# Experimental Investigation and Analysis of Triggering Mechanism for Fault-Slip Bursts of the Tunnel Surrounding Rock with External Disturbance

Authors: Hai-ming Jiang; Jie Li; Shu-xin Deng; De-rong Wang; Xiao Zhao
Journal: Shock and Vibration
 (2018)

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## Abstract

Shear-slip type rockburst is one of the most common geohazards confronted in deep underground excavations, which can easily occur after external disturbances. Owing to the sudden occurrence and significant damage caused, investigating the mechanism of these shear-slip type disasters is of tremendous significance in ensuring the safety of underground construction projects. In this paper, our attentions are mainly paid to investigate the necessary conditions and critical energy conditions of fault-slip bursts of the tunnel surrounding rock triggered by external disturbances. First, a simplified model for simulating the sliding instability phenomenon occurring in a blocky rock system under external disturbance is established. Next, using a newly developed testing system for the dynamic behaviour of blocky rock masses, a series of experiments to reproduce the sliding instability phenomenon are conducted; the purple sandstone block system is subjected to the combined effect of a vertical impact load and horizontal constant force. The influence of vertical impact energy on the sliding instability is analysed. The experimental results show that the critical energy of the impact load triggering the blocky rock mass slip instability depends on the shear force, and the higher the shear force, the lower is the external disturbance required. Furthermore, a one-dimensional dynamic calculation model is established to develop a better insight regarding the mechanism of the slip instability induced by external disturbances. A dimensionless energy parameter was introduced to quantifiably characterize the critical conditions of different types of fault-slip events. Theoretical analysis and calculations are presented, and the results agree with experimental observations.


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## Body

## 1. Introduction

With the depths and locations for underground engineering having become increasingly challenging, an increasing number of natural or artificial disasters have been observed, such as rockburst and excavation-induced seismicity [1–3]. Both of the above geohazards unexpectedly occur during the excavation of deeply buried tunnels and mines, accompanied with a violent and dynamic release of the residual energy of the surrounding rock masses [4, 5]. These dynamic disasters frequently pose a serious threat to the safety of construction workers and cause the destruction of machines and equipment. For example, on November 28, 2009, an extremely severe rockburst occurred in parallel tunnels in the Jinping II hydropower station, causing the death of seven workers and majorly damaging a tunnel boring machine (TBM) that was present inside [1].Ortlepp and Stacey [6] classified rockbursts into five types (strainburst, buckling, face crush/pillar burst, shear rupture, and fault-slip burst). In a broad sense, buckling type rockbursts can be grouped into strainbursts, and shear rupture type rockbursts can be considered as fault-slip rockbursts, thus resulting in three generalised types of rockbursts: strainbursts, pillar bursts, and fault-slip bursts [7, 8]. Fault-slip bursts are caused by the dynamic reactivated shear on existing faults and/or shear rupture existing discontinuities [6], and the extent of this shear failure zone could be hundreds of metres. Consequently, the dynamic damage caused by shear-slip events is typically far more extensive than other rockbursts, as confirmed by the fact that several tens or even hundreds of metres of tunnels would be damaged in a single excavation-induced seismicity [6, 9]. In recent years, efforts have been made to investigate shear-slip incidents caused by sliding along preexisting discontinuities or structural planes [10–17]. Although these advances have improved our understanding of shear-slip incidents, the involvement of a specific feature in dynamic failure as well as development of an effective physical calculation model has not been examined yet. Consequently, more research is required to completely understand such dynamic disasters.In building tunnels and other open excavations, the surrounding rock mass that has a hierarchical block structure is divided by the discontinuities of different scales and is known as a “blocky rock mass” (Figure1(a)). The interfaces of the blocky rock have a much lower effective strength and poor strain characteristics compared to the bulk material of the blocks; consequently, they exhibit strong responses, in terms of their mobility and sensitivity, to even very weak disturbances [18, 19]. As shown in Figure 1(a), after the falling of the first blocky rock masses of a tunnel sidewall, the boundary conditions are changed, and a progressive collapse, even a shear-slip rockburst, may occur [20]. Thus, the physical nature of the sliding bursts is considered as the deformation instability of the contact surface [21]. During the construction of the Jinping II headrace tunnels, certain structural planes in the vicinity of the tunnels were closely related to the occurrence of rockburst [13]. The excess shear stress (ESS) is used to numerically assess the possible magnitude and relative likelihood of seismic activity induced by fault slip in African mines [10, 22, 23]. The fault-slip events always take place after external disturbances, which can be caused by earthquake, nearby blasting, construction disturbance, and so on [24–27]. Whyatt and Board [26] have reported that 75% of rockbursts happened on blasting or several hours after blasting. Kie [27], based on the failure mechanism of brittle rocks and the statistical results of practical engineering, pointed out that the rocks can transform from stability to instability while affected by disturbance induced by mining or blasting. Therefore, he stressed that attention should be paid to the triggering effects of dynamic load on the occurrence of rock burst. Interestingly, compared with the released energy, the energy applied by the dynamic load is tiny and negligible [8].Figure 1
Dynamic instability of an underground tunnel:Pv and Ph denote the geostresses. (a) Diagram. (b) Typical field image.
(a)
(b)In spite of the many attempts to understand the mechanism of fault-slip bursts, the triggering mechanism for fault-slip events induced by external disturbances is still unclear. In this paper, our attentions are mainly paid to investigate the necessary conditions and critical energy conditions of fault-slip bursts of the tunnel surrounding rock triggered by external disturbances. Using a self-developed testing system for studying the dynamic behaviour of blocky rock masses, a series of experiments have been conducted for reproducing the sliding instability phenomenon in a blocky rock system subjected to the combined effect of a vertical impact load and horizontal static force. The effects of the vertical impact energy and horizontal static force on the sliding instability are analysed. Further, a one-dimensional dynamic calculation model is established for developing better insight into the mechanism of a slip instability induced by external disturbances. The theoretical analysis and calculations are presented, and it is found that the results agree with the experimental observations. The results provide a theoretical reference on the safety of underground tunnel construction.


## 2. Simplified Model and Test System

### 2.1. Simplified Model for Sliding Instability in Blocky Rock Systems under External Disturbance

Choosing the rock mass of a tunnel sidewall shown in Figure1(a) as the research object, the mechanism for triggering shear-slip type disasters in underground openings was investigated. Figure 2 shows the schematic of a physical model test of the block sliding instability under external disturbance in a blocky rock system consisting of five similar blocks stacked from the top to bottom. Of these blocks, the third block (block #3) was defined as the working block on which the applied horizontal static force acts. In the vertical direction, the block model system was subjected to dynamic disturbance loading. Blocks #2 and #4 were horizontally fixed to prevent horizontal sliding. Under different horizontal forces and vertical loadings, the absolute horizontal displacement of block #3 was measured.Figure 2
Schematic of the triggering sliding instability caused by external disturbance in a blocky rock system.Purple sandstone blocks were adopted in the sliding instability physical model tests. The test model was a vertical block system stacked by five purple sandstone blocks (with dimensions of 160 × 125 × 125 mm and each block weighing 6.2 kg). The surfaces between the blocky rock masses were flattened to ensure a close contact and overall stability of the blocky system.


### 2.2. Test System and Measurement Methods

Based on the test scheme presented above, a new testing system was developed for studying the dynamic behaviour of blocky rock masses. The testing system consisted of a work platform, loading devices, and measurement system. The overall design of the testing device is shown in Figure3. The work platform was used to hold the blocky rock model with a guide groove in the horizontal direction. Therefore, the horizontal dynamic load device could move along the guide groove to match the different sizes of the blocky rock masses.Figure 3
Testing system for studying the dynamic behaviour of blocky rock masses.The loading devices included horizontal static loading and vertical dynamic loading. The horizontal pulling force applied on block 3 was provided by a wire-wheel-weight plate system. The weights were regulated to set the magnitude of the horizontal pulling force. This was a very simple but effective way to control the horizontal static loading. The vertical dynamic loading was applied with an electrodynamic vibration exciter. A vibration exciter is an electric device that converts electrical energy into mechanical energy, making the excited object to vibrate. Unlike the previous studies using drop weight apparatuses [28, 29], the electrodynamic vibration exciter can precisely control the whole disturbance process, which is convenient for quantitative analysis.In the experiment, the impact force curve induced by the vibration exciter was measured by the force transducer shown in Figure4. To accurately measure the absolute displacement of the working block (#3 block), a fibre-optic displacement sensor (Figure 5) was applied with a sensitivity of 1.1 μm/mV, measurement range of 20 mm, and frequency response of 20 kHz.Figure 4
Force transducer.Figure 5
Fibre-optic displacement sensor.


## 2.1. Simplified Model for Sliding Instability in Blocky Rock Systems under External Disturbance

Choosing the rock mass of a tunnel sidewall shown in Figure1(a) as the research object, the mechanism for triggering shear-slip type disasters in underground openings was investigated. Figure 2 shows the schematic of a physical model test of the block sliding instability under external disturbance in a blocky rock system consisting of five similar blocks stacked from the top to bottom. Of these blocks, the third block (block #3) was defined as the working block on which the applied horizontal static force acts. In the vertical direction, the block model system was subjected to dynamic disturbance loading. Blocks #2 and #4 were horizontally fixed to prevent horizontal sliding. Under different horizontal forces and vertical loadings, the absolute horizontal displacement of block #3 was measured.Figure 2
Schematic of the triggering sliding instability caused by external disturbance in a blocky rock system.Purple sandstone blocks were adopted in the sliding instability physical model tests. The test model was a vertical block system stacked by five purple sandstone blocks (with dimensions of 160 × 125 × 125 mm and each block weighing 6.2 kg). The surfaces between the blocky rock masses were flattened to ensure a close contact and overall stability of the blocky system.


## 2.2. Test System and Measurement Methods

Based on the test scheme presented above, a new testing system was developed for studying the dynamic behaviour of blocky rock masses. The testing system consisted of a work platform, loading devices, and measurement system. The overall design of the testing device is shown in Figure3. The work platform was used to hold the blocky rock model with a guide groove in the horizontal direction. Therefore, the horizontal dynamic load device could move along the guide groove to match the different sizes of the blocky rock masses.Figure 3
Testing system for studying the dynamic behaviour of blocky rock masses.The loading devices included horizontal static loading and vertical dynamic loading. The horizontal pulling force applied on block 3 was provided by a wire-wheel-weight plate system. The weights were regulated to set the magnitude of the horizontal pulling force. This was a very simple but effective way to control the horizontal static loading. The vertical dynamic loading was applied with an electrodynamic vibration exciter. A vibration exciter is an electric device that converts electrical energy into mechanical energy, making the excited object to vibrate. Unlike the previous studies using drop weight apparatuses [28, 29], the electrodynamic vibration exciter can precisely control the whole disturbance process, which is convenient for quantitative analysis.In the experiment, the impact force curve induced by the vibration exciter was measured by the force transducer shown in Figure4. To accurately measure the absolute displacement of the working block (#3 block), a fibre-optic displacement sensor (Figure 5) was applied with a sensitivity of 1.1 μm/mV, measurement range of 20 mm, and frequency response of 20 kHz.Figure 4
Force transducer.Figure 5
Fibre-optic displacement sensor.


## 3. Static Friction Coefficient of #3 Block

With the aim to investigate sliding phenomenon of the working block along the structural plane under a static force and an impact load, the maximum static frictionf0 of the purple sandstone in the blocky system should be first measured.With the increase in the horizontal force, the frictional force generated between the rock blocks increased. When the two contact surfaces were in a critical state to slip, the value of horizontal force was considered the maximum static friction. In the experiments, the horizontal pull was gradually increased by adding weights, and the associated horizontal displacement curve of #3 block was recorded by the fibre-optic displacement sensor. All the experiments were performed in sets of three to ensure the accuracy of the data. The displacement of the #3 block displacement versus the horizontal force is shown in Figure6.Figure 6
Variation of the displacement as a function of the horizontal pull force.Clearly, the irreversible displacement of the block increases linearly with the horizontal force. When the horizontal pull increases to 200 N, the horizontal displacement of #3 block increases drastically. Thus, the maximum static friction of #3 block isf0=200N. The working block is subjected to both upper and lower interface friction; that is, the normal force between block #2 and block #3 is 2mg and the normal force between block #3 and block #4 is 3mg. So that the static friction coefficient μs can be calculated as follows:(1)μs=f02mg+3mg≈0.65,where μs denotes the static friction coefficient and g is 10 m/s2.


## 4. Combined Effect of Vertical Impact Load and Horizontal Static Force

### 4.1. Experimental Procedures

In Section3, the maximum static friction force of the #3 block in the blocky system was obtained. In this section, the stability of the blocky system was investigated, which is subjected to the combined effect of a horizontal static force fh and vertical impact load pt.The horizontal pull forces applied on the working block were set as 190, 180, 170, 160, 150, 130, 90, and 50 N. The external impact energies on the top of the model were chosen as 2, 4, 10, 20, 40, 80, 160, and 300 mJ, until the #3 block slid freely. In the experiments, the peak disturbing force was increased to obtain a larger disturbance energy. A positive stop device was employed to prevent the collapse of the system; that is, when the working block attains a limited displacement, the motion of the rock mass was stopped.The force-time curve caused by the vibration exciter was recorded by the force transducer, as shown in Figure7. The initial velocity of the disturbed block was assumed to be zero, and the disturbance time was considerable short. Then, the relation between the impulse Im and the disturbance energy W was deduced as follows:(2)W=12m∫0∞ptdt2=Im22m,where pt represents force-time curve.Figure 7
Curve of the impact force.


### 4.2. Experimental Results

The horizontal displacement of the working block was recorded by a fibre-optic displacement sensor. Figure8 shows the displacement-time curves of the working block under a combined effect of different vertical impact loads and horizontal static forces.Figure 8
Displacements of block #3 under the joint action of a vertical impact load and horizontal force. (a)fh=190N. (b) fh=180N. (c) fh=170N. (d) fh=160N. (e) fh=150N. (f) fh=130N. (g) fh=90N. (h) fh=50N.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The experimental results shown in Figure8 can be described as follows:First, for a given horizontal static force, the horizontal residual displacement of the working block increases with increasing vertical impact energy. Considering Figure8(b) as an example, where the horizontal pull force is 180 N, the residual displacements of #3 block are 94, 374, and 700 μm, corresponding to the impact energies of 2, 4, and 10 mJ, respectively. According to the experimental data, Figure 9 shows the influence of the vertical impact energy on the displacement of #3 block with the horizontal static force ranging from 50 to 190 N. As shown in Figure 9, it was found that the block system became increasingly sensitive to the disturbance energy as the horizontal static force increased. When the horizontal static force was close to the peak static friction force, the displacements strongly depended on the disturbance energy, and even a considerably small disturbance was capable of causing a large irreversible displacement.Figure 9
Horizontal displacement versus impact energy for #3 block.Second, in the case of an impact energy of 4 mJ and horizontal pull force of 190 N (Figure8(a)), the working block slides freely, implying that the sliding instability phenomenon occurs. The same phenomena are similarly observed in Figures 8(b)–8(d), and the vertical impact energies of impact load triggering sliding instability are 20, 80, and 300 mJ, corresponding to the horizontal static force of 180 (Figure 8(b)), 170 (Figure 8(c)), and 160 N (Figure 8(d)), respectively.Finally, when the horizontal shear force decreases to a certain threshold, regardless of how the impact energy increases, there is only an irreversible displacement between the rock blocks, and the slip instability does not occur. For example, when the working rock mass is reduced horizontally toF=150N (Figure 8(e)), even if we increase the impact energy to 300 mJ, the #3 block does not slip out, and only an irreversible displacement of 2640 μm occurs. According to the subsequent theoretical analysis, this critical threshold agrees with the dynamic friction between the block rock mass.


### 4.3. Analysis of the Mechanism of Sliding in Blocky Rock System

We have attempted to present the mechanism of the irreversible displacements, induced by the vertical impact disturbances, occurring in the blocky rock mass. In the experiment, the impact load applied to the blocky rock model can be approximately regarded as a one-dimensional wave propagation. During this process, the total normal stress between the blocky rock interfaces increases when the dynamic compression phase passes, and the normal stressσ decreases when the tension phase passes, compared to the original static stress. Considering there are no fillings between the rock masses in experiment, the cohesion C≈0; hence, the shear strength τp is mainly proportional to the normal stress στp=μ⋅σ. Therefore, when the dynamic stress is compressive, the shear strength increases, and when the dynamic stress is tensile, the shear strength decreases. If the ratio of the constant shear stress τ to the shear strength τp exceeds the critical value of τ/τp= 1, the sliding of the rock block along with its interface occurs. Furthermore, during the process of shear deformation, the shear strength decreases more significantly because the friction coefficient μ reduces from the static friction coefficient μs to the dynamic friction coefficient μd, which presents the product effect. Thus, when τ/τp > 1 is satisfied, the relative motion of the block is accelerated; otherwise, the relative motion slows down. Furthermore, during the process of the one-dimensional impact load, dynamic sliding of the blocks along the structural plane occurs intermittently, as confirmed by Figure 8.


## 4.1. Experimental Procedures

In Section3, the maximum static friction force of the #3 block in the blocky system was obtained. In this section, the stability of the blocky system was investigated, which is subjected to the combined effect of a horizontal static force fh and vertical impact load pt.The horizontal pull forces applied on the working block were set as 190, 180, 170, 160, 150, 130, 90, and 50 N. The external impact energies on the top of the model were chosen as 2, 4, 10, 20, 40, 80, 160, and 300 mJ, until the #3 block slid freely. In the experiments, the peak disturbing force was increased to obtain a larger disturbance energy. A positive stop device was employed to prevent the collapse of the system; that is, when the working block attains a limited displacement, the motion of the rock mass was stopped.The force-time curve caused by the vibration exciter was recorded by the force transducer, as shown in Figure7. The initial velocity of the disturbed block was assumed to be zero, and the disturbance time was considerable short. Then, the relation between the impulse Im and the disturbance energy W was deduced as follows:(2)W=12m∫0∞ptdt2=Im22m,where pt represents force-time curve.Figure 7
Curve of the impact force.


## 4.2. Experimental Results

The horizontal displacement of the working block was recorded by a fibre-optic displacement sensor. Figure8 shows the displacement-time curves of the working block under a combined effect of different vertical impact loads and horizontal static forces.Figure 8
Displacements of block #3 under the joint action of a vertical impact load and horizontal force. (a)fh=190N. (b) fh=180N. (c) fh=170N. (d) fh=160N. (e) fh=150N. (f) fh=130N. (g) fh=90N. (h) fh=50N.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The experimental results shown in Figure8 can be described as follows:First, for a given horizontal static force, the horizontal residual displacement of the working block increases with increasing vertical impact energy. Considering Figure8(b) as an example, where the horizontal pull force is 180 N, the residual displacements of #3 block are 94, 374, and 700 μm, corresponding to the impact energies of 2, 4, and 10 mJ, respectively. According to the experimental data, Figure 9 shows the influence of the vertical impact energy on the displacement of #3 block with the horizontal static force ranging from 50 to 190 N. As shown in Figure 9, it was found that the block system became increasingly sensitive to the disturbance energy as the horizontal static force increased. When the horizontal static force was close to the peak static friction force, the displacements strongly depended on the disturbance energy, and even a considerably small disturbance was capable of causing a large irreversible displacement.Figure 9
Horizontal displacement versus impact energy for #3 block.Second, in the case of an impact energy of 4 mJ and horizontal pull force of 190 N (Figure8(a)), the working block slides freely, implying that the sliding instability phenomenon occurs. The same phenomena are similarly observed in Figures 8(b)–8(d), and the vertical impact energies of impact load triggering sliding instability are 20, 80, and 300 mJ, corresponding to the horizontal static force of 180 (Figure 8(b)), 170 (Figure 8(c)), and 160 N (Figure 8(d)), respectively.Finally, when the horizontal shear force decreases to a certain threshold, regardless of how the impact energy increases, there is only an irreversible displacement between the rock blocks, and the slip instability does not occur. For example, when the working rock mass is reduced horizontally toF=150N (Figure 8(e)), even if we increase the impact energy to 300 mJ, the #3 block does not slip out, and only an irreversible displacement of 2640 μm occurs. According to the subsequent theoretical analysis, this critical threshold agrees with the dynamic friction between the block rock mass.


## 4.3. Analysis of the Mechanism of Sliding in Blocky Rock System

We have attempted to present the mechanism of the irreversible displacements, induced by the vertical impact disturbances, occurring in the blocky rock mass. In the experiment, the impact load applied to the blocky rock model can be approximately regarded as a one-dimensional wave propagation. During this process, the total normal stress between the blocky rock interfaces increases when the dynamic compression phase passes, and the normal stressσ decreases when the tension phase passes, compared to the original static stress. Considering there are no fillings between the rock masses in experiment, the cohesion C≈0; hence, the shear strength τp is mainly proportional to the normal stress στp=μ⋅σ. Therefore, when the dynamic stress is compressive, the shear strength increases, and when the dynamic stress is tensile, the shear strength decreases. If the ratio of the constant shear stress τ to the shear strength τp exceeds the critical value of τ/τp= 1, the sliding of the rock block along with its interface occurs. Furthermore, during the process of shear deformation, the shear strength decreases more significantly because the friction coefficient μ reduces from the static friction coefficient μs to the dynamic friction coefficient μd, which presents the product effect. Thus, when τ/τp > 1 is satisfied, the relative motion of the block is accelerated; otherwise, the relative motion slows down. Furthermore, during the process of the one-dimensional impact load, dynamic sliding of the blocks along the structural plane occurs intermittently, as confirmed by Figure 8.


## 5. Dynamic Calculation Model of Induced Slip Instability of Block Rock

The above experimental results show that an irreversible slippage occurs even if the sliding instability of the working rock under dynamic actions is closely related to the dynamic deformation and friction characteristics of the block interface. It is essential to understand the normal and tangential dynamic responses of an interface to dynamic actions. Based on this, a one-dimensional calculation model was established for gaining better insight into the mechanism of the slip instability induced by external disturbances.


### 5.1. Establishment and Solution of Motion Equations

A rock mass is a complex structural system in which the rock blocks are nested with each other and interconnected by a middle layer of weaker and fractured rocks. A model of a chain of masses connected by elastic springs and damping elements is proposed [30, 31], as shown in Figure 10(a). The entire blocky rock system as a whole is affected by the external dynamic force pt that can be represented as a half-sine load:(3)pt=pmsinωt,0≤t≤T,0,t≥T,where T denotes the duration of impact load, ω is the angular velocity ω=π/T, pm denotes the peak force, and fh is a horizontal static force representing a lateral force applied to the working block.Figure 10
Modelling and analysis of the blocky rock system. (a) Analytical model in vertical direction [31]. (b) Mechanical analysis of #3 block.
(a)
(b)The dynamic equations of the blocky rock structure can be expressed in a matrix form as(4)My¨t+Cy˙t+Kyt=pt,where M is the mass matrix, M=m1m2⋱m5, yt is the displacement vector, yt=y1y2⋮y5, C is the damping matrix, C=c1−c1−c1c1+c2−c2−c2c2+c3−c3−c3c3+c4−c4−c4c4+c5, K is the stiffness matrix, K=k1−k1−k1k1+k2−k2−k2k2+k3−k3−k3k3+k4−k4−k4k4+k5, and pt is the vertical loading vector, pt=pt0⋮0.For the working block subjected to a horizontal static forcefh (Figure 10(b)), the equation of motion is(5)mx¨=fh−μN2,3t+N3,4t,where x and x¨ are the horizontal displacement and acceleration of the working block, respectively, N2,3t is the normal force between block #2 and block #3, N3,4t is the changing normal force between block #2 and block #3, and μ is the friction coefficient of the blocky rock.It is accepted that sliding of the blocky rock mass is initiated when the ratio of the shear to normal stress on the surface attains a valueμs, referred as the static friction coefficient. Once the sliding initiates, the frictional resistance decreases and has a lower dynamic friction coefficient μd. The weakening of the sliding resistance is closely related to the microstructure, normal stress, temperature, and sliding velocity and may result in a dynamic instability [18, 32]. It is to be noted that the focus of this study is not on determining the mechanism of this problem. Here, only the velocity weakening behaviour of the friction coefficient is considered, and it can be expressed as [33](6)μ=μs,v≤vm,μd+μs−μd∗vmv,v≥vm,where v is the sliding velocity, vm is the critical velocity, and vm=1×10−2m/s.


### 5.2. Calculation Results

Considering the purple sandstone block in the above experiment as the object of calculation, the massm=6.2kg, the static friction coefficient μs=0.65, dynamic friction coefficient μd=0.5, assumed spring stiffness k=3×106N/m, and damping c=2.5×103N⋅s/m were employed [34, 35]. The theoretical result of the sliding of the working block thereby obtained is shown in Figure 11, where a horizontal constant pull force of fh=160N, series of a half-sine load with different magnitudes of the peak force pm, and duration of vertical action T=4ms and ω=250π are used.Figure 11
Theoretical results of the sliding displacement of the working blockfh=160N. (a) Acceleration time histories. (b) Velocity time histories. (c) Displacement time histories.
(a)
(b)
(c)For a given acceleration-time curve, when the acceleration is higher than zero (Figure11(a)), the velocity of the block increases (Figure 11(b)) and the block starts to slide (Figure 11(c)). The velocity of the block is obtained by integrating the acceleration-time curve and the displacement is calculated by integrating the velocity-time curve. When the acceleration is less than zero, the velocity of the block decreases, but the displacement continually increases until the velocity decreases to zero. The above process repeats several times until the acceleration is no longer larger than zero. It can be seen from Figure 11 that the irreversible displacement of the #3 block rock mass increases with an increase in the vertical impact disturbance, for a given constant horizontal force. When the impact disturbance exceeds a critical value (pm=650N), the working block slips freely, indicative of the sliding instability of the blocky structure.Furthermore, the theoretical result of the effects of the vertical impact load on the sliding instability is presented in Figure12, where the solid lines represent the theoretical results, and the scatter symbols represent the experimental results shown in Figure 9. Compared with the experimental results, it can be found that theoretical result can well describe fault-slip events induced by external disturbance.Figure 12
Theoretical results of the slip trend and critical combination condition.


### 5.3. Critical Energy Condition of Fault Sliding Events

A dimensionless energy parameterI is introduced to characterize the energy conditions for fault-slip events and can be expressed as [36](7)I=WτsV=Wf0H,where τs denotes the static shear strength, V is the volume of the rock block, and H is the height of the rock block.Figure13 shows the critical values of the block system required to obtain irreversible displacements and sustained slip failures in experiments. The round symbols and square symbols represent the experimental results, while the solid lines represent the calculation results. The dotted line represents the supplementary boundary for zone III. In Figure 13, there are three zones that represent different statuses of the work block after the vertical dynamic disturbance loads. In zone I, the horizontal pulling force fh cannot exceed the peak static friction force f0 from the beginning to end, and no apparent displacement in horizontal direction aside from that of elastic deformation can be observed. In zone II, the horizontal pulling force is too low or the impact energy is not large enough to cause a sustained slip failure, and irreversible displacements can be observed. In zone III, both the horizontal pulling force fh exceeds the dynamic friction force and the impact energy is large enough, and the work block cannot stop slipping, which may cause slip type rock bursts or other engineering hazards. Thus, the calculation results are consistent with the experimental results, validating the feasibility of this calculation model. The dimensionless energy parameter in Equation (7) is an important characteristic parameter that can reflect the relationship between the external disturbance and the stability of the rock blocks.Figure 13
Critical energy conditions of fault sliding events.


## 5.1. Establishment and Solution of Motion Equations

A rock mass is a complex structural system in which the rock blocks are nested with each other and interconnected by a middle layer of weaker and fractured rocks. A model of a chain of masses connected by elastic springs and damping elements is proposed [30, 31], as shown in Figure 10(a). The entire blocky rock system as a whole is affected by the external dynamic force pt that can be represented as a half-sine load:(3)pt=pmsinωt,0≤t≤T,0,t≥T,where T denotes the duration of impact load, ω is the angular velocity ω=π/T, pm denotes the peak force, and fh is a horizontal static force representing a lateral force applied to the working block.Figure 10
Modelling and analysis of the blocky rock system. (a) Analytical model in vertical direction [31]. (b) Mechanical analysis of #3 block.
(a)
(b)The dynamic equations of the blocky rock structure can be expressed in a matrix form as(4)My¨t+Cy˙t+Kyt=pt,where M is the mass matrix, M=m1m2⋱m5, yt is the displacement vector, yt=y1y2⋮y5, C is the damping matrix, C=c1−c1−c1c1+c2−c2−c2c2+c3−c3−c3c3+c4−c4−c4c4+c5, K is the stiffness matrix, K=k1−k1−k1k1+k2−k2−k2k2+k3−k3−k3k3+k4−k4−k4k4+k5, and pt is the vertical loading vector, pt=pt0⋮0.For the working block subjected to a horizontal static forcefh (Figure 10(b)), the equation of motion is(5)mx¨=fh−μN2,3t+N3,4t,where x and x¨ are the horizontal displacement and acceleration of the working block, respectively, N2,3t is the normal force between block #2 and block #3, N3,4t is the changing normal force between block #2 and block #3, and μ is the friction coefficient of the blocky rock.It is accepted that sliding of the blocky rock mass is initiated when the ratio of the shear to normal stress on the surface attains a valueμs, referred as the static friction coefficient. Once the sliding initiates, the frictional resistance decreases and has a lower dynamic friction coefficient μd. The weakening of the sliding resistance is closely related to the microstructure, normal stress, temperature, and sliding velocity and may result in a dynamic instability [18, 32]. It is to be noted that the focus of this study is not on determining the mechanism of this problem. Here, only the velocity weakening behaviour of the friction coefficient is considered, and it can be expressed as [33](6)μ=μs,v≤vm,μd+μs−μd∗vmv,v≥vm,where v is the sliding velocity, vm is the critical velocity, and vm=1×10−2m/s.


## 5.2. Calculation Results

Considering the purple sandstone block in the above experiment as the object of calculation, the massm=6.2kg, the static friction coefficient μs=0.65, dynamic friction coefficient μd=0.5, assumed spring stiffness k=3×106N/m, and damping c=2.5×103N⋅s/m were employed [34, 35]. The theoretical result of the sliding of the working block thereby obtained is shown in Figure 11, where a horizontal constant pull force of fh=160N, series of a half-sine load with different magnitudes of the peak force pm, and duration of vertical action T=4ms and ω=250π are used.Figure 11
Theoretical results of the sliding displacement of the working blockfh=160N. (a) Acceleration time histories. (b) Velocity time histories. (c) Displacement time histories.
(a)
(b)
(c)For a given acceleration-time curve, when the acceleration is higher than zero (Figure11(a)), the velocity of the block increases (Figure 11(b)) and the block starts to slide (Figure 11(c)). The velocity of the block is obtained by integrating the acceleration-time curve and the displacement is calculated by integrating the velocity-time curve. When the acceleration is less than zero, the velocity of the block decreases, but the displacement continually increases until the velocity decreases to zero. The above process repeats several times until the acceleration is no longer larger than zero. It can be seen from Figure 11 that the irreversible displacement of the #3 block rock mass increases with an increase in the vertical impact disturbance, for a given constant horizontal force. When the impact disturbance exceeds a critical value (pm=650N), the working block slips freely, indicative of the sliding instability of the blocky structure.Furthermore, the theoretical result of the effects of the vertical impact load on the sliding instability is presented in Figure12, where the solid lines represent the theoretical results, and the scatter symbols represent the experimental results shown in Figure 9. Compared with the experimental results, it can be found that theoretical result can well describe fault-slip events induced by external disturbance.Figure 12
Theoretical results of the slip trend and critical combination condition.


## 5.3. Critical Energy Condition of Fault Sliding Events

A dimensionless energy parameterI is introduced to characterize the energy conditions for fault-slip events and can be expressed as [36](7)I=WτsV=Wf0H,where τs denotes the static shear strength, V is the volume of the rock block, and H is the height of the rock block.Figure13 shows the critical values of the block system required to obtain irreversible displacements and sustained slip failures in experiments. The round symbols and square symbols represent the experimental results, while the solid lines represent the calculation results. The dotted line represents the supplementary boundary for zone III. In Figure 13, there are three zones that represent different statuses of the work block after the vertical dynamic disturbance loads. In zone I, the horizontal pulling force fh cannot exceed the peak static friction force f0 from the beginning to end, and no apparent displacement in horizontal direction aside from that of elastic deformation can be observed. In zone II, the horizontal pulling force is too low or the impact energy is not large enough to cause a sustained slip failure, and irreversible displacements can be observed. In zone III, both the horizontal pulling force fh exceeds the dynamic friction force and the impact energy is large enough, and the work block cannot stop slipping, which may cause slip type rock bursts or other engineering hazards. Thus, the calculation results are consistent with the experimental results, validating the feasibility of this calculation model. The dimensionless energy parameter in Equation (7) is an important characteristic parameter that can reflect the relationship between the external disturbance and the stability of the rock blocks.Figure 13
Critical energy conditions of fault sliding events.


## 6. Conclusion

To study the initiation mechanism of shear-slip type disasters occurring in underground openings, a series of experiments were performed to investigate the triggering of the sliding instability phenomenon in blocky rock system. In addition, the corresponding theoretical analysis and calculations were conducted. The primary conclusions of this study can be summarized as follows:(1)
A new test system for studying the dynamic behaviour of blocky rock masses was designed and developed, including the sliding of blocky rock masses along the structural plane and one-dimensional wave propagation characteristics. This test system exhibited several advantages such as shorter experimental periods, convenience, and high reliability and efficiency.(2)
A series of experiments were conducted to reproduce the sliding instability phenomenon in a blocky rock system that was subjected to the combined effect of a vertical impact load and horizontal static force. The experimental results showed that the critical energy of the impact load triggering the slip instability depended on the level of shear force; the higher the shear force, the lower was the external disturbance required.(3)
A one-dimensional dynamic calculation model was established to gain better insight into the mechanism of the slip instability induced by external disturbances. A dimensionless energy parameter was introduced to quantifiably characterize the critical conditions of different types of fault-slip events. Theoretical analyses and calculations were presented, and the results agreed with the experimental observations.In conclusion, a shear-slip type rockburst is characterised by contact instability. The main factors influencing the slip rockburst include the property of the contact surface, stress state, and external dynamic disturbances. The triggering mechanism of this dynamic phenomenon is that when the rock mass structure is at a high shear stress state, the external disturbance helps the rock mass overcome the frictional resistance, facilitating the sliding of the key block from the constraint.



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*Source: 1687519-2018-09-25.xml*