Experiments on rockburst proneness of pre-heated granite at different temperatures:Insights from energy storage,dissipation and surplus

Lei Xu,Fengqing Gong,b,*,Zhixing Liu

a School of ResourcesandSafety Engineering,CentralSouthUniversity,Changsha,410083,China

b School of CivilEngineering,Southeast University,Nanjing,211189,China

Keywords:Pre-heated granite Temperature effect Linear energy storage law Rockburst proneness Residual elastic energy index

A B S T R A C T Many underground engineering projects show that rockburst can occur in rocks at great depth and high temperature,and temperature is a critical factor affecting the intensity of rockburst.In general,temperature can affect the energy storage,dissipation,and surplus in rock.To explore the influence of temperature on the energy storage and dissipation characteristics and rockburst proneness,the present study has carried out a range of the uniaxial compression(UC)and single-cyclic loading-unloading uniaxial compression(SCLUC)tests on pre-heated granite specimens at 20 °C-700 °C.The results demonstrate that the rockburst proneness of pre-heated granite initially increases and subsequently decreases with the increase of temperature.The temperature of 300 °C has been found to be the threshold for rockburst proneness.Meanwhile,it is found that the elastic strain energy density increases linearly with the total input strain energy density for the pre-heated granites,confirming that the linear energy property of granite has not been altered by temperature.According to this inherent property,the peak elastic strain energy of pre-heated granites can be calculated accurately.On this basis,utilising the residual elastic energy index,the rockburst proneness of pre-heated granite can be determined quantitatively.The obtained results from high to low are:317.9 kJ/m3(300 °C),264.1 kJ/m3(100 °C),260.6 kJ/m3(20 °C),235.5 kJ/m3(500 °C),158.9 kJ/m3(700 °C),which are consistent with the intensity of actual rockburst for specimens.In addition,the relationship between temperature and energy storage capacity(ESC)of granite was discussed,revealing that high temperature impairs ESC of rocks,which is essential for reducing the rockburst proneness.This study provides some new insights into the rockburst proneness evaluation in high-temperature rock engineering.

1.Introduction

Rockburst,as one of the typical engineering geological hazards,frequently occurring in deep rocks,has the characteristics of suddenness,randomness and destructiveness(Ortlepp et al.,1994;Hoek et al.,1995;Qi et al.,2004,2008;Wu et al.,2010;Ranjith et al.,2017;Gao et al.,2021).As the depth increases,the temperature of surrounding rock gradually rises,and the frequency of rockburst also increases(Rybach et al.,1994;Suggate et al.,1998;Jiang et al.,2010;Zhang et al.,2012).Particularly,severe rockburst disasters have been reported during tunnel constructions in high geothermal areas.For instance,Gaoligong mountain tunnel,the longest tunnel in China(Zhang et al.,2009),and Sangzhuling tunnel(Yan et al.,2018),one of the most important tunnels in China’s Sichuan-Tibet Railway,are significantly affected by high temperature and rockburst.The surrounding rock temperature of Sangzhuling tunnel has reached up to 89.5°C,and the number of rockburst events is more than 90,000;the accumulated mileage of rockburst section accounts for 55%of total mileage(Yan et al.,2019,2020).Temperature is a crucial factor affecting the intensity of rockburst.Therefore,assessing accurately the influence of temperature on rockburst proneness for rock materials is of great significance for not only deep mining but also rock engineering in high-geothermal areas.

To reveal the effect of temperature on rockburst proneness for hard rock,many scholars have analysed the stress state of hightemperature surrounding rock and thermal effect of rock materials.The common heating method can be the real-time high temperature(Chen et al.,2017a;Kumari et al.,2017b)and preheating treatment(Gautam et al.,2018;Jiang et al.,2020).Considering the fact that the deep rock mass of high temperature is in a multidimensional stress state,the space and free surface are formed inside it after the excavation.Li et al.(2018)established a two-dimensional(2D)geological model employing thermalmechanical coupling,and adopted a method of“l(fā)oad first,then excavate”to simulate rockburst around the tunnel with high temperature.It was found that the higher the temperature(20°C-80°C)was,the severer the brittle failure of the surrounding rock was,and the more violent the phenomenon of rockburst could be.Yan et al.(2018,2019)numerically analysed the stress distribution characteristics of tunnel under thermal-mechanical coupling,and concluded that high temperature would enhance the intensity of rockburst.In order to simulate the temperature effect on rockburst disaster in deep roadway,some scholars conducted simulations of rockburst on pre-heated granites with different temperatures(Su et al.,2017;Ren et al.,2019)and different thermal damage degrees(Akdag et al.,2018;Jiang et al.,2020)through threedimensional(3D)compression of rock mass.It was found that thermal damage would delay the occurrence of rockburst,with increased intensity.By comparing the failure phenomenon of granites at room temperature,it was found that the rockburst proneness of granites decreases only when the temperature is higher than 500°C(Su et al.,2017;Jiang et al.,2020).Although these works have reproduced the rockburst process at different temperatures,most of them are only qualitative analyses of temperature effect on rockburst proneness.Therefore,if the rockburst proneness at different temperatures can be quantitatively described by the driving mechanism of rock failure,this defect can be perfectly compensated.

In essence,rockburst is a dynamic failure process of rock being attributed to a sudden release of strain energy accumulated within rock(He et al.,2012;Kaiser and Cai,2012;Li et al.,2012,2017).The energy storage and dissipation of rock are closely related to the intensity of rockburst(Kidybinski,1981;Wang and Park,2001;Gong et al.,2018a,2018b;Xu et al.,2021).It is universally acknowledged that temperature will change the internal structure and mineral composition of rock materials,leading to significant variations in mechanical properties and energy evolution characteristics of rock.Therefore,analysis of temperature effect is the key to accurate evaluation of the rockburst proneness of pre-heated rocks,and it is also the basis for evaluating rockburst proneness in high-temperature rock engineering.Under unknown in situ stress state,the UC test is one of the widely used testing methods to evaluate the rockburst proneness(NB/T 10143-2019,2019).Based on this,many scholars have used UC tests to assess the rockburst proneness(e.g.Chen et al.,2014;Zhang et al.,2015;Leveille et al.,2017;Sepehri et al.,2020).Common rockburst proneness criteria include the strain energy storage index(WET)(Kidybinski,1981),energy impact index(ACF)(Tan,1992),potential elastic strain energy(PES)(Wang and Park,2001),peak energy impact index(A′CF)(Gong et al.,2018b),and peak strain energy storage index(Wpet)(Gong et al.,2019a;He et al.,2021a).However,the present evaluation methods mainly consider the elastic strain energy and dissipated energy in the pre-peak compression process of pre-heated(high-temperature)rocks.The results are mainly in the form of ratio(Gong et al.,2018b),as a relative quantity,they cannot accurately reflect the absolute energy released by the pre-heated(hightemperature)rock failure.All in all,few scholars have considered the temperature effect on rockburst proneness from energy change of whole process for pre-heated rocks failure.Therefore,the present study intends to focus on this perspective and comprehensively investigate the energy storage,dissipation,and surplus during the compression of pre-heated granite at different temperatures,for an accurate and quantitative assessment of rockburst proneness.

In this study,in order to maintain the stress state of the rock under UC,the SCLUC test method has been used to separate the elastic strain energy and dissipation energy of pre-heated granite specimens.First,based on a range of SCLUC tests,the failure behaviour and energy evolution of pre-heated granite were analysed.Second,through accurately computing the peak strain energy densities,the residual elastic energy index was used to determine the rockburst proneness of the pre-heated granite specimens.Finally,the influence of temperature on the energy storage capacity as well as the relationships among the related parameters and rockburst proneness for the pre-heated granite samples was discussed.While revealing the effect of temperature on mechanism of rockburst proneness,the present work offers theoretical foundations for rockburst proneness assessment in high-geothermal rock engineering.

2.Test procedure and method

In the test,the granite was first subjected to heat treatment from 20°C to 700°C.Then,a range of SCLUC tests were conducted on the pre-heated granite specimens to accurately acquire the energy storage,dissipation and surplus characteristics of pre-heated granite.

2.1.Specimen preparation

The fresh specimens were obtained from Yueyang at the Southern China,as shown in Fig.1a.The specimens were all drilled from macroscopically dense granite block with good uniformity.The rock cores were taken in the same direction.Black and white mineral particles can be clearly identified with naked eyes.According to the International Society for Rock Mechanics and Rock Engineering(ISRM)standard for specimen size(Fairhurst and Hudson,1999),the specimens were prepared as cylindrical,with height of 100 mm and diameter of 50 mm.Both the specimens’size and processing accuracy satisfied the ISRM requirements.The average P-wave velocity of granite specimens at 20°C was 4431 m/s.The average density was 2626 kg/m3,and the average uniaxial compressive strength(UCS)was 154.78 MPa.

Fig.1.Granite specimens used in the present test:(a)Fresh granite specimens and(b)Pre-heated granite specimens.

Subsequently,five temperature levels(20°C,100°C,300°C,500°C and 700°C)were set to heat the granite specimens.The test used an SX-12-13 resistance furnace with a power of 12 kW,and the accuracy of the matched temperature controller is±1°C,as shown in Fig.2.The maximum heating temperature is 1300°C,and the furnace temperature uniformity is less than 2°C.To prevent thermal shock due to uneven heating of the specimens,we employed the commonly used heating rate of 5°C/min(Kumari et al.,2017a,b;Isaka et al.,2018)to reach the objective temperature.Meanwhile,to prevent the temperature difference between the inside and outside of specimen,when the temperature reached the target value,the specimens were kept in the resistance furnace for 2 h.Finally,the pre-heated granite specimens were naturally cooled to the room temperature(i.e.the power supply of the muffle furnace was turned off,and the specimens were cooled slowly in the furnace),as shown in Fig.1b.As the temperature increased(especially above 300°C),the specimens experienced the following macroscopic changes:the surface colour gradually became warmer and whiter,and the percussion sound between the specimens became crisper.

To quantitatively describe the physical property variations of granite,the relationships between its density,P-wave velocity and temperature were analysed,as shown in Fig.3.The specimen density gradually decreased with the increase of temperature,and the rate of reduction gradually increased(see Fig.3a).Fig.3b shows that the standard deviation of specimen P-wave velocity was low,indicating that fresh granite was complete and homogeneous.As the temperature increased,the P-wave velocity decreased significantly,and the reduction rate first increased and then decreased.Above 300°C,the variations of the P-wave velocity and density were similar-both decreased with the increase of temperature.The P-wave velocity of the specimen at 700°C was 1137 m/s,which was 25.67% of that at 20°C.This is mainly due to the influence of high temperature,as it changes the internal structure of the rock,e.g.mineral dehydration and evaporation.In addition,the initiation and propagation of micro-crack on the rock surface and inside the rock lead to an increase in its volume(in axial and lateral directions)(Zuo et al.,2017;Jin et al.,2019),reducing the density.The internal defects can also filter high-frequency harmonics and decrease the dominant frequency of the incident waves,thereby significantly reducing the wave velocity(Fan et al.,2017).

Fig.2.SX-12-13 muffle furnace for heating rock specimen.

Fig.3.Physical property changes of granite specimens before and after pre-heated treatment:(a)Density changes and(b)P-wave velocity changes.

2.2.Mechanical test equipment and method

Before the mechanical test,we excluded specimens whose size and accuracy did not meet the ISRM standard that caused by thermal treatment.The pre-heated granite specimens were tested by the INSTRON 1346 material testing machine of the modern analysis in the testing centre at the Central South University,China.The loading and data-collection system are shown in Fig.4.

To accurately separate the rock energy under different stress levels,the UC test was performed first following the SCLUC test procedure.Given granite is a typical brittle hard rock(Saroglou and Kallimogiannis,2017),force-controlled followed by displacementcontrolled mode was adopted to prevent the unexpected instability of granite.The force-controlled mode(1.0 MPa/s)was used to load the rock specimen to 80% of the peak compressive strength(σc),and then it was converted to displacement-controlled mode(0.1 mm/min)until specimen failure.

Fig.4.INSTRON 1346 rock material mechanical testing system.

The test curves and basic mechanical parameters of specimen were first obtained through the UC test.Then,based on σc,a set of five unloading pointskσc,wherekis the setting unloading stress level(k=10%,30%,50%,70%,90%),were used to perform the SCLUC tests.The specimen was first loaded to the target unloading point by force control,and then unloaded to zero.After that,it was finally loaded to failure according to the UC testing process,as shown in Fig.5.Therefore,we have obtained theas peak strength of preheated granite specimen,andkσc／as the actual unloading stress level.During the mechanical test,a rigid block is placed between the specimen and indenter(see Fig.4),to solve inaccurate measurement problem of specimen deformation to account for the excessive local compressive stress of the indenter.Notably,in the subsequent calculation of strain energy,the deformation of rigid block had been deducted.

Fig.5.Schematic diagrams of the stress path of the SCLUC test(taking k=90% as an example,k=10%,30%,50%,70% are not given at present):(a)Stress-time and(b)Stress-strain diagrams.

Fig.6.Typical stress-strain relationships of pre-heated granite specimens:(a)UC test and(b)SCLUC tests(actual unloading stress levels are shown in brackets below each temperature).

3.Test results and analyses

3.1.Stress-strain relationships of pre-heated granite specimens in UC and SCLUC tests

The typical stress-strain relationships for pre-heated granite specimens in UC and SCLUC tests are illustrated in Fig.6.Comparing the results of UC and SCLUC tests,it can be clearly observed that the secondary loading curve basically passed through the unloading point.Specifically,for the secondary loading curve with the stress higher than the unloading point,the transition from the initial loading curve to the secondary loading was smooth.This indicates that the granites have a“memory effect”during the secondary compression,and the mechanical properties are not changed by the SCLUC tests.

As illustrated in Fig.6,the concavity of stress-strain curves for the pre-heated granite specimens increased with the temperature.In other words,as the temperature increased,the compaction stage gradually became longer.The nonlinearity of compaction phase increased,while the slope of elastic stage decreased.The peak strain increased,and the overall ductility was enhanced.The strain in the rock compaction stage at 20°C was approximately 2×10-3,while it reached 9×10-3at 700°C.Meanwhile,the average peak strain of the specimens at 700°C was approximately 2.6 times of those at 20°C.In the tests,the internal micro-cracks and pores were closed rapidly and compacted due to the load.In addition,the melting of mineral grains at high temperatures,which altered the initial structure of mineral grains,enhanced the plasticity and ductility of the specimen(Zuo et al.,2017).Furthermore,when the temperature was below 500°C,the linear phase in the rock specimen loading curve was long,and there was no obvious yield phase.After reaching the peak strength,the specimens exhibited brittle failure in tests with all different temperatures,as manifested by the sudden drop of stress after the peak value.

Fig.7.Relationships between the temperature and peak compressive strength for granite specimens(data from Homand-Etienne and Houpert,1989;Du et al.,2004;Qiu et al.,2006;Zhu et al.,2006,2018;Shao et al.,2014,2015;Liu et al.,2015;Chen et al.,2017b;Huang et al.,2017;Kumari et al.,2017a,b;Yang et al.,2017;Gautam et al.,2018;Isaka et al.,2018;Jin et al.,2019).Abbreviations for the rock materials and cooling methods:H-Harcourt granite;J-Jalore granite;B-Beishan granite;S-Strathbogie granite;QQinling granite;FG-Fine-grained granite;CG-Coarse-grained granite;Se-Senones granite;Re-Remiremont granite;*-Rapid cooling;Δ-High temperature.The other specimens were naturally cooled.

3.2.Mechanical characteristics of pre-heated granite specimens

For the UC and SCLUC tests on pre-heated granite specimens,the main mechanical parameters are reported in Table 1.As the temperature increased,the peak strain(εp)of specimen increased gradually,whereas the σcand elastic modulus(Em)initially increased and subsequently decreased.Here,we took the σcof specimen as an example to analyse its relationship with temperature in detail.

Table 1The σc,εp and Em of the pre-heated granite specimens at different temperatures.

Fig.7 presents a comprehensive review of existing data on preheated granite in the literature,for a comparison with data obtained in this study.In the analyses,the temperature factor of peak strength was defined,i.e.represent the σcof granite specimen at T and 20°C,respectively,to analyse the variation trend of the σcfor different rock specimens.In this figure,three temperature intervals were defined to examine the change in the specimen intensity.In Region I(20°C-300°C),the σcof the granite increased with the temperature,the strength of specimen at 300°C was approximately 10%higher than that at 20°C.In Region II(300°C-400°C),the σcdecreased gradually with the temperature.In Region III(＞400°C),the σcdecreased rapidly with the temperature with the most significant reduction in this interval.In this study,the variation trend of the average σcof pre-heated granite specimen is consistent with the published data,as shown in Fig.7.The standard deviation of the σcof pre-heated granite at different temperatures was 0.0483-0.0801.As temperature increased from 20°C to 100°C,σcincreased by 2.88 MPa(1.86%).From 100°C to 300°C,σcincreased by 14 MPa(8.88%).This is due to the thermal expansion that reduced the distance between interfaces of rock mineral particles and enhanced the interaction and bonding between them(Kumari et al.,2017b;Yang et al.,2017;Akdag et al.,2018).Accordingly,for test at 300°C,the σcwas the highest(171.66 MPa).From 300°C to 500°C and 500°C-700°C,σcdecreased by 24.17 MPa(14.08%)and 35.29 MPa(23.93%),respectively.Compared with specimens at 20°C,σcat 700°C was reduced by 42.58 MPa.In this process,the granite’s internal structure and mineral composition were destructed due to the high temperature.As the expansion of micro-cracks destroyed the strong connections between the mineral particles(Gautam et al.,2018;Isaka et al.,2018),the σcof the specimen decreased significantly.

4.Rockburst proneness of pre-heated granite specimens

4.1.Rockburst characteristics of pre-heated granites at different temperatures

Rockburst is an extremely violent failure phenomenon,often accompanied by vast quantities of rock fragments ejecting in a short time(He et al.,2018;Wang et al.,2019a;Zhu et al.,2019;Li,2021).For this reason,using the high-speed camera system to record the laboratory“rockburst phenomenon”of pre-heated granite specimens.The camera began to record at macroscopic microparticle ejection,rock fragment exfoliation,or crack occurrence on the surface of specimen.It stopped recording at the final failure as shown in Fig.8.During the rock rapid failure,the interval between adjacent photographs was 0.04 s,and the last photograph in Fig.8 shows the rock sample after test.

According to Fig.8,the failure of the pre-heated granite specimens at different temperatures were similar.First,the rock particle ejection or fragment exfoliation occurred,and then as axial load gradual raised,the crack expanded and rock fragment detached from the specimen.Finally,abundant rock fragments and powders were produced with a loud cracking sound.For all pre-heated granite specimens whose temperature was below 500°C,a strong rock fragment ejection phenomenon occurred during failure.At 700°C,the specimens had a lower rockburst proneness,and the ejection speed of rock pieces was low with very short ejection distance.Notably,above 500°C,the duration of rock macroscopic failure has increased significantly,i.e.the failure times of specimens at 500°C and 700°C were 11.256 s and 12.040 s,respectively.This phenomenon was consistent with the conclusion that high temperature promoted the initiation of micro-cracks within rock,thereby delaying the occurrence of rockburst(Akdag et al.,2018).Because of the high temperature,the micro-defects of granite increased obviously,which reduced its ability to resist deformation and destruction,as well as prolonged the stable failure stage of rock specimen(Shao et al.,2015;Chen et al.,2017b).

In addition,the analysis of energy released during rockburst quantitatively remains to be the most critical issue,whereas it was almost impossible to accurately measure the kinetic energy of each rock fragment.In deep rock engineering,comprehensive judgment was frequently made based on the ejection distance,distribution range,and acoustic properties of the rock fragments ejected during rockburst.Therefore,the mass of ejected rock fragments was analysed in this study.The ejection mass ratio outside the indenter,ME(mass ratio of rock fragment outside the indenter to total exfoliated rock fragment,defined by Gong et al.,2018b)was used as a semiquantitative indicator to evaluate the degree of rockburst proneness.While reflecting the distance and mass of the ejected rock fragments,ME(in certain degree)also reflects their kinetic energy.The classification criterion ofME(Gong et al.,2018b,2020)was

The statistical results ofMEfor the pre-heated specimens are presented in Fig.9.As the temperature increased,the averageMEincreased slightly and then decreased.When the temperature was below 500°C,the averageMEwas above 0.69 for the specimens,and for 700°C,the averageMEwas 0.41.The results suggest that in the actual failure,the specimens at temperatures ranging from 20°C to 500°C all had high rockburst proneness,whereas the specimens at 700°C had medium rockburst proneness.

4.2.Quantitative evaluation of rockburst proneness of the preheated granite specimens at different temperatures

It is well-known that the occurrence of rockburst is an outward expression of residual elastic energy release inside the rocks(Kaiser and Cai,2012;Huang and Li,2014;Wang et al.,2019b,2020;Liu et al.,2020;He et al.,2021b).A larger residual elastic energy corresponds to a higher ejection speed of the rock fragments and higher proneness of rockburst.Therefore,it is extremely important to calculate the residual energy accurately during the compression of pre-heated granite specimens with respect to energy storage and dissipation.

It is assumed that the pre-heated granite specimens follow the first law of thermodynamics in the compression;in other words,the specimen does not interchange energy with the outside,and the rock energy only comes from the specimen compression by testing machine(Xie et al.,2008,2009).In order to eliminate the influence of specimen volume,the energy density(i.e.the integral of stress-strain curve)was used as the characterisation of strain energy results.Thus,the strain energy variations of the pre-heated granite specimens can be characterised as(Xie et al.,2008):

whereutis the total input strain energy density;ueis the releasable strain energy stored in rock,i.e.elastic strain energy density;andudis the energy used for the pore compaction,crack propagation,and plastic deformation within rock(Xie et al.,2008),i.e.the dissipated strain energy density.

In the SCLUC tests,ueandudof the pre-heated granite specimens at five stress levels were computed accurately.Theut,ueandudof pre-heated granites could be calculated quantitatively based on the actual path of the stress-strain curve,as depicted in Fig.10.The calculation formulae ofut,ueandudare as follows:

Fig.8.Failure process of typical pre-heated granite specimens(Take the 300 °C and 500 °C specimens as examples,please refer to the Appendix for complete).300 °C:(a)0 s,(b)0.968 s,(c)4.360 s,(d)4.400 s,(e)4.448 s,(f)4.480 s,(g)4.520 s,(h)4.560 s,and(i)final failure;500 °C:(j)0 s,(k)4.424 s,(l)10.528 s,(m)11.120 s,(n)11.160 s,(o)11.176 s,(p)11.216 s,(q)11.256 s,and(r)final failure.

Fig.9.ME of the pre-heated granite specimens at different temperatures(the classification criterion follows Gong et al.,2018b,2020).

Fig.10.Relationship between ue and ud at the unloading point.

Fig.11.Linear relationships between the three energy densities of pre-heated granite specimens:(a)ue versus ut and(b)ud versus ut.

wheref(ε)andfu(ε)represent the loading and unloading curves,respectively;εuis the strain at unloading point;and ε0represents the plastic deformation of specimen after unloading.

According to Eq.(3),we could obtain theut,ue,andudof preheated granite specimen with different unloading stress levels’values.By analysing the results of these strain energies,the highly linear relations betweenueandut,udandutwere found during the compression of pre-heated granites,as illustrated in Fig.11.These results show that the linear energy storage and dissipation laws are also applicable to pre-heated granite under UC,which is consistent with the existing research results(Gong et al.,2018a,b,2019a,b,2021;Luo and Gong,2020;Su et al.,2021).Theoretically,the external loading is a prerequisite for rock energy accumulation;in other words,whenutis zero,ueandudof the rock are both zero.This is why the point(0,0)was added as the correction point.The coefficient of determination(R2)of linear fitting forueandut,udandutwere larger than 0.9977 and 0.9828,respectively.The linear fitting results are shown in Table 2.Therefore,the energy variations of the pre-heated granite can be expressed by

Table 2Linear fitting functions between ue and ut,ud and ut of pre-heated granite specimens.

whereAandBare the fitting parameters.Therefore,we argue that the pre-peak strain energy variations of the pre-heated granite specimens at different temperatures all obey the linear energy storage and dissipation laws.

Fig.12.of pre-heated granite specimens.

Fig.13.Schematic diagram of calculation for AEF(Gong et al.,2018b).

Fig.14 presents the variation ofAEFof pre-heated granite specimens with the temperature.The results indicate that as the temperature increases,the rockburst proneness of pre-heated granite specimens initially increases and then decreases.The pre-heated granites with a temperature lower than 500°C all had high rockburst proneness,while the pre-heated granites with a temperature of 700°C had medium rockburst proneness.Specifically,the highest and lowestAEFof pre-heated granites occurred at 300°C and 700°C,respectively(317.9 kJ/m3and 158.9 kJ/m3,respectively).The values ofAEFfor tests at 20°C,100°C and 500°C were 260.6 kJ/m3,264.1 kJ/m3and 235.5 kJ/m3,respectively.

4.3.Comprehensive analysis of rockburst proneness of pre-heated granites at different temperatures

MEandAEFreflect the failure degree and the remaining energy of the pre-heated granites when rockburst occurs,respectively.Fig.15 shows that there is a strong correlation betweenMEandAEFof the pre-heated granite specimens at different temperatures.AsAEFincreased,MEgradually increased.This indicates that the results ofAEFare consistent with the actual rockburst intensity,which meansAEFcould accurately reflect the rockburst proneness of the preheated granites at different temperatures(see Fig.14).Specifically,when the temperature increased from 20°C to 300°C,the rockburst proneness of the pre-heated granites increased gradually.When the temperature increased from 300°C to 700°C,the rockburst proneness decreased gradually.Thus,300°C could be considered as the threshold temperature for rockburst proneness for the pre-heated granites.This can be explained as that below 300°C,the rock thermal dilation reduced the distance between the internal particle interfaces,increasing the interaction force

Fig.14.AEF of pre-heated granite specimens at different temperatures(the classification criterion follows Gong et al.,2018b,2020).Fig.14.AEF of pre-heated granite specimens at different temperatures(the classification criterion follows Gong et al.,2018b,2020).

°

Fig.14.AEF of pre-heated granite specimens at different temperatures(the classification criterion follows Gong et al.,2018b,2020).Fig.14.AEF of pre-heated granite specimens at different temperatures(the classification criterion follows Gong et al.,2018b,2020).

Fig.15.Relationship between the ME and AEF.

In addition,Su et al.(2017)also concluded that the rockburst proneness of the pre-heated granite specimens gradually enhanced when the temperature increased from 20°C to 300°C,whereas it reduced above 300°C.Specimens tested at 300°C had the highest rockburst proneness as manifested by the largest volume of rockburst pit,the highest kinetic energy ejected by rock fragments,and the highest decibel value of rockburst sound.Thereafter,Jiang et al.(2020)studied the rockburst proneness of granite specimens with different initial thermal damage degrees by using the coupled static-dynamic tests,and observed that the most violent rockburst occurred when the thermal damage was 0.3(pre-treated temperature approximately 300°C).These results could match well with the findings of the present study,indicating that theAEFcriterion improved via the linear energy storage law could be used to evaluate the rockburst proneness of the pre-heated granites at different temperatures.This provides a feasible approach to determine the rockburst proneness of rocks with respect to energy storage,dissipation and surplus.Meanwhile,this method provides an important guidance for rockburst proneness assessment as well as rockburst disasters warning in high-temperature rock engineering,e.g.deep mining,excavation of high geothermal tunnels,and high temperature assisted rock breaking.

5.Discussions

5.1.Effect of temperature on ESC

High temperature will give rise to variations of internal components and structure of rock materials,e.g.moisture contents,mineral constituents,micro-flaws,and micro-pores,thereby significantly changing the mechanical characteristics of rocks(Shao et al.,2014;Kumari et al.,2017a;Jin et al.,2019).In essence,rock compression destruction is an energy-driven process(Xie et al.,2008),while the energy storage is a prerequisite for the internal absolute energy.Therefore,analysing the ESC of the pre-heated granites at different temperatures is necessary for determining the proneness of rockburst.According to Section 4.2,ueandut,udandutof the pre-heated granite are strongly linearly correlated during compression.Eqs.(4)and(5)can thus be used to describe the linear relationships,which are consistent with previous energy laws of rock compression at 20°C(Gong et al.,2018b,2019b).The constantBis adopted in the linear fitting model for each temperature(see Table 2),while the maximum value is only 0.0075(at 500°C).To reflect the general linear relationship of rock energy density,the constantBcan be ignored.To this end,Aand 1-Aare regarded as the compression energy storage and dissipation coefficients,which represent the ESC and energy dissipation capacity(EDC)of the pre-heated granite specimens,respectively.By comparing the linear fitting functions of different temperatures(see Table 2),it is found that high temperature could significantly change the ESC and EDC of pre-heated granite specimens,i.e.Aand 1-Aare changed.

To characterise the temperature effect more accurately on ESC and EDC of the pre-heated granite specimens,nonlinear regression was performed on the parametersAand 1-Aatdifferent temperatures(R2of 0.9915),as shown in Fig.16.In detail,with the increasing temperature,the ESC of the pre-heated specimens initially increased and subsequently decreased.However,its EDC exhibited an opposite trend.From 20°C to 100°C,the ESC of the specimen increased by 2.21%(Aincreased by 0.0183).Within the whole temperature scope,the ESC reached the peak value(A=0.8468)at 100°C.This revealed that during loading,the specimen absorbed a great quantity of energy and stored in the form of internal elastic strain energy.Because the moisture content in the specimen at 100°C was reduced,the brittleness was enhanced,while plastic deformation was reduced under theexternalloading.Therefore,theenergydissipationwaslow.Above 100°C,the ESC of granite decreased as temperature increased,particularly in the range of 500°C-700°C(reduction by 29.44%).The ESC of granite specimens was minimised at 700°C(A=0.5246),indicating that the high temperature could significantly degrade the ESC of granite specimens.This is owing to the fact that the high temperature had induced more internal micro-cracks and thus enlargedthe inter-particle pores.The mineralgrain structure wasalso changed.Under the external loading,a large amount of the energy was dissipated by fracture closure,pore compaction,dislocations between mineral particles,slippage,and plastic deformation.The mechanism can also explain why the duration of macroscopic rock failure increased with the EDC of the pre-heated granite specimens(see Fig.8).

Fig.16.The A and 1-A of pre-heated granite specimens.

5.2.Relationships between the mechanical,energy parameters,and rockburst proneness

The σcis a key mechanical parameter measured via the rock material compression test,which symbolises the maximum antifailure capability of rock.The parameterAproposed in the present work reflects ESC of rocks and is bounded up with their energy storage.Hence,the σcandAare two crucial mechanical and energy parameters of the rock specimens of this study.On this basis,we examined the relationships between these two important parameters and the rockburst proneness.Two indicesAEFandMEwere used to characterise the rockburst proneness of the pre-heated granite specimens.The specific relationships are shown in Fig.17.

Fig.17.Relationships between σc,A and rockburst proneness of pre-heated granite specimens:(a)Residual elastic energy density AEF and(b)Ejection mass ratio outside the indenter ME.

As shown in Fig.17a and b,AEFandMEof the pre-heated granite specimens were directly proportional to σcandA,respectively.We argue that during the compression failure of granite specimens,higher σcand largerAcorrespond to higher values ofAEFandME,as well as a higher rockburst proneness.Specifically,the compressive deformation of the brittle hard rock was negligibly small,and σcoften controlled the value ofupt.On the other hand,asAbecame larger,the ESC of rock became stronger.The stored energy inside rock also became higher,so did the released energy by instability failure.Therefore,based on the σcandAof rock materials obtained from UC and SCLUC tests,we can roughly assess the rockburst proneness of high-geothermal rock engineering.

It is worth noting that we have employedAEFto quantitatively evaluate the rockburst proneness of the pre-heated granite specimens at different temperatures(see Section 4.2).The parameterAEFwas proposed based on energy storage,dissipation and surplus during the rock compression.It strongly relied on the accurate calculation of theupeandua.In other word,the precise measurement of total stress-strain curve for rock compression is a premise for the calculation of theAEF.When the temperature was less than 500°C,the pre-heated granites tested in this study exhibited strong brittleness,and severe brittle failure occurred after the peak strength(see Fig.8),which was accompanied by rapid stress drop.The post-peak strain was extremely small(see Fig.6).Although the displacement-controlled mode on the testing machine was adopted to carry out the UC and SCLUC tests,it is sometimes arduous to accurately measure the post-peak stress of granites.Hence,the calculation of theuahas a certain estimation.Additionally,the statistical results ofMEfor the specimens had a certain discreteness,especially for specimens tested at 100°C and 500°C(see Fig.9).Meanwhile,the results ofAEFandMEfor some specimens were not perfectly correlated,and there were a few deviations from its divided areas,as shown in Fig.15.For example,the results of a few 500°C and 700°C specimens did not fall into the classification region ofME,or were only located at the edge of the classification region.This may be attributed to two factors:(i)Rock is a heterogeneous natural material,and the rock fragments ejected during the failure process are disordered;thus,there are certain limitations in quantitative statistics.(ii)It is inadequate to determineMEquantitatively by using the edge of indenter as the boundary of rock fragment ejection area.Ideally,the specimen should be placed at the centre of a circular area.From the centre gradually outward,the mass of rock fragments and powders located at different radius ranges were measured.Thus,the selected area and ratio range ofMEare worthy of further consideration and optimisation.Apart from that,the energy storage characteristic and rockburst proneness for granite tested at different cooling rates,real-time high temperature as well as microwave heating will be investigated in future works.

6.Conclusions

The present study implemented a range of UC and SCLUC tests on pre-heated granite specimens(i.e.20°C,100°C,300°C,500°C and 700°C).Through these tests,the temperature effect on rockburst proneness of granite was systematically analysed,with respect to energy storage,dissipation and surplus.The following main conclusions can be summarised:

(1)As the temperature increased,the concavity of stress-strain curves increased and the compaction stage became longer.Based on the existing results of σcin the literature,three temperature intervals have been defined to investigate the characteristics of σcin response to the temperature.The value of σcfirstly increased and subsequently decreased as the temperature increased.In a series of tests,σcreached the peak value at 300°C.

(2)Below 500°C,a strong ejection phenomenon occurred in the pre-heated granite,i.e.abundant rock fragments and powders were ejected at failure.At 700°C,the ejection speed of rock fragments was low,as well as their ejection distance was short.Specifically,below 500°C,the average value ofMEwas more than 0.69,whereas at 700°C,the average value ofMEwas 0.41.

(3)At different temperatures,strong linear relationships existed between theueandut,udandutduring the compression of pre-heated granite,i.e.the temperature did not alter the linear energy storage and dissipation laws of granite.As the temperature increased,ESC of pre-heated granite initially increased and then decreased,while the variation of EDC exhibited the opposite trend.Furthermore,the macroscopic failure time increased with EDC of pre-heated granite.

(4)Based on accurately calculation ofupeanduafor the preheated granite specimens at different temperatures,AEFwas employed to evaluate the rockburst proneness.Its values at different temperatures were found as 317.9 kJ/m3(300°C),264.1 kJ/m3(100°C),260.6 kJ/m3(20°C),235.5 kJ/m3(500°C),and 158.9 kJ/m3(700°C),which match well the statistical results of theME.

(5)The rockburst proneness first increased and subsequently decreased with temperature increasing;the peak value was found at 300°C.Notably,compared with the granites at 20°C,the following characteristics were obtained:(i)when the temperature was below 300°C,the rockburst proneness enhanced with the rising temperature;(ii)when the temperature was above 500°C,the rockburst proneness gradually decreased.Therefore,in deep mining,excavation of high geothermal tunnels,and high temperature assisted rock breaking,the burst proneness of surrounding rock could be enhanced after the high-temperature rock masses being excavated and cooled,which may trigger even more serious rockburst disasters.

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 work was supported by the National Natural Science Foundation of China(Grant No.41877272),the Fundamental Research Funds for the Central Universities(Grant No.2242022k30054),and the Fundamental Research Funds for the Central Universities of Central South University(Grant No.2021zzts0861).

List of symbols

ACompression energy storage coefficient

1-ACompression energy dissipation coefficient

AEFResidual elastic energy density

BConstant term of linear fitting

EmElastic modulus

IActual unloading stress level

KSetting unloading stress level

kσcSetting unloading points

MEEjection mass ratio outside the indenter

σcPeak compressive strength

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2021.08.004.