraulic fracturing is 23 MPa. The maximum pressure of cyclic loading hydraulic fracturing is 15 MPa at 20 Hz and 11 MPa at 15 Hz, which is 47.83% of that of monotonic hydraulic fracturing. However, the maximum extraction flow rate of monotonic loading hydraulic fracturing is only 0.103 m³/min, and the maximum extraction flow rate of cyclic loading hydraulic fracturing can reach 0.230 m³/min, which is 1.23 times that of monotonic hydraulic fracturing. After 5 days of extraction, the gas extraction mixture of borehole #2 was reduced to 0.027 m³/min, and the later fluctuation was small. The extraction mixture of boreholes #3 and #4 tended to be stable after 15 days, at about 0.041 m³/min and 0.062 m³/min, respectively. In the same experimental site, the same extraction negative pressure was used for extraction, and the extraction amount can be used to characterize the damage degree of coal around the borehole. The more serious the damage degree of coal around the borehole, the higher the development of surrounding fractures, and the smoother the gas migration, resulting in an increase in the extraction amount. The gas drainage volume at the initial stage of 15 Hz cyclic loading was 0.021 m³/min higher than that at the initial stage of 20 Hz cyclic loading.

It can be seen from the gas extraction concentration diagram that the gas concentration of ordinary boreholes was maintained at 20.5~9.1% within 21 days of extraction. Single fracturing was maintained at 27.1~2.0%, and the gas concentration of single fracturing was generally higher than that of ordinary drilling, but the difference was not large. During the extraction period, the concentration of ordinary drilling was higher than that of fracturing drilling in some days, which may have been caused by the influence of nearby mining and the blockage of internal cracks in the extraction process. The concentration of cyclic loading fracturing boreholes was significantly higher than that of boreholes 1# and 2#. Due to the cyclic loading hydraulic fracturing, the fracture network around the borehole is more developed, and the extraction concentration can reach 86.7% at the highest and 16.2% at the lowest. The gas drainage concentration of borehole 3# is 70.1~16.2%, and that of borehole 4# is 86.7~24.1%. Gas concentration in boreholes #3 and 4# decreased continuously during drainage. In the late stage of extraction, borehole 3# tended to be flat, while borehole 4# still had a downward trend. The gas concentration of the 15 Hz cyclic load was higher than that of 20 Hz cyclic load. The gas concentration increased by 23.6% at the initial stage of extraction; the gas concentration is shown in Figure 18.

Due to the propagation characteristics of waves, the larger the frequency of waves, the faster the energy loss, and the shorter the propagation distance in coal seam fractures. Therefore, hydraulic fracturing with low-frequency cyclic loading is more effective. In summary, cyclic loading has a strong anti-reflection effect, and the lower the frequency of cyclic loading, the better the cracking effect.

6. Conclusions

(1) By establishing a numerical model, the hydraulic fracturing process under different conditions was simulated. The results show that after fracturing, the fracture extends along the direction of the prefabricated fracture, the pore pressure in the fracture is high pressure, and the pore pressure around the fracture decreases step by step. At both ends of the crack, the pore pressure has an irregular oval distribution, and stress concentration occurs; the pressure value reaches 41.48 MPa. In the fracturing process of the model, the central part of the fracture is the widest, and in the direction of fracture development, the fracture tip width decreases gradually.

(2) After the cyclic loading was applied to the model, the maximum pressure value at the crack initiation of the model was reduced by 46.27% compared with that of the monotonic loading model, and the time was also advanced by about 3 s, indicating that multiple loading and unloading of the injected liquid pressure could reduce the pressure at the crack initiation of the model. In addition, the unconstrained initiation pressure was 2.48 MPa, but after the constraint was applied, the initiation pressure increased to 4.58 MPa, and the pressure increase reaches about 55%. The crack initiation mode under monotonic loading can only produce a limited number of cracks. After several loading and unloading loads, the peak pressure of the specimen can be significantly reduced, and the number of cracks will also increase. The fatigue damage of the specimen can be achieved by using low-amplitude cyclic loading. The crack follows the principle of minimum energy in the propagation process; it always tends to the direction of small resistance and deviates from the direction of large resistance.

(3) The gas extraction rate of ordinary borehole was maintained at about 0.019 m³/min, and the gas extraction rate of ordinary fracturing borehole fluctuated at 0.025 m³/min after 21 days. The mixing amount of the 15 Hz and 20 Hz boreholes tended to be stable after 15 days, which stabilized at 0.041 m³/min and 0.062 m³/min, respectively. The effect of cyclic loading hydraulic fracturing was better than that of monotonic loading hydraulic fracturing, and the extraction flow rate was 1.23 times that of monotonic loading hydraulic fracturing. Lower cyclic loading frequency is conducive to crack formation, and the crack initiation effect at 15 Hz was about 23.6% higher than that at 20 Hz at the beginning of the test.