A testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression

Xia-Ting Feng,Mian Tian,Chengxiang Yang,Benguo He

Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines,Northeastern University,Shenyang,110819,China

Keywords: Low-frequency and low-amplitude full surface disturbance True triaxial system Prepeak and postpeak dynamic disturbance Rockburst-induced stress wave Blasting-induced stress wave Hard rock

ABSTRACT In this context,a testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression was developed.The system is mainly composed of a static loading subsystem,a dynamic loading subsystem,a specimen box subsystem,and a data measurement subsystem.The static loading subsystem uses low stiffness loss frame structure technology,which greatly improves the frame stiffness in the three principal stress directions (up to 20 GN/m) and ensures the demand of the disturbance experiment in both the prepeak and postpeak stages.The disturbance loads with frequency of 0-20 Hz and stress level of 0-30 MPa were applied using large flow parallel oil source technology characterized with high heat dissipation efficiency.For the disturbance loads with frequency of 100-500 Hz and stress level of 0-30 MPa,they were realized by using high-frequency and centimeterper-second-scale low-speed disturbance rod technology.Three rigid self-stabilizing specimen boxes were utilized to provide support for the specimen and deformation sensors,ensuring the stability and accuracy of the data obtained.To verify the performance of the true triaxial test system,disturbance experiments were conducted on granite specimens.The results show that the experimental device satisfies the requirements of original design,with an excellent repeatability and reliable testing results.

1.Introduction

During excavation in deep projects,rockburst-and blastinginduced stress waves can induce dynamic disturbance hazards such as rockbursts (Kaiser et al.,1996;Feng et al.,2013),largevolume collapses (Kuszmaul,1987),and continuous cracking of surrounding rocks (Martin et al.,2001).This can seriously threaten the safety of construction workers and equipment.For example,a very strong rockburst induced by blasting stress waves occurred in the connecting areas #7 and #8 of the Jinping underground laboratory on August 23,2015 and resulted in rock failure with distance larger than 100 m recorded by the multipoint extensometer DSP-04,as shown in Fig.1a.Fig.1a-c shows that a sudden displacement change occurred at the north sidewall of #4 laboratory.The displacements at measuring points DSP-04-A and DSP-04-D are shown in Fig.1c and d,respectively.A displacement of 0.0744 mm was monitored at pointAlocated 0.5 m from the north sidewall of #4 laboratory,and a displacement of -0.0023 mm was recorded at pointDlocated 8.5 m from the north sidewall.As shown in Fig.1e and f,the amplitude of the rockburst-induced vibrations was higher than that of blasting vibrations,with low dominant frequency.The resulting stress wave can induce rock cracks with a distance beyond 100 m.The dominant frequency of rockburst-and blasting-induced stress waves is mainly of 0-500 Hz,and the stress amplitude of 0-30 MPa (Wang,2015;Du et al.,2016;Zhang,2016;Su et al.,2017).From October 2010 to September 2011,a total of 38 delayed rockburst events were reported in the diversion tunnel and construction drainage tunnel of the Jinping II Hydropower Station (Feng et al.,2013).These rockbursts are mainly of fracturing processes induced by excavation and blasting disturbances.

Fig.1.Rockburst-induced failure of surrounding rocks beyond 100 m at Jining-II underground laboratory excavated in granite with an overburden of 2400 m on August 23,2015:(a)Rockburst location and layout of multipoint extensometers;(b) Layout of measuring points along DSP-04;(c) Displacement of measuring point DSP-04-A;(d) Displacement of measuring point DSP-04-D;(e) Velocity-time curve;and (f) Spectrum diagram.

The development of true triaxial rock mechanics test equipment is an important means to reveal the mechanism of the rock failure process induced by deep excavation (Mogi,1970;Alexeev et al.,2008;Chang and Haimson,2000;Descamps et al.,2012;Ingraham et al.,2013;Feng et al.,2016,2018,2021).For example,hydraulic equipment has been developed and used to study the behavior of rocks subjected to disturbance stress of 0-10 MPa with frequencies of 0-10 Hz and 0-1 Hz,in addition to local disturbance with the stress level of 0-30 MPa and frequency of 0-20 Hz under true triaxial compression,as shown in Table 1.An RMT-401 intermediate strain rate triaxial test system with fully digitalized and servo-controlled functions was developed by Li et al.(2022).The above equipment has made great contribution to the development of the dynamic disturbance equipment.As summarized in Table 1,the disturbance timing of all the equipment mentioned above is in prepeak stage.But the test conducted at postpeak stage has not been reported.Some equipment focuses on the uniaxial test(Bagde and Petroˇs,2005;Fuenkajorn and Phueakphum,2010),but the rock in deep project is under true triaxial stress condition.Some equipment simulates the true triaxial stress condition successfully(Zhou et al.,2014;Du et al.,2016;Su et al.,2017),considering only the local disturbance.For this case,the full surface disturbance may be more suitable.All the equipment has made great contribution to disturbance tests at 0-20 Hz frequency (Bagde and Petroˇs,2005;Fuenkajorn and Phueakphum,2010;He et al.,2012;Zhou et al.,2014;Du et al.,2016;Su et al.,2017),but a higher frequency test also needs to be done.

Table 1 Characteristics of different disturbance equipment.

Table 2 Bullet length table.

In order to simulate the real stress state of rocks in deep engineering,the true triaxial loading must be realized.Because the disturbance timing may be at postpeak (Renaud et al.,2011),the postpeak stage should be obtained and maintained.When the disturbance form is local disturbance,local failure will occur.Traditional stress-strain cannot describe the results (Zhou et al.,2014).Therefore,the disturbance load should be applied on thefull surface of rock.The wave frequency of rockburst-and blastinginduced stress is mainly of 0-500 Hz,with stress amplitude mainly of 0-30 MPa (Wang,2015;Du et al.,2016;Zhang,2016;Su et al.,2017),the frequency characteristic of disturbance load cannot be fully simulated within 0-20 Hz.Thus,to simulate the rock fracturing process caused by excavation and rockburst-or blastinginduced stress waves,a testing system was developed to study the rock failure process by different dynamic disturbances under true triaxial compression.This equipment can provide support for experimental laboratory research on the mechanism of deep hazards.

Fig.2.Schematic diagram of the disturbance stress state of deep rock engineering and indoor test simulation.σdc is the stress applied by the disturbance cylinder,and σdr is the stress applied by the disturbance rod.

Fig.3.Testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression:(a)System diagram;and(b)Photo of the system.

Fig.4.Diagram of the high stiffness static loading system.

Fig.5.Large flow parallel oil source with high heat dissipation efficiency (capacity of 430 L/min).

2.Principles,key technology,and configuration of the system

2.1.Design principles of the system

The system is developed to mimic the full surface disturbance process of rockburst-or blasting-induced stress waves on the surrounding rocks under true triaxial static stress,in both the prepeak and postpeak stages,as shown in Fig.2.The system uses a threerigid true triaxial system to simulate the prepeak and postpeak stages under the true triaxial static stress.An integrated design is used to increase the stiffness of the frame and force the transmitting system to reduce the influence of the frame on the wave.Then,the hydraulic dynamic cylinder is used to simulate stress waves with a frequency of 0-20 Hz and stress amplitude of 0-30 MPa in the direction of σ2or σ3.The disturbance rod is used to simulate stress waves with a frequency of 100-500 Hz and a stress amplitude of 0-30 MPa in the direction of σ1.When the disturbance load is applied on the full surface of the specimen,the stresses in the other principal stress directions remain unchanged.The disturbance load on the specimen can then be measured.

2.2.Key technology and configuration of the system

The testing system is shown in Fig.3.The system is mainly composed of a static loading subsystem,a disturbance loading subsystem,a specimen box subsystem,and a data measurement subsystem.Static loads are applied by the static loading subsystem.A disturbance load can be applied by the disturbance loading subsystem.

2.2.1.High stiffness static loading system

The stiffness of the frame is critical to the postpeak data acquisition(Xu and Cai,2017).In this study,low stiffness loss frame structure technology was used to optimize the stiffness of the equipment.The true triaxial frame is shown in Fig.4.The circular horizontal frame was processed by integral forging,in order to realize high stiffness levels.The cylindrical vertical frame was inserted into the circular horizontal frame,which decreased the space between the vertical and horizontal frames to almost zero and provided stiffness support for the success of the postpeak disturbance test.

The static loading system mainly consists of a low stiffness loss frame and servo cylinders,as shown in Fig.4.The frame is composed of horizontal and vertical frames.The stiffness of the frames in the three principal stress directions can reach a maximum of 20 GN/m.The servo cylinders include four static cylinders in theX-andY-direction and two dynamic cylinders in theZdirection,which are fixed on the horizontal and vertical frames,respectively.Their static loading capacities are 2000 kN,3000 kN,and 2000 kN in theX-,Y-,andZ-direction,respectively.Two lifting cylinders are symmetrically set to the test location on the vertical frame before the load is applied.After the test,the lifting cylinders lift the vertical frame to remove the specimen.Two guiding columns are symmetrically distributed to ensure the verticality of the vertical frame during the process of upward and downward movements.The upper limit rings set the limit of the upper position of the vertical frame to ensure that the specimen box can be pushed into the specimen box-carrying platform.The lower limit rings are set at the test location to limit the lower position of the vertical frame.Therefore,the center of the specimen coincides with the center of the cylinder when the vertical frame moves down at the test location.

Fig.6.MOOG G761 large flow servo shuttle valve.

Fig.7.Schematic diagram of piston moving forward and backward.

Fig.8.Centimeter-per-second-scale low-speed disturbance rod.

Fig.9.Schematic of high-and low-pressure dual gas path launch technology: (a) Unlaunched status;and (b) Launched status.

2.2.2.High heat dissipation efficiency of a largeflow parallel oil source for 0-20 Hz and 0-30 MPa full surface disturbance

For the high-pressure hard rock testing machine,the application of full surface disturbance loads under high static loading requires a large-diameter piston,that is,a piston with a large cross-sectional area,which leads to an increase in the flow of oil.At the same time,to conduct the 0-20 Hz full surface disturbance test,the required flow rate must be increased.This increased flow will heat the oil source,and will affect the service life of the hydraulic oil and systems.Therefore,a large flow parallel oil source with high heat dissipation efficiency is designed(see Fig.5)to provide a frequency range of 0-20 Hz.The MOOG G761 large flow servo shuttle valve(Fig.6)was assembled on the cylinder to control the reciprocating motion of the piston.The DOLI I50 dynamic servo control system was used to control the action of the valve.

Fig.10.Schematic of dual-channel high-voltage trigger with low-voltage acquisition technology.

The parallel large oil source adopts the parallel oil pump design,which consists of four large pumps,one small pump,one circulating pump,and one oil tank.When the dynamic test is conducted,four 100 L/min high-flow pumps work simultaneously.First,the oil is pumped out from the bottom of the oil tank,and the oil flows from the oil inlet pipe to the cylinder to promote the movement of the cylinder piston.Then,the return oil flows through the returnoil pipe and to the oil tank.The returning hot oil starts from the return-oil port and circulates organically according to the uniquely designed pipeline in the oil tank to achieve heat dissipation and continuously provide power for the reciprocating movement of the piston.

Fig.7a and b shows the forward and backward state principles of the dynamic cylinder,respectively.When the piston moves forward,as shown in Fig.7a,the computer sends an instruction signal to the EDC I50 servo controller as the target value,and the latter collects the load value of the dynamic load sensor as the measured value.The proportional-integral-derivative(PID)control algorithm circuit in the EDC I50 servo controller uses the target and measured values to obtain a control signal.Then,the EDC I50 servo controller sends the control signal to the MOOG G761 servo shuttle valve,which further forges connections between the oil inlet pipe and the upper chamber of the cylinder and that between the oil return pipe and the lower chamber of the cylinder,and determines the oil inlet level.Under the pressure of the oil in the upper chamber of the cylinder,the piston is pushed forward.In this system,the oil source supplies high-pressure oil.The high-pressure oil from five oil pipes is collected in the collecting and diverting valve seat #1 and then diverted to different cylinders.Finally,the oil in the lower chamber of the cylinder returns to valve seat#2 and finally returns to the oil source.When the piston needs to move backward,as shown in Fig.7b,the oil inlet pipe is connected to the lower chamber of the cylinder,and the oil return pipe is connected to the upper chamber of the cylinder.Under the pressure of the oil in the lower chamber of the cylinder,the piston is pushed backward.

Fig.11.Splicing technology.

2.2.3.Centimeter-per-second-scale low-speed disturbance rod for 100-500 Hz and 0-30 MPa full surface disturbance

The disturbance loads with frequency of 100-500 Hz and stress level of 0-30 MPa are provided by a centimeter-per-second-scale low-speed disturbance rod (Fig.8).The rod includes a gas cylinder,a launcher,a bullet,and an incident rod.The rod drives the bullet through low-pressure compressed air,which causes the bullet to hit the incident rod and transmit the 0-30 MPa disturbance load to the rock specimen.

The piston in the launcher has a high friction with the barrel wall of the launcher,and the minimum working pressure of the pneumatic ball valve is relatively high.The same set of gas circuits cannot simultaneously address the contradiction between the launch switch and the low-pressure launch.Therefore,it is difficult to achieve a low-speed launch using a conventional launch system.The system uses high-and low-pressure dual gas path launch technology to solve this problem.The high-pressure gas path is separated from the low-pressure gas path and causes the lowpressure gas to enter the launcher to achieve a low pressure.At the same time,a low-friction polyethylene sleeve is used to reduce the frictional force when the bullet is launched to make it out of the barrel at a lower speed.

Fig.9a and b shows the unlaunched and launched status of the launch system,respectively.In the unlaunched state,S is connected to B,and P is connected to A in pneumatic valves#1 and#2.S and R are connected to air (the gas can be discharged from these ports).Pneumatic valves#1 and#2 are connected through ports B1and P1.A1is connected to the back chamber of the launcher,B2is connected to the ball valve and middle chamber of the launcher,and A2is connected to another port of the ball valve.Air pump#1 supplies high-pressure gas to P1,and then the high-pressure gas flows through P1and A1to the back chamber of the launcher,which further pushes the piston forward(the gas in the middle chamber is discharged through the ball valve,which is open and connected to air when the launcher has not been operated) and closes the launcher.Then,#2 air pump pushes the compressed air to the air tank and the front chamber of the launcher.The high-pressure air is adjusted to low-pressure air by a high precision (0.001 MPa)regulator valve.When launch buttons on the pneumatic valve are pressed,the state changes to the working state.The connections in the pneumatic valve change:B is connected to P,and A is connected to R.Once the high-pressure air from air pump #1 flows through P1-B1-P2-B2to the ball valve and the middle chamber of the launcher,the ball valve is closed,the piston is pushed back by the high-pressure air (the air in the back chamber of the launcher is discharged through A1-R1),and the launcher is then open.Finally,the low-pressure gas in the air tank and front chamber of the launcher is released to the gun barrel to cause the bullet to move at a low speed.A polyethylene sleeve is used to reduce the friction between the gun barrel and the bullet,which further reduces the threshold of the launch pressure.

Fig.12.Structural diagram of the self-stabilizing specimen box.

Fig.13.Section of the true triaxial loading system along σ1.

The axial cylinder piston of the disturbance rod is designed as a hollow piston.The incident rod passes through the hollow piston and is close to the bottom of the indenter.When the bullet hits the incident rod,a stress wave is generated and transmitted to the indenter through the incident rod and finally to the specimen.

The disturbance stress amplitude is low,and the required trigger voltage is low.However,if the trigger voltage is too low,it will be falsely triggered by the interference of magnetic field chaos in the environment,making it impossible to collect 0-30 MPa disturbance stress data.In this system,dual-channel high-voltage trigger with low-voltage acquisition technology is used to solve this problem (Fig.10).A strain gauge is attached to the incident rod to measure high voltages and ensure the triggering function.The middle of the incident rod uses damping technology to attenuate the stress,and the high-voltage signal is attenuated to the low-voltage signal corresponding to the low stress level.The attenuated low-voltage signal is collected by the strain gauge attached to the indenter.After obtaining the low-voltage signal on the indenter,the disturbance stress is calculated by multiplying the disturbance strain of the indenter by its elastic modulus.Because the indenter is positioned close to the specimen,the stress is considered approximately equal to the stress on the specimen.

Fig.14.Section of the true triaxial loading system perpendicular to σ1.

The splicing rod is used to hit the fixture directly to achieve a frequency disturbance of 100 Hz.The fixture is already under a high static load controlled by the cylinder servo before the 100-500 Hz disturbance is applied.The static stress on the fixture undergoes servo-controlled small fluctuations in the indenter.The strain gauges on the indenter generate a small fluctuation voltage.Using the strain gauge channel at the fixture end as the data acquisition trigger channel will cause false triggering due to small fluctuations in voltage.In this system,clutter trigger technology is used to employ the clutter signal generated in the 100 Hz frequency disturbance test as the trigger signal of the data acquisition function and to acquire the low-voltage strain on the fixture.

To simulate the blasting stress wave using the disturbance rod,a similar method is used.First,a fast Fourier transform (FFT)is performed on the monitored blasting vibration data to obtain the dominant frequency of the blasting stress wave.Then,the cycle and half-cycle times are obtained according to the dominant frequency of the blasting vibration.Finally,a simulation similar to that for a half-sine wave is realized by the disturbance rod.

To achieve full surface disturbance,the rod end surface should cover specimen surface of 50 mm×50 mm.Therefore,a square of 50 mm×50 mm is circumscribed by the circumference of the rod,which has a radius ofR==35 mm?

Fig.15.3D schematic diagram of the fixture.

Fig.16.Relationship between the load and the deformation of the frame in three principal stress directions.

Due to the complexity of the true triaxial system,the specimen boundary is simplified to two cases: no reflection boundary and a fixed boundary.Through numerical simulation,the approximate relationship between the bullet velocity and the stress on the specimen is obtained.Finally,the bullet velocity is inferred to be 0-200 cm/s according to the required stress (0-30 MPa) on the specimen.

According to the blasting vibration waveform monitored on site,FFT is performed to extract the dominant frequency,and the corresponding sine wave frequencyfis obtained.Based on rod impact theory,the rod length can be obtained:

whereLis the length of the bullet,Cis the wave speed of the rod material,andfis the frequency.

The wave speed of the rod material is 5197 m/s.The values of the frequencyfare assumed to be 100 Hz,300 Hz,350 Hz,400 Hz,450 Hz,and 500 Hz,and then the bullet lengthLcan be calculated as listed in Table 2.

Table 3 Testing plan for the dynamic disturbance of granite specimens under true triaxial compression.

Fig.17.Verification test results of the 0-20 Hz full surface disturbance induced by the cylinder on the cuboid steel specimen: (a) Location of strain gauges on the specimen;(b)Testing results of strain-time for each strain gauge;and (c) Testing results of 6 strain gauges by amplifying the time scale in (b).

Fig.18.Curves of minimum and maximum disturbance loads at different frequencies on a cuboid granite specimen.

Stress waves with frequencies of 300-500 Hz were generated by bullets hitting the incident rod.The frequency of 100 Hz was achieved using rod splicing technology,and the 4.33-m bullet and 9-m incident rod were spliced into a new bullet that then directly impacted the specimen.A schematic diagram of the rod splicing technology is displayed in Fig.11.As shown in Fig.11,there is a splicing barrel between the bullet and the incident rod,two grooves are processed at the two sides of the splicing barrel to install the seal ring,and one hole is processed on the splicing barrel.The bullet and incident rod are fixed together by the friction of the sealing ring,and air in the splicing barrel is discharged through the hole.The splicing barrel can be vacuumed to increase the splicing force between the two rods.The new bullet length is 13.33 m,and the frequency is 100 Hz.

2.2.4.Self-stabilizing specimen box system

The six indenters of the fixtures of the three-rigid true triaxial testing machine are fixed by screws.The screws are removed before the test.In the dynamic test,after the disturbance causes the specimen to be destroyed,the fixture module structure is unstable,which causes the instability of the deformation sensors fixed on the fixture.Therefore,the measured hard rock deformation data will not be accurate.In addition,the unstable deformation signal will cause the machine to lose control,leading to catastrophic damage to the machine.Therefore,a three-rigid specimen box(Fig.12)was independently developed to ensure the accuracy of the deformation data and the safety of the machine.

The specimen box system is shown in Fig.12.The skeleton,force transmission column,and support plate are assembled to form a skeleton assembly.The fixture and base are assembled to form a base assembly.The skeleton assembly and the base assembly can be separated or combined by a lifting plate.The locations of the skeleton assembly and the base assembly are set by a position ring fixed on the support plate and a position column fixed on the base.The signal cable is transmitted to the outside through the sensor signal cable connectors.After the skeleton assembly and the base assembly are combined,the lifting plate is disassembled from the skeleton assembly,and the entire specimen box is pushed into a vertical frame.Through this type of mechanical structure,the selfstabilization of the specimen and the force transmission mechanism can be realized.

2.2.5.Data measurement system

The data measurement system is composed of a load measurement subsystem,a displacement measurement subsystem,and a deformation measurement subsystem.The 0-20 Hz load measurement subsystem includes dynamic load cells(load cells 01 and 02 in Figs.13 and 14) and static load cells (load cells 03-06 in Figs.13 and 14),which are fixed on the cylinder pistons.The 100-500 Hz disturbance load is indirectly measured by a strain gauge(Fig.15),and the disturbance load is calculated by multiplying the strain by the elastic modulus.The load cells are used to measure the load on the specimen and send feedback on the load signal to the controller,and then the controllers send instructions to control the movement of the cylinder pistons to set the load to the target value.The displacement measurement subsystem includes linear variable differential transformers (LVDTs) (LVDTs 01-06 in Figs.13 and 14)fixed on the cylinder pistons.The LVDTs are used to measure the displacement of the cylinder pistons in each direction,and the feedback displacement signal is fed to the controller.Then,the controllers send instructions to control the cylinder pistons to the target value.To obtain more realistic specimen deformation data,LVDTs 07-12(Fig.15)are fixed on the six indenters.Two LVDTs are fixed in one direction,and the deformation data are the average of the data from the two sensors.

Fig.19.Verification test results of 100-500 Hz full surface disturbance induced by the disturbance rod on the cuboid granite specimen.

Fig.20.Minimum and maximum pulse stresses on the granite specimens at different frequencies: (a) 500 Hz,(b) 300 Hz,and (c) 100 Hz.The pulse stress was calculated by multiplying the strain measured by the strain gauge by the elastic modulus of the indenter.

To ensure the accuracy of the deformation data,the deformation sensors are fixed on the fixture,as shown in Fig.15.The six indenters of the fixture are connected and fixed by right-angle spring parts,which are manufactured by a combination of mechanical design and special processing technology.The clamping function can be achieved,and force values in the range of 1-2 kN do not affect the test process.At the same time,the clamping function will not fail when the specimen is damaged and deformed.When installing the specimen,only one of the indenters needs to be removed.The specimen is placed into the fixture,and then the removed indenter is installed on the fixture.The specimen can be installed conveniently and quickly.Because the force of the spring is very low,with a value of 1-2 kN compared to the loading force of 2000 kN during the test,the clamping force of the right-angle spring has little effect on the test and does not need to be disassembled.The fixture is not loose during the disturbance test,the deformation sensors can be fixed on the fixture,and two pull-wire sensors are arranged in one principal stress direction.The data of the two sensors are averaged to ensure the stability and accuracy of the data.Based on the above technology,the specimen box can provide stable support for the fixture and deformation sensor.As a result,more real specimen deformation data can be obtained.

3.Testing verification

To verify that the performances of the above design are achieved,verification tests were performed.

Fig.21.Complete stress-strain curves and failure mode of granite under static true triaxial compression experiments: (a) Stress-strain curves of specimens Nos.1-3;(b) Static failure mode of specimen No.1;(c) Static failure mode of specimen No.2;and (d) Static failure mode of specimen No.3.

3.1.Verification tests of the frame stiffness of the apparatus

A steel block specimen was used in the test.Through the uniaxial compression test,the loads in the three principal stress directions and the deformations of the horizontal and vertical frames were measured.The test results in Fig.16 demonstrate that the loads in the three principal stress directions are roughly linear with the deformation,and the calculated stiffness is approximately 20 GN/m.

3.2.Verification tests of the 0-20 Hz and 0-30 MPa full surface disturbance of the specimen

Local disturbance will cause a uniform disturbance stress and lead to uniform rock failure.Therefore,the uniformity of the disturbance stress should be ensured.Based on the above principles,disturbance load with a frequency of 0-20 Hz can be supplied.Fig.17 shows the stress uniformity in the horizontal and vertical directions,verifying the full surface disturbance performance of the test system.Fig.18 shows the minimum and maximum loads achieved at frequencies of 1 Hz,10 Hz,and 20 Hz.

3.3.Verification tests of the 100-500 Hz and 0-30 MPa full surface disturbance of the specimen

To verify the full surface disturbance performance of the test system,Fig.19 shows the stress uniformity in the horizontal and vertical directions.The 100-500 Hz and 0-30 MPa disturbance performance curves are shown in Fig.20.The minimum and maximum pulse stresses occur at frequencies of 500 Hz,300 Hz,and 100 Hz.Fig.20 also shows that the expected characteristics of 100-500 Hz and 0-30 MPa are basically realized.

4.Testing methods and results

To verify the reliability of the test system,a series of disturbance experiments was conducted.The granite specimens had a size of 50 mm × 50 mm × 100 mm with accuracy of ±0.02 mm,and a perpendicularity accuracy of 0.025 mm.According to ultrasonic test results in the three principal stress directions of the specimen,six specimens with good homogeneity and anisotropy were selected for the disturbance test,as shown in Table 3.

4.1.Static experiment of hard rocks under true triaxial compression

The test is conducted as follows.First,σ3,σ2,and σ1were loaded to prescribed values in a stress-controlled manner at a rate of 0.5 MPa/s.Subsequently,σ3and σ2were kept unchanged,and σ1was loaded to the pre-set value in a stress-controlled manner and then in a deformation-control mode with a loading rate of 0.015 mm/min until the specimen was destroyed in the residual stage.Finally,the static stress-strain curve of the specimen was obtained.

Fig.21 shows the results of the static experiments conducted at σ3=5 MPa and σ2=20 MPa under true triaxial compression.The full stress-strain curves,brittle failure process and failure mode were obtained.The repeatability of the experimental results proves the reliability of the system.

Fig.22.Test results of disturbance along the σ3 direction at the prepeak stage of granite specimen No.4 under true triaxial compression:(a)Stresses(σ1,σ2,and σ3+disturbance stress at the prepeak of σ1)vs.time curves of specimen;(b)Disturbance stress with an amplitude of 4 MPa and a frequency of 20 Hz vs.time curves in 1 s;(c)Complete stress-strain curves;and (d) Disturbance failure mode.

4.2.Testing disturbance along σ3 direction under true triaxial compression

First,σ1,σ2,and σ3were loaded to the predetermined stress levels.Then,σ3and σ2kept stable,and σ1was set to the given stress level before the prepeak strength was reached.Dynamic disturbance began at σ3until the specimen was broke.As an example,Fig.22 shows the test results of specimen No.4.σ1,σ2,and σ3were loaded to the predetermined stress levels at a rate of 0.5 MPa/s using the stress-controlled mode.The dynamic disturbance along the σ3direction was 4 MPa with a frequency of 20 Hz,as shown in Fig.22b.Fig.22 indicates that the deformation of the specimen increased as the disturbance began and continued until the specimen failed.

When σ2and σ3were unchanged and σ1was kept at 288 MPa,the specimen did not fail.After a disturbance load was applied to the specimen along σ3direction,the deformation began to increase,and finally the specimen failed,showing the significant influence of the disturbance load.The broken specimen in this test was more serious than that in the static test.The advantage of the test system is proven.

A similar method was used to conduct the experiments of postpeak disturbance in σ3direction.First,σ1,σ2,and σ3were loaded to the prescribed stress levels at a rate of 0.5 MPa/s using the stress-controlled mode.Then,σ3and σ2were kept stable,and σ1was set to a given stress after the postpeak strength was reached.The dynamic disturbance was set to σ3until the specimen failed.Fig.23 shows the test results of specimen No.5.The dynamic disturbance along σ3direction was 4 MPa with a 20 Hz frequency for specimen No.5,as shown in Fig.23b.Fig.23 reveals that the deformation of the specimen increased after the disturbance began and continued until the specimen failed.

When σ2and σ3were unchanged and σ1was 293.4 MPa (postpeak),the specimen did not fail.After the disturbance load was applied to the specimen along σ3direction,the deformation began to increase,and failure occurred.Comparing Fig.23a with Fig.22a,the postpeak failure time was shorter than the prepeak failure time,implying that when σ1was close to the peak strength,the disturbance at the postpeak stage was more severe than that at the prepeak stage.Therefore,it is meaningful to consider the disturbance at the postpeak stage.The failure mode at the postpeak stage was different from that at the prepeak stage and in the static tests.The advantage of the postpeak function under which disturbance occurs is proven.

Fig.23.Test results of disturbance along the σ3 direction at the postpeak stage of granite specimen No.5 under true triaxial compression: (a) Three stress (σ1,σ2,and σ3+disturbance stress at postpeak of σ1)vs.time curves;(b)Disturbance stress with an amplitude of 4 MPa and a frequency of 20 Hz vs.time curves in 1 s;(c)Complete stressstrain curves;and (d) Disturbance failure mode.

4.3.Testing disturbance along σ1 direction under true triaxial compression

A similar method was used for the prepeak disturbance experiment process in σ1direction.σ1,σ2,and σ3were first loaded to the predetermined stress levels at a rate of 0.5 MPa/s.Then,σ3and σ2were kept stable,and σ1was set to a given stress before the prepeak strength was reached.Dynamic disturbance began in σ1direction in the range of 100-500 Hz and continued until the specimen failed.As an example,Fig.24 displays the results of specimen No.6.The dynamic disturbance along σ1direction had a frequency of 500 Hz,as shown in Fig.24a-c.Fig.24 illustrates that the specimen deformation increases as the disturbance occurs until the specimen fails.

When σ2and σ3were unchanged and σ1was 284 MPa,the specimen did not fail.After the disturbance load was applied on the specimen along σ1direction,the deformation began to increase,and finally the specimen was broke,showing the influence of the disturbance load.The failure mode was different from that in the static test.The advantage of disturbance along the σ1direction is proven.

5.Discussion

The test results in Figs.17 and 18 indicate that the testing system has a good capacity for 20 Hz dynamic disturbances along σ2or σ3direction on the full surface of the specimen.The test results in Fig.20 show that the testing system has a good capacity for disturbances of 100-500 Hz and a maximum dynamic disturbance of 30 MPa along σ1direction on the full surface of the specimen.

The failure modes of granite in Fig.21b-d,22d,23d,and 24c indicate similar tensile fracturing processes under static and dynamic disturbances during true triaxial compression.The macrofracture in each specimen are approximately parallel to σ2direction.All three granite specimens have coincident and complete stress-strain curves under static true triaxial compression(see Fig.19a).The constant σ1and σ2are loaded under dynamic disturbance along σ3direction,as shown in Figs.22a and 23a.The testing system achieves excellent results for the postpeak dynamic disturbance along σ3or σ1direction for brittle rock(granite)under true triaxial compression,as shown in Figs.23c and 24a.The test results indicate that the testing system has an adequately high rigidity(nearly 20 GN/m in each stress direction,as shown in Fig.16)and constant loading.In addition,the rock specimens are not offcentered,and the system exhibits an excellent postpeak servocontrolled capability for brittle rocks during dynamic disturbance under true triaxial compression.These techniques guarantee the good repeatability and reliability of the test results.

6.Conclusions

Fig.24.Test results of disturbance along the σ1 direction at the postpeak stage of granite specimen No.6 under true triaxial compression: (a) Complete stress-strain curve;(b)Disturbance stress-time curve;and (c) Disturbance failure mode.

A testing system for the rock failure process by the full specimen surface and prepeak and postpeak dynamic disturbances (frequency of 0-20 Hz and stress of 0-30 MPa)in σ2or σ3direction and that (frequency of 100-300 Hz and stress of 0-30 MPa) in σ1direction under true triaxial compression was successfully developed to obtain a better understanding of rock failure induced by dynamic disturbances in deep rock engineering.The system design,key technology,configuration of the disturbance testing system,testing methods,and meaningful experimental results are presented in this paper.The main conclusions are as follows:

(1) Using the integrated high stiffness design of the frame,disturbance at the postpeak stage can be realized,and the repeatability of the disturbance load is ensured.

(2) Using high heat dissipation efficiency large flow parallel oil source technology,disturbance loads (0-20 Hz and 0-30 MPa) were realized.Using 100-500 Hz and centimeterper-second-scale low-speed disturbance rod technology,disturbance loads of 100-500 Hz and 0-30 MPa were realized.Blasting stress waves and rockburst-induced stress waves in deep rocks were simulated.

(3) The system can obtain complete stress-strain curves and failure modes of rocks under static and dynamic disturbance and true triaxial compression.Dynamic disturbance is a major factor causing the failure of rocks that have not broken under high static true triaxial compression.The failure process of rocks under dynamic disturbance with true triaxial compression differs from that of rocks under static true triaxial compression alone.The differences are reflected in the stress-strain curves and failure modes of rocks.The obtained test results prove the advantages of the developed dynamic testing system.

(4) The test results also indicate that when σ1is close to the peak,the postpeak disturbance is more severe than the prepeak disturbance,and the postpeak disturbance must be considered.

Due to the limitations in the performance of the hydraulic and rod equipment,the testing system lacks a dynamic disturbance performance of 20-100 Hz under true triaxial compression.Improvements are needed in the future.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Grant No.51839003),for which we are grateful.The authors thank Prof.Haibo Li for his improvements to the paper and Profs.Jingcai Gu,Mingyang Wang,Xinping Li,Lixing Huang,Xiwei Zhang,and Fengpeng Zhang,Mr.Donghui Ma,Mr.Daoquan Wei,Dr.Jianyu Peng,Dr.Jianqing Jiang,and Mr.Jun Tian for assisting in the development of the equipment.