Influence of Bidirectional Impact Loading on Anomalously Low-Friction Effect in Block Rock Media

,e anomalously low-friction effect is a key scientific problem in deep mining. ,e deep coal rock media is usually a block structure with joint fracture. When the deep block coal rock is subjected to repeated strong dynamic impact caused by long-term excavation activities, the anomalously low-friction effect will occur, resulting in dynamic disasters such as rock bursts. Taking granite block rock media as research object and using bidirectional impact loading to simulate the dynamic disturbance of rock media, a numerical model was established.,e vertical acceleration and the horizontal displacement on working blockmedia were defined as the characteristic parameters of the anomalously low-friction effect. ,e effects of delay time and horizontal impact loading amplitude and frequency on the characteristic parameters under bidirectional impact loading were examined by numerical simulation. ,e generation and variation of the anomalously low-friction effect of block rock media subjected to bidirectional impact loading were presented. ,e results show that the delay time has a significant effect to the vertical acceleration amplitude and horizontal displacement on the working block media under bidirectional impact loading. ,ere exists a delay time threshold; when reach to the threshold, quasiresonance and the anomalously low-friction effect on block media will easily occur. With the increase in horizontal impact amplitude, the residual horizontal displacement on the working block media also increases by power function, while it decreases by power function with the increase of horizontal impact loading frequency. Finally, this study denotes that it is great significance to investigate the bidirectional impact loading in order to capture the mechanism of anomalously low-friction effect.

e rock near the excavation surface is highly fractured and cannot be simplified as an elastic continuous medium.It is usually deemed as block rock mass.e deep block rock would cause vibrations under dynamic impact loading; when the impact energy reached to a certain energy level, the friction between the interacting blocks would be reduced, or even be extremely low, and the friction disappearance effect would occur.
is phenomenon was first observed by Russian scholars Kurlenya et al. [9][10][11] in the simulation experiment of block rock subjected impact loading.
In order to verify the existence of anomalously lowfriction effect, many studies were developed by domestic scholars.Qian [12] pointed out that the anomalously lowfriction effect was a key scientific problem in deep mining and closely related to dynamic disaster.Wang et al. [13,14] explained theoretically the anomalously low-friction effect.
e theoretical model was adopted and further improved by Wang et al. [15,16] to derive the analytical expression of horizontal displacement of working block and reveal the mechanism of the anomalously low-friction effect.
Considering the volatility characteristics of block rock under impact loading, the occurrence criterion of anomalously low friction was given by Pan and Wang [17] through the maximum value of relative displacement between adjacent blocks in the tensile direction based on the pendulum wave propagation dynamic model.Wu et al. [18] extended Kurlenya's conclusion about peak frequency to extreme frequency in situ test.In addition to carry out the experiment on anomalously low-friction e ect, quasiresonance characteristics and pendulum wave of deep rock mass, Wang et al. [19] developed a multifunctional dynamic test system for the deep rock media.However, deep rock mass is in high stress state.Li et al. [20][21][22][23] presented a theoretical model of deep block rock media subjected to normal impact loading and overburden pressure and a new concept of anomalously lowfriction rock burst, which combined the study of anomalously low-friction e ects with rock burst.
ese studies have mainly focused on the theoretical and experimental research and the numerical simulation was poorly employed.e numerical simulation method is one of the important means of scienti c research, and it is convenient to carry out sensitivity research of parameters and simulate physical experiments that are di cult to carry out under current technical conditions.In addition, there might be an explanation in the case of single vertical impact loading, but they little explain the bidirectional impact behavior in deep block mass.In fact, the phenomenon is closely associated with the bidirectional impact and a ected by many factors, such as vertical impact loading amplitude and frequency, horizontal impact loading amplitude and frequency, and delay time.Especially, no scholar has studied how the amplitude and frequency of the horizontal impact a ect the anomalously friction e ect.Based on previous studies, in this paper, the vertical acceleration and the horizontal displacement of the working block are regarded as the characteristic parameter of anomalously low-friction e ect.e in uences of delay time and horizontal impact loading amplitude and frequency on anomalously lowfriction e ect under bidirectional impact loading are analyzed with numerical simulation, which makes it possible to reveal the damage mechanism of anomalously low-friction rock burst.It also veri es the feasibility of FLAC-3D for numerical simulation of anomalously low-friction e ects.

Model Establishment and Verification
Based on the research results of Kurlenya et al. [9][10][11], a numerical model of anomalously low-friction e ect in block rock media was established.Considering the need to apply force on the numerical model, it is necessary to convert impact energy into force loading on the surface of block rock media.

Energy Conversion.
Based on Hertz's law, ignoring system vibration, the impact energy W is converted into half sine force where the action time is t 0 and the amplitude of the half sine force is P m .e function of the impact loading is as follows: where P m is dynamic loading amplitude, N; t is the time, s; ω 2πf, in which f is dynamic loading frequency, Hz; and P m and ω are calculated by Hertz's law.Mechanical transformation of impact energy is shown in Figure 1.

Model Design.
e numerical model consists of six granite blocks of 300 mm × 120 mm × 90 mm, respectively.e blocks are vertically stacked from top to bottom and the third block is de ned as the working block for monitoring.
e interconnections between the blocks are chosen as a Kelvin viscoelastic models.Each block is divided into 8 hexahedral units.Model meshing, boundary conditions, and forces are shown in Figure 2.
e Mohr-Coulomb model suitable for rock-like materials is selected as the constitutive model for the numerical simulation.Using static boundary conditions, the model boundary conditions are set as shown in Figure 2(b).e mechanical damping is the form of Rayleigh damping [24], and the mechanical parameters of the model are determined by literature [25] (Table 1).e impact is loaded based on Hertz's law.
e vertical impact loading is applied to the central point of the top surface of the rst block and its direction straight down.
e horizontal impact loading is applied to the central point of right surface on the third block and the direction is horizontal to the left.e center of the bottom surface of the sixth block is regarded as the origin of coordinates.In this paper, the vertical acceleration of the block is along the z-axis direction, and the horizontal displacement of the block is along the x-axis direction.e values of positive and negative are the same as the axis direction.

Validation of Numerical Simulation.
To verify the feasibility of using FLAC-3D to simulate the anomalously lowfriction e ect, the simulation results were compared with previous experimental results [7], as shown in Figure 3, based on the response of granite blocks under the combined action of vertical impact energy and horizontal static force.
It can be seen from Figure 3 that the numerical simulation results are consistent with the experimental results in the overall trend.e feasibility of using FLAC-3D to simulate anomalously low-friction e ect is further proved.

E ect of Delay Time.
e delay time re ects the time interval of vertical and horizontal impact energy loading on the blocks model for simulating the sequence of dynamic disturbances of coal rock media under deep mining conditions.e e ect of delay time on the anomalously low-friction e ect is investigated when the time sequence of vertical and horizontal impact loading is di erent (negative values represent horizontal impact is loaded before vertical impact).Advances in Civil Engineering (1) e delay time has an important e ect on vertical acceleration of the working block.When the model is rst subjected to vertical impact loading, the maximum amplitude of vertical acceleration of the working block is greater than rst subjected to the horizontal impact loading.When t d < 0, the delay time is di erent and the maximum amplitude of vertical acceleration of the working block under vertical impact loading is also di erent.When t d > 0, the delay time is di erent and the maximum amplitude of vertical acceleration of the working block under horizontal impact loading is also di erent.e relationship between the maximum vertical acceleration of the working block and the delay time is shown in Figure 4. e working block vibrates under the vertical impact loading and the vertical acceleration uctuates near the equilibrium position.Under the horizontal impact loading, if the vertical acceleration amplitude of the working block is large, the horizontal displacement is less than that under the horizontal impact.If the vertical acceleration of the working block is small, as the block gravity is constant, that is, the normal force between the blocks is smaller.As a result, the horizontal displacement is larger caused by the impact loading of the working block, which is prone to the anomalously lowfriction e ect.(2) Horizontal impact loading is the main reason for the residual displacement of the working block.However, the delay time has a greater e ect on the residual displacement when the working block is rstly subjected to vertical impact loading.When the block model is loaded respectively by the vertical and horizontal bidirectional impact loading, the horizontal displacement curve of the working block at di erent delay time t d is shown in Figure 5.
In Figures 5(a)-5(c), t d < 0, the working block is moved from the original equilibrium position by horizontal impact loaded rst and is gradually stabilized at the new equilibrium position and generates residual displacement.
en, the vertical impact also generates a smaller residual displacement.e horizontal residual displacement of the working block is mainly determined by the horizontal impact loading.e delay time has little e ect on the value of the nal residual displacement.Residual displacement is all 6.75 μm, and the direction is same.But the delay time a ects the time required for the horizontal displacement to nal stability.When the delay time is di erent, the time required for the uctuation stability in Figures 5(a)-5(c) is 3.6 ms, 2.6 ms and 3.9 ms, respectively.
From Figures 5(d)-5(f ), when t d > 0, the horizontal displacement of the working block slightly uctuates due to vertical impact loading and results in small uctuations.After that, the main residual displacement is produced under the horizontal impact loading and the magnitude and direction of the residual displacement change with delay time.
At the appropriate time of t d , the vibration of the block suddenly intensi es and its amplitude becomes larger than that of the single load, as shown in Figures 5(d)-5(f ).e residual displacement is respectively −3.8 μm, 1.8 μm, and 6.6 μm.When the model is rst subjected to vertical impact loading, the vertical movement of the working block intensi es, and periodic compaction and relative detachment states or high-stress and low-stress states occur between blocks.When the blocks are in the compaction state or highstress state, the horizontal impact is loaded on the working block.e horizontal friction resistance between the blocks is large and working block has smaller horizontal displacement.When the horizontal impact acts on the working block in a relatively detachment or low-stress state between   Advances in Civil Engineering the blocks, a large horizontal displacement occurs due to the smaller horizontal frictional resistance (anomalously low friction) between the blocks.At this time, the anomalously low-friction e ect will occur.is is consistent with the quasiresonance phenomenon mentioned in literature [26].

E ect of Horizontal Impact Loading Amplitude.
e strength of impact energy is closely relevant to the amplitude of impact loading.In the process of fully mechanized top coal caving, the coal pillar in the section is not only loaded under the gravity of the overburden, but also be a ected by various disturbances in the mining operations, such as blasting vibration, mine shock, and cyclical pressure.Among them, the periodic pressure is the common impact disturbance in caving coal mining.It has the characteristics of short period, great impact force, and so on.To simulate the above impact disturbance, the amplitude and frequency of impact loading are changed.According to Wang et al. [19] experimental data, the impact loading amplitudes are speci ed as 500 N, 1000 N, 1500 N, and 2000 N. e horizontal impact frequency and vertical impact energy are xed values, respectively, 5000 Hz and 63 mJ, and the delay time is 2 ms.
(1) e maximum vertical acceleration of the working block subjected to secondary impact gradually increases with the increase in horizontal impact loading amplitude.When the block model is subjected to vertical and horizontal bidirectional impacts and the amplitude of the horizontal impact loading is di erent, the vertical acceleration response curve on monitoring point of working block is shown in Figure 6.
From Figure 6(a), the model is loaded by a vertical impact loading rst and results in vertical acceleration uctuation of the working block.e uctuation form is similar to the quasiperiodic sine curve and the amplitude 4 Advances in Civil Engineering gradually decreases.e maximum amplitude is 25.6 m/s 2 and the positive amplitude is greater than the negative amplitude.At about 1.67 ms, the vertical acceleration of the working block generates slight uctuation again and the maximum amplitude is 6.6 m/s 2 .At 2 ms subjected to horizontal impact loading, the uctuation amplitude of the working block's vertical acceleration increases again.
After the second impact loading, the maximum vertical acceleration of the working block increases exponentially with the increase in the horizontal impact loading.e maximum vertical acceleration is 5.9 m/s 2 , 6.4 m/s 2 , 9.4 m/s 2 , and 13.1 m/s 2 , as shown in Figure 7.Because there is a gap and the connections between the blocks are Kelvin viscoelastic models and between the blocks, that is, the blocks are assumed to be connected by springs and dampers.When subjected to horizontal impact, the blocks begin to horizontally move and the spring between the blocks is deformed to cause the vertical acceleration.When the working block frequency is determined, the energy of the horizontal impact increases with its amplitude increase.
e horizontal movement of the working block is more intense.As a result, the magnitude of vertical acceleration of the working block gradually increases.
(2) e horizontal residual displacement of working block increases by power function with the increase of horizontal impact loading amplitude.
e horizontal displacement response curve of monitoring point of working block is shown in Figure 8.For accurate analysis, before impact loading, the displacements in x, y, z direction of each node of the model is cleared.
From Figure 8, the working block moves back and forth in a horizontal direction under the vertical impact loading.
e amplitude and stability time are small and no residual displacement.At t 2 ms, the horizontal displacement of working block is changed greatly due to the horizontal impact loading.After the horizontal impacting, the uctuation of horizontal displacement of the working block gradually stabilizes and has a residual displacement.e residual displacements of Figures 8(a)-8(d) are 0.1366 μm, 0.5462 μm, 1.079 μm and 1.668 μm, and the curve is shown in Figure 7. ere is the power function increase relationship between the horizontal residual displacement and impact amplitude.is is because that when the horizontal impact loading frequency is determined, its amplitude and impact energy increases, resulting an increases in the horizontal motion and the horizontal residual displacement of the working block.e above result is consistent with the fact that the anomalously low-friction e ect is more likely to occur under strong shock disturbances.

E ect of Horizontal Impact Loading Frequency.
e frequency of impact loading is a key parameter re ecting the impact action.According to Hertz's law and relevant literature [7], the impact loading frequency of four levels including 1000 Hz, 2500 Hz, 5000 Hz, and 7500 Hz was set.Horizontal impact loading amplitude, vertical impact energy, and delay time were taken as a xed value, respectively, 1000 N, 63 mJ, and 2 ms.Considering that the block model is subjected to the vertical and horizontal bidirectional impact loading, the horizontal impact loading frequency gradually increases to study the response curve of vertical acceleration and horizontal displacement in monitoring point of working block.
(1) With the increasing frequency of the horizontal impact loading, the amplitude of vertical acceleration of working block in the model is signi cantly affected.e decay rate of the vertical acceleration amplitude gradually also increases.Advances in Civil Engineering curve changes due to the vertical impact loading.However, the uctuation gradually decreases and tends to stabilize.At 1.67 ms, the secondary uctuation occurs, and the uctuation is superimposed on the uctuations of the working block by the horizontal impact loading at 2 ms, but the uctuation amplitude is generally small.e stabilization times of the secondary uctuations in Figures 9(a)-9(d) are, respectively, 2.1 ms, 1.8 ms, 1.4 ms, and 1.4 ms. e maximum amplitude of the second uctuation is, respectively, 3.3 m/s 2 , 5.8 m/s 2 , 6.4 m/s 2 , and 9.4 m/s 2 .Since the period is inversely proportional to the frequency, the horizontal impact loading frequency is gradually increased, and the natural period is shortened.e time that the block model subjected to the impact is also reduced.
e energy is more concentrated, resulting in a gradual increase in the decay rate of the vertical acceleration amplitude.Meanwhile, the maximum amplitude gradually increases too.
(2) As the horizontal impact loading frequency gradually increases, the horizontal residual displacement of the working block decreases with the power function.It is indicated that the amplitude of horizontal movement of working block is getting smaller and smaller.e stability of the block model is enhanced.
e phenomenon of anomalously low friction is less obvious, and the possibility of occurrence such as rock bursting and other disasters induced by anomalously low-friction e ect gradually reduced.
Figure 10 shows the response curve of working block horizontal displacement when the block model was subjected to vertical and horizontal bidirectional impact loading, and the horizontal impact loading frequency gradually increased.
From Figure 10, we can see that the horizontal displacement of the working block uctuates when the block model is rst subjected to the vertical impact loading, but the uctuation is very small.e higher the frequency, the longer time required for the uctuations to stabilize, but the nal residual displacement can be ignored.At t 2 ms, due to the horizontal impact loading, the horizontal displacement of the working block changes greatly.e time required for horizontal displacement to stabilize decreases with frequency increasing.
e stable times of Figures 10(a e variation of the two curves is shown in Figure 11.When the amplitude of the horizontal impact loading is determined, the increases in frequency lead to reduce the cycle of impact loading.e time that the model is a ected by horizontal impact is decreased and the impact energy is reduced.
e block motion tends to be moderated.e horizontal residual displacement also gradually decreases with the impact frequency increases.at is to say, the lowfrequency disturbance is more prone to the anomalously low-friction e ect.It is easier to induce the dynamic disaster such as the rock bursts, which is consistent with the fact that low-frequency signal before rock bursts is mainly based on low-frequency [27].

Discussion
(1) Deep underground conditions are extremely complicated, and the research of anomalously lowfriction e ect provides a feasible way to reveal the mechanism of some deep dynamic disasters.For example, on November 11, 2017, the rock bursts of the Hongyang no. 3 Mine in Liaoning Province of China have observed that the total amount (214 m × 31.7 m × 3 m) of coal rock was slipped to the roadway 1 m∼3 m; however, the roof remains basically intact.is phenomenon can be explained reasonable by anomalously low-friction e ects under high ground stress condition.In the accident area of Hongyang no. 3 Mine, the roof of the coal pillar is mudstone.Under the cutting action of the fault, the coal pillar formed a separation body.Under the dynamic disturbance such as roof break, the friction between the coal seam and the roof and the bottom was weakened.
e coal pillars had a large horizontal displacement and overall sliding when it is su ered by the horizontal thrust induced for roof break.e accident area composed of roof, coal pillar, bottom, (2) e stress condition of deep rock mass divided by the joints and fractures and the strati cation of deep rock media are considered, idealized into one-dimensional block dynamic model.erefore, it has theoretical and practical signi cance to study the occurrence of dynamic disasters such as impact and in situ stress from the perspective of anomalously low-friction e ect.In this paper, based on previous researches, the numerical simulation method is used to study the vertical acceleration and horizontal displacement of the working block.e conclusion is basically consistent with that in the literature [7], but its application needs to be further expanded.is process does not consider the in uence of overburden pressure and con ning pressure on the rock mass.erefore, the mechanism of the anomalously low-friction e ect still needs further research.

Conclusions
Using FLAC-3D numerical simulation software, the anomalously low-friction phenomenon of granite block rock media model under vertical and horizontal bidirectional impact loading was investigated.e following conclusions are presented: (1) e vertical impact loading is the precondition for the occurrence of anomalously low-friction e ect.e horizontal impact loading is the direct cause of the anomalously low-friction e ect, which may even lead to the deep rock media dynamic disasters.is is consistent with phenomena such as earthquakes in which the shear waves produce more damage than longitudinal waves.

Advances in Civil Engineering
(2) e horizontal residual displacement is mainly affected by the horizontal impact loading.e delay time has a direct effect on the vertical acceleration and horizontal residual displacement of the working block.
(3) With the amplitude of the horizontal impact loading increases, the horizontal residual displacement of the working block increases with the power function.(4) e low-frequency disturbance makes the anomalously low-friction effect between the blocks more likely to occur.

Figure 1 :
Figure 1: Mechanical transformation of impact energy.

Figure 3 :Figure 2 :
Figure 3: Relation curve between horizontal static and horizontal residual displacement.

Figure 5 :Figure 4 :
Figure 5: Horizontal displacement curve of work block under the action of di erent delay time.(a) t d −3 ms.(b) t d −2 ms.(c) t d −1 ms.(d) t d 1 ms.(e) t d 2 ms.(f ) t d 3 ms.

Figure 9 ( 2 )
Figure 9(a)  shows that the vertical acceleration begins to uctuate from the steady state with a quasiperiodic sine

Figure 6 :R 2
Figure 6: Vertical acceleration response of working block under di erent impact loading amplitudes.(a) P m 500 N. (b) P m 1000 N. (c) P m 1500 N. (d) P m 2000 N.

Figure 7 :
Figure7: Relation curve between the horizontal residual displacement, the maximum amplitude of acceleration after the horizontal shock of the working block, and the impact loading amplitude.

Figure 8 :
Figure 8: Horizontal displacement curve of work block under the action of di erent impact loading amplitudes.(a) P m 500 N. (b) P m 1000 N. (c) P m 1500 N. (d) P m 2000 N.

Table 1 :
e mechanical parameters of mode.