Thermal effects on fracture toughness of cracked straight-through Brazilian disk green sandstone and granite

Lei Zhou,Weiting Go,Liyun Yu,Zheming Zhu,*,Jinxing Chen,Xingki Wng

a Key Laboratory of Deep Earth Science and Engineering,Ministry of Education,Sichuan University,Chengdu,610065,China

b State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology,Xuzhou,221116,China

c Failure Mechanics and Engineering Disaster Prevention and Mitigation,Key Laboratory of Sichuan Province,Sichuan University,Chengdu,610065,China

d Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province,Shaoxing University,Shaoxing,312000,China

Keywords:High temperature Cracked straight-through Brazilian disc(CSTBD)sample Fracture toughnessm Scanning electron microscope(SEM)

A B S T R A C T Cracked straight-through Brazilian disc(CSTBD)samples prepared using two rock materials were used for thermal treatment from room temperature to 700 °C.Uniaxial splitting experiments were performed using an automatic electro-hydraulic servo press to study the evolution laws of physical and fracture properties of different deep rock materials under high-temperature geological conditions.The fracture characteristics were measured using an industrial camera and digital image correlation technology to analyze the effect of high temperature on fracture properties and failure modes of the CSTBD samples after different thermal treatments.The micro-damage properties of green sandstone and granite materials were obtained using a scanning electron microscope(SEM).The following conclusions were drawn from the test results:(1)With the increasing temperature,the fracture characteristics of green sandstone and granite change from brittle fracture to plasticity fracture,the longitudinal wave velocity of granite decreases sharply at 600 °C,and the damage factor reaches 0.8748 at 700 °C.(2)The fracture toughness of green sandstone and granite decreases with increasing temperature;however,the decreasing range of granite is larger than that of green sandstone.(3)As the temperature increases,the fracture morphologies of green sandstone and granite materials become rougher,whereas thermal damage cracks of granite and intergranular fractures inside sandstone as well as pores of sandstone increase.(4)The crack tip opening displacement and peak strain corresponding to peak load increase with the temperature.

1.Introduction

Many deep engineering processes,such as rock drilling,ore crushing,deep petroleum boring,geothermal energy exploitation,and deep disposal of nuclear waste,suffer from high-temperature environments(Heuze,1983;Rathnaweera et al.,2018;Ji et al.,2021;Yin et al.,2021).For example,the Guangdong-Hong Kong-Macao Greater Bay Area is a crucial geothermal energy carrier for China.It is important to rapidly develop geothermal energy extraction in this area to balance the energy demand for regional economic development and environmental conservation.Granite and sandstone are the main rock media in this area(Xie et al.,2019).It is known that cracks,joints,and faults are the key factors for rock stability evaluation and geothermal energy extraction.These defects significantly impact the occurrence and expansion of cracks in rock materials.Therefore,high-temperature rock mechanics and fracture properties have become an active area of research.This study investigated the fracture characteristics of a cracked rock mass after heat treatment under the coupled effects of temperature and cracks.

Several studies have been conducted on the effects of thermal treatments on the physical and mechanical parameters of rock masses(Liu et al.,2016;Wang et al.,2018a;Ge et al.,2021).Zuo et al.(2017)found that the distribution of high-temperature micro-cracks and mineral grains may affect early crack initiation using three-point bending tests,and they explored the effect of high temperature on the failure mechanisms of granite.Liu et al.(2019)investigated the cooling-related mechanical properties of granite heated from 200°C to 800°C using two different cooling methods.They found that when the temperature increased from 400°C to 800°C,the compressive strength of granite samples decreased dramatically.Li et al.(2020a)investigated the effect of high temperature on the stability and compactness of gypsum using semicircular bend samples.They demonstrated that the fracture toughness of gypsum changed with elevated temperature in four stages.Wu et al.(2019)used Brazilian disc specifications to test the tense mechanical characteristics of granite material after exposure to heating and cooling treatments.They found that the watercooled samples had the largest decrease in P-wave velocity,but they did not consider the effect of cracks on cracking behavior.In general,rock thermal treatment research can be divided into two categories:real-time high-temperature treated rock(Ma et al.,2020;Tao et al.,2021)and high-temperature treated rock under different cooling rates(Huang et al.,2020;Chen et al.,2021).The former is mainly applied to study rock drilling and hightemperature rock fragmentation,and the latter is applied primarily to study post-disaster rock fires and geothermal water injection.These findings demonstrate the importance of studying the fracture characteristics of rock materials subjected to thermal treatments.

The study of the microphysical and mechanical parameters of rock materials subjected to high-temperature treatment was performed using rock micromechanics.Investigation of microphysical properties is critical for addressing the process of high temperature(Li et al.,2020b).In recent years,three main methods have been adopted to study the micromechanical properties of rock materials:X-ray diffraction(XRD)(Shao et al.,2014;Zhao et al.,2017),scanning electron microscopy(SEM)(Zhang and Zhao,2013a,2014),and computer tomography(CT)scanning(Yao and Xia,2019;Yang et al.,2020).Feng et al.(2017)analyzed the variation in the mineral composition of heating-cracked sandstone samples using XRD,and the fracture toughness of the heated samples was also calculated.Vázquez et al.(2015)applied optical microscopy to explore the signs of heating decay,and quartz,feldspar,and biotite contents were used as variables in the simulation model to reveal the effect of mineral composition on the heated granite.Guo et al.(2020)analyzed the distribution of intergranular(IG)cracks in marble samples after high-temperature treatment at 400°C-600°C using SEM,and the causes were also discussed.Chen et al.(2020)used the CT scanning approach to improve the recognition of mineral grains and topological grain skeleton structure,emphasizing mechanical rock crystal measurements.These studies have promoted understanding of the attenuation properties of high-temperature rocks,but there are few systematic microscopic analyses of two or more types of high-temperature rocks.Therefore,microscopic analysis of the influence of high temperatures on the mineral composition and fracture morphologies of rock materials is an important research approach.

Digital image correlation(DIC)technology has been used to measure the strain field around crack tips in several research fields.This method has been widely used to determine the crack tip open displacement(CTOD)and strain evolution process of an entire sample under different conditions(Wasantha et al.,2012;Li et al.,2017;Dong et al.,2020).Gao et al.(2015)used the DIC method and an ultra-high-speed camera testing system to determine the failure parameters of notched semi-circular bend samples subjected to impact loads.Li et al.(2020c)applied the DIC method to collect real-time cracking processes of granite samples with precracks in the vicinity of a circular opening loaded using a split Hopkinson pressure bar.Similarly,DIC and industrial camera testing methods were used to measure the cracking processes of the samples,and the strain field was calculated in real-time.

This study aims to understand how the physical parameters and fracture properties of cracked rock mass change after exposure to high temperatures.A traditional cracked straight-through Brazilian disc(CSTBD)sample was selected as the research object to conduct static experiments.The DIC method was applied to measure the CTOD and strain field around each crack tip.The physical characteristics and mechanical properties of the two types of rock materials and the micro-fracture morphologies of high-temperature rock were determined after high-temperature treatment.

2.Experimental method

2.1.Manufacture of CSTBD sample

Fig.1.Sketch map of CSTBD samples:(a)Schematic diagram and(b)Photographic view.

The effects of several high-temperature treatments on different rock materials were investigated using CSTBD samples,as shown in Fig.1.The sample radius wasR=50 mm,the crack length was 2a=50 mm,the sample thickness wasB=30 mm,and the crack length to radius ratio was α=a/R=0.5.To investigate the impact of high-temperature treatment on hard and soft rocks,green sandstone and granite were selected as raw materials to prepare samples.The samples were obtained mainly from Xinyang,Henan Province,China.The physical parameters of the two rock materials are presented in Table 1.Green sandstone primarily consists of 70%quartz,12%feldspar,5%cuttings,8%mud,1%muscovite,1%biotite,and 3% others,as shown in Fig.2.According to polarizing microscope observation results,granite primarily consists of 45%alkaline feldspar,33% plagioclase,18% quartz,1% biotite,and 3% others.

Table 1Physical and mechanical parameters of rock materials.

The CSTBD sample was made using high-pressure water cutting.The pre-crack was made with a diamond-impregnated fine saw with a length of 50 mm,and the width of the pre-crack was no more than 1 mm.A medium roughness grinding wheel was applied for mechanical polishing and grinding of the sample surfaces to ensure that the unevenness and non-perpendicularity of the samples were less than 0.05 mm.

A standard Brazilian disc test was conducted to characterize the difference in tensile strength between granite and green sandstone.It can be observed that the tensile strength of granite is greater than that of green sandstone,and the peak strain of granite corresponding to the peak load is also greater than that of green sandstone,as shown in Fig.3.

Fig.2.Polarizing microscope observation results of(a)Green sandstone and(b)Granite.

Fig.3.Tensile strength of granite and sandstone determined using Brazilian disc.

Fig.4.High-temperature treatment plan:(a)High-temperature furnace and(b)Temperature-time plots.

Fig.5.Loading test device and data collection system.

2.2.Heat treatment scheme

CSTBD samples were used to measure fracture toughness after thermal treatment in this study,and each group consisted of three granite and three sandstone samples.A total of 48 CSTBD samples were prepared.The samples were heated in an air environment from 23°C(room temperature)to target temperature,setting seven heating groups:100°C,200°C,300°C,400°C,500°C,600°C,and 700°C,with a constant heating speed of 10°C/min in a high temperature muffle furnace,as shown in Fig.4a.This furnace can reach a maximum temperature of 1200°C at a rate of 0-1°C/s.As shown in Fig.4b,once the goal temperatures are reached,the samples are held in the furnace for 3 h at the target temperature before being naturally cooled to room temperature at a speed of 0.5°C/min because such cooling rate can avoid the thermal shock effect from causing additional thermal damage.

2.3.Splitting test of CSTBD sample with DIC analysis

The loading system was an electro-hydraulic servo press,as shown in Fig.5.The fracturing process of granite following hightemperature treatment was studied in detail using an industrial camera shooting system to determine the initiation and propagation of cracks in real-time.Before loading,a small amount of Vaseline was smeared onto the loading plate as a lubricant to reduce the effect of the friction coefficient on the experimental results.Two thin steel wires were placed at both ends of the CSTBD samples to ensure that the sample loading was close to line loads.According to the pre-tests of the tensile strength of the standard Brazilian disc(Backers and Stephansson,2012;Kuruppu et al.,2014),the loading rate was set at 0.1 mm/min.The computer automatically recorded the load-displacement curve during the test loading process,and the industrial camera automatically recorded the entire static fracturing process.When the crack initiates,the fracture toughness of the CSTBD samples can be determined according to the load-strain curve.

The widely used and recognized DIC method was used to analyze the strain field and displacement field of CSTBD samples during the fracturing process.The DIC method is deemed ideal by dealing with a reference photo collected before deformation and a series of deformed images collected after deformation.The fundamental principle is to capture the same pixel points in a series of deformed photos.Instead of catching a single pixel in deformed photos,a sub-photo centered at the considered point is captured in deformed photos using a selected correlation function,such as zero mean normalized cross-correlation.By minimizing or maximizing the correlation coefficient,the location of a sub-photo in the deformed photo can be found,and displacement values of this subset center can be measured,as illustrated in Fig.6.After deformation,the matching nodeM(x′,y′)relating to the original nodeO(x,y)in the reference photo is written as(Li et al.,2019;Dong et al.,2020):

Fig.6.Schematic diagram of DIC technology.

Fig.7.Photograph of the sample during ultrasonic testing.

whereuandvindicate the displacement values of the subset center nodeOin thexandydirections,respectively;ΔxandΔyindicate the distances from nodeMto nodeO;and?u/?x,?u/?y,?v/?x,and?v/?yare the gradients of the displacement values for the subset.The horizontal and vertical displacements,uandv,can be measured by improving the correlation function.Furthermore,the strain and displacement fields around the fracture surface and crack tip can be determined by repeating the same catching process on the other nodes of interest.

2.4.Ultrasonic measurements

The contact transmission technique was used to perform ultrasonic measurements on green sandstone and granite samples before and after heating.As illustrated in Fig.7,the wave signals from the wave generator can be conveyed to the sample at the top end and picked up by a second sensor close to the bottom side of the sample.The signals were digitized and recorded using an analyzer to acquire the longitudinal wave velocity.To achieve tight contact between the sample and transducers,constant pressure was applied methodically.Butter can be used as a coupling agent between the samples and transducers,allowing ultrasonic energy to be transferred to the samples.

The damage factorDcan be written as(Wang et al.,2018b):

where ρ0and ρ1are the sample densities before and after heat treatment,respectively;andc0andc1indicate the longitudinal wave velocities of the sample before and after thermal treatment,respectively.

3.Experimental results and analyses

3.1.Load-displacement curves

The load-displacement curves of the CSTBD samples after various heating temperatures are shown in Fig.8.The ductile failure characteristics of green sandstone and granite increase with increasing temperature.At the low-temperature stage(23°C-400°C),green sandstone and granite materials exhibit brittle fracture characteristics,and at the high-temperature stage(500°C-700°C),they exhibit ductile failure characteristics.

Fig.8.Load-displacement curves of(a)Green sandstone and(b)Granite under different temperatures.

3.2.Apparent color change of rock

It can be observed that the appearances of the two types of rock materials have undergone tremendous changes after thermal treatment,as shown in Figs.9 and 10.With increasing thermal temperature,the color of the green sandstone gradually changed from green to red,while the color of the granite gradually changed from sesame white to sesame red.The surface pore density of green sandstone increased as the temperature increased(black spots represent the surface pore structure).For granite,the number of heat damage cracks at the surface increased(red lines indicate thermal damage).It was found that the density of thermal damage cracks gradually increased,reaching a maximum value at 700°C.The granite sample was grey and fine-grained before it was heated.The color of the granite sample gradually changed to reddishbrown when the heating temperature exceeded 300°C,and small cracks can be observed on the surfaces.When the temperature was 700°C,the color turned to brownish-yellow.

Fig.9.Changes of green sandstone after different temperature treatments:(a)23 °C;(b)100 °C;(c)200 °C;(d)300 °C(e)400 °C;(f)500 °C;(g)600 °C and(h)700 °C.

Fig.10.Changes in granite after different temperature treatments:(a)23 °C;(b)100 °C;(c)200 °C;(d)300 °C(e)400 °C;(f)500 °C;(g)600 °C and(h)700 °C.

3.3.Longitudinal wave velocity and damage factor

Fig.11 illustrates the evolution laws of the longitudinal wave velocity and damage factor of green sandstone and granite materials after different thermal treatments.The longitudinal wave velocity decreased with temperature for the green sandstone,but the damage factor increased with temperature.At 700°C,the damage factor reached 0.7368,indicating that the physical and mechanical parameters of green sandstone have undergone significant changes after different thermal treatments,as illustrated in Fig.11a.

The longitudinal wave velocity and damage factor evolution laws for granite are comparable with those for green sandstone;however,there are some differences between them.At 500°C-600°C,the longitudinal wave velocity decreased sharply with the temperature,and the damage factor increased sharply with the temperature.At 700°C,the damage factor reached 0.8748,which was larger than that of green sandstone under the same thermal treatment.The thermal treatment threshold value of mechanical characteristics of granite material was between 500°C and 600°C,as shown in Fig.11b.

Fig.11.Variations in the longitudinal wave velocity and damage factor of(a)Green sandstone and(b)Granite with temperature.

3.4.Fracture toughness and fracture morphology characteristics

According to the fracture mechanics theory,the fracture toughness of CSTBD samples can be determined theoretically.According to the size requirements of CSTBD samples,the theoretical calculation formula of mode I fracture toughness can be expressed as follows(Dong et al.,2004;Hua et al.,2017):

whereKICis the mode I fracture toughness;Pmaxis the maximum force;Ris the sample’s radius;Bis the sample’s thickness;andfIis the mode I normalized stress intensity factor,which can be calculated according to Dong et al.(2004)and Hua et al.(2017).

Table 2 lists the test results of all green sandstone and granite samples after different thermal treatments.Fig.12 shows the variations of the peak load and the fracture toughness of green sandstone and granite using the fracture toughness calculation formula.The variations of the fracture toughness of green sandstone and granite after thermal treatment are different,and the variation of the peak load is similar to the fracture toughness.For green sandstone,the fracture toughness fluctuates at 23°C-200°C.At 600°C-700°C,the fracture toughness of green sandstone is greater than that of the granite.The final attenuation ratio of the fracture toughness of green sandstone is smaller than that of granite at 700°C.After heat treatment of 700°C,the fracture toughness of green sandstone is 0.2375 MPa m1/2,which is only 40.31%of the fracture toughness at room temperature.For granite,the fracture toughness decreases with increasing temperature.At 500°C,the fracture toughness of granite samples decreases sharply,which is only 48.03%of room temperature.The granite sample has a fracture toughness of 0.1767 MPa m1/2at 700°C,which is lower than the green sandstone sample at the same temperature stage and only 21.29% of the fracture toughness of granite at room temperature.

Table 2The experimental data of mode I fracture toughness.

After different thermal treatments,the damage behavior caused by a concentrated force was assessed by studying the fracture characteristics,including the fracture morphology and material mesoscopic properties.It is important to understand the influence of heat treatment on the mesoscopic fracturing parameters of green sandstone and granite materials(Li et al.,2020a).

The microcracks in the mineral crystal are deemed as transgranular(TG)fractures,and those microcracks along the mineral crystal are considered as IG fractures(Zhang and Zhao,2013a,2014).SEM images of the fracture morphologies of green sandstone and granite following various thermal treatments are shown in Figs.13 and 14.The failure modes and fracture characteristics influenced the fracture toughness.TG fractures appear on smooth surfaces or surfaces that are less rough owing to more energy consumption during the fracture process,but IG fractures can be deemed as a rough surface or less smooth fracture morphology inside fracture morphologies(Zhang and Zhao,2013b;Liang et al.,2015;Mahanta et al.,2016).

Green sandstone observation results plotted in Fig.13 indicate that microcracks cannot be seen at 100°C because of the reduced influence on the crystal of green sandstone at a lower temperature.As the samples were subjected to a concentrated load,the tensile stress formed in the green sandstone produced the TG and IG fractures.It is known that the strengths of cuttings and mud are lower than those of quartz and feldspar in green sandstone,and IG fractures usually occur among the weaker related crystals.TG fractures of the crystals also occurred at certain times.The sample was crushed with a heavily focused force owing to the high strength of green sandstone at low temperatures.The fracture morphology was less rough when comparing the lower temperature treatment with the higher temperature treatment.Hence,TG fractures at 23°C are dominant for green sandstone,as illustrated in Fig.13a.

As the temperature exceeds 500°C,the effect of high temperature on the green sandstone is more significant.Fig.13g and h indicates two rough and messy fracture morphologies,which means that with increasing plastic fracture characteristics,fracture modes with more IG fractures and holes inside the green sandstone.Some microcracks merged in the same orientation to produce larger cavities.This fracture mode occurs because the medium-crystal green sandstone is generally porous,and crystals are not very close to one another.More pores,microcracks,and layers exist inside the green sandstone.The increase in temperature facilitated the development of pores and cracks after thermal treatment.Hence,the crystals are severely deformed,the particles are disconnected from each other,and the structure deteriorates,producing many cracks and pores inside the rock materials.It can be seen in Fig.13g and h that many holes produce in green sandstone when the temperature is over 600°C,revealing that high temperature treatment increases the ductile failure characteristics and causes the peak displacement to increase.

The granite observation results plotted in Fig.14 indicate that the mesoscopic properties of granite are different from those ofgreen sandstone after thermal treatment.The crystal cementation of granite is much denser than that of green sandstone.As illustrated in Fig.14g and h,when the heating temperature is over 600°C,thermal damage cracks increase significantly.The thermal damage cracks merged into a main crack that penetrated the entire fracture morphology.In addition,TG fractures inside the granite are mainly cleavage morphology at a heating temperature of over 600°C.

Fig.12.Variations in(a)Peak loads and(b)Fracture toughness versus temperature.

Fig.15 shows the fracturing process of green sandstone CSTBD samples after 23°C,400°C,and 700°C,which were recorded using an industrial camera system.It can be observed that the time required for the crack to penetrate the entire sample increases with the temperature.For green sandstone at room temperature,we define the crack initiation time as the zero time,and the crack propagation time is 33.33 ms.The crack propagation time may be shorter because the test interval of the industrial camera is 33.33 ms.For green sandstone heated at 700°C,it takes 13000 ms for the crack to propagate and produces a macro-crack at the surface of the sample.As the temperature increased,the crack propagation time along the original crack increased,indicating that the plastic fracture characteristics of the green sandstone and granite increased after thermal treatment.As shown in Fig.15,the precrack was a pure mode I crack,but several inflexion points along the original direction of the pre-crack throughout the propagation process were created by the accumulation of thermal damage cracks and pores inside the green sandstone.

3.5.Strain evolution and CTOD

Fig.13.SEM photos of green sandstone under different thermal treatments:(a)23 °C;(b)100 °C;(c)200 °C;(d)300 °C;(e)400 °C;(f)500 °C;(g)600 °C;and(h)700 °C.

Fig.14.SEM photos of granite under different thermal treatments:(a)23 °C;(b)100 °C;(c)200 °C;(d)300 °C;(e)400 °C;(f)500 °C;(g)600 °C and(h)700 °C.

Figs.16 and 17 show the strain field evolution laws around the crack surfaces of the CSTBD samples,which were measured using the DIC method after different thermal treatments.With the increase of thermal treatment for green sandstone and granite,the maximum strain corresponding to the maximum load increases gradually.When the temperature was room temperature for green sandstone,the peak strain corresponding to the peak load was 0.279%(C23in Fig.16a).When the temperature was 500°C,the peak strain corresponding to the peak load was 0.505%(C500in Fig.16c).When the heating temperature was 700°C,the peak strain corresponding to the peak load was 2.998%(C700in Fig.16d).Therefore,the peak strain increases sharply when the temperature is over 500°C.

When the temperature is room temperature for granite,the peak strain corresponding to the peak load was 0.221%(C23in Fig.17a).When the temperature was 500°C,the peak strain corresponding to the peak load was 1.35%(C500in Fig.17c).When the heating temperature was 700°C,the peak strain corresponding to the peak load was 3.194%(C700in Fig.17d),which was 14.45 times that at 23°C.This indicates that the high heating temperature significantly affects the peak strain of green sandstone and granite.The peak strain of granite at the same temperature is generally greater than that of green sandstone.

Fig.15.Analysis of the static cracking process of green sandstone after thermal treatment:(a)23 °C;(b)400 °C and(c)700 °C.

Similarly,the peak strains were measured using the DIC method.Fig.18 shows the peak strains of typical samples versus temperature.The peak strain near the crack tip also increased when the temperature increased.It can be observed that the peak strain values increased sharply at 500°C-600°C.When the temperature reached 600°C,the peak strains of green sandstone and granite increased by 97.03%and 417.14%,respectively,compared to those at 500°C.This indicates that 400°C-600°C is the critical temperature region for the variation in mechanical parameters of green sandstone and granite.For green sandstone,the high-temperature treatment threshold must be in the range of 500°C-600°C;however,for granite,the high-temperature treatment threshold must be in the range of 400°C-600°C.

The CTOD of each representative sample was determined using the DIC method to better understand the crack failure parameters,as shown in Fig.19.For the granite and green sandstone samples,the time at which the CTOD increased can be deemed as the crack initiation time.According to the CTOD of green sandstone and granite,the critical value of the CTOD in rock material can be determined when the crack is initiated.For the green sandstone at room temperature,the CTOD was 0.0317 mm when the crack initiated.However,when crack initiation occurred at 700°C,the CTOD of green sandstone was 0.0751 mm,indicating that the CTOD of green sandstone at lower temperatures was smaller than that at higher temperatures.When the heating temperature approached 600°C,the CTOD exhibited a slowly upward trend,as shown in Fig.19a.When the temperature was less than 500°C,the CTOD of each group exhibited a jumping point in their curves.

The CTOD of typical granite samples after various heating treatments is plotted in Fig.19b.It can be seen that the CTOD of granite CSTBD samples at the initiation time was larger than that of the green sandstone samples.For granite samples at 23°C,the CTOD was 0.0207 mm when the crack initiated.However,for granite samples at 700°C,the CTOD was 0.3319 mm when the crack initiated.In addition,at high temperatures(600°C-700°C),the CTOD of the granite sample increases slowly,and there was no apparent jumping point,which is similar to the evolution law of green sandstone samples at high-temperature stage.

4.Conclusions

This study explores the failure characteristics of cracked green sandstone and granite samples subjected to different thermal treatments.The fracture morphologies of cracks and failure modes after thermal treatment were scanned using SEM to explore the mesoscopic damage characteristics.The DIC method was also implemented to determine the strain field and CTOD.Finally,meaningful conclusions were drawn:

(1)As the temperature reached 500°C,the longitudinal wave velocity of granite dropped sharply,and the damage factor of granite increased rapidly to 0.8748 at 700°C.However,the longitudinal wave velocity of green sandstone decreased linearly with temperature.There was no sharp change at 500°C-600°C.The damage factor of green sandstone was 0.7368 after the 700°C treatment.

Fig.16.Results of strain field around crack surface of high temperature treated green sandstone CSTBD samples:(a)23 °C;(b)300 °C;(c)500 °C and(d)700 °C.

Fig.17.Results of strain field around crack surface of high temperature treated granite CSTBD samples:(a)23 °C;(b)300 °C;(c)500 °C and(d)700 °C.

Fig.18.Evolution law of the peak strain at the crack tip with the temperature.

(2)The fracture toughness of the granite CSTBD sample decreased more than that of the green sandstone CSTBD sample after the high-temperature treatment.With increasing temperature,the peak displacement corresponding to the peak load of granite and green sandstone materials increased,and the ductile failure characteristics exhibited a similar trend.

(3)The variations in the fracture toughness and longitudinal wave velocity of rock materials,and the apparent ductile failure characteristics in the compression stage were mainly caused by the IG fractures inside the green sandstone and the thermal-damage cracks inside granite that increase with temperature.

(4)With increasing temperature(23°C-500°C),the peak strain and the CTOD at crack initiation increased.When the temperature reached 700°C,the CTOD of the rock material exhibited no apparent inflexion point characteristics and just gradually increased until the samples were destroyed.

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.

Fig.19.Evolution law of the CTOD at the crack tip with temperature:(a)Green sandstone and(b)Granite.

Acknowledgments

We acknowledge the funding support from the Sichuan Science and Technology Program(Grant No.2021YJ0511),the State Key Laboratory for Geo-Mechanics and Deep Underground Engineering,China University of Mining & Technology(Grant No.SKLGDUEK2111),the Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province(Grant No.ZJRMG-2020-01).