Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

Bing Chen, Botng Shen,b,*, Hiyng Jing

a State Key Laboratory of Mining Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao, 266590, China

b CSIRO Mineral Resources, Queensland Centre for Advanced Technologies,1 Technology Court, Pullenvale, QLD, 4069, Australia

c No.1 Institute of Geology and Mineral Resource Exploration of Shandong Province, Jinan, 250010, China

d College of New Energy and Environment, Jilin University, Changchun,130012, China

Keywords:Thermo-mechanical (TM) coupling Peak shear strength Three-dimensional (3D) morphological characterization Failure mode Quadrangular pyramid model

ABSTRACT The shear failure of intact rock under thermo-mechanical (TM) coupling conditions is common, such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance, shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional (3D) morphologies of fracture surfaces have been conducted, the understanding of shear-formed fractures under TM coupling conditions is limited.In this study, direct shear tests of intact granite under various TM coupling conditions were conducted, followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy, roughness value, and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensile-shear and shear failures.As the normal stress increases, intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensile-shear to shear failure.Finally, 3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

1.Introduction

With the recent expansion of underground engineering construction to greater depths, the coupling environment under high temperature and high stress causes intact rocks to be more prone to shear failure (Prassetyo et al., 2017).For example, in the construction processes for enhanced geothermal drilling and deep tunnel excavation,the surrounding rock mass of a chamber and that near a shaft wall are prone to shear failure and instability due to stress release.Therefore, for deep engineering construction, it is particularly important to determine rock shear strength parameters under the condition of thermo-mechanical (TM) coupling.

Several studies regarding the mechanical parameters determined by uniaxial compression tests, tensile tests, and triaxial compression tests of rocks under TM coupling conditions have been conducted(Zuo et al.,2012;Ma et al.,2020;Jiang et al.,2021a;Yang et al., 2021).However, due to the limitation of direct shear testing equipment, studies regarding the shear behavior of intact rocks under TM coupling conditions remain limited.So far, laboratory experimental studies regarding the shear behavior of intact rocks,including the analyses of boundary conditions, loading mode, and shear failure process, are mainly based on stress field merely.Considering the boundary conditions of surrounding rocks, sheartests of intact rock have been conducted under constant normal stress (Bewick et al., 2014; Liao et al., 2020; Zhang et al., 2020),constant normal stiffness (Jiang et al., 2004; Thirukumaran et al.,2016; Meng et al., 2021), and three-dimensional (3D) stress conditions(Jiang,2018;Shen et al.,2020;Feng et al.,2021a,b)to obtain the shear strength parameters and deformation characteristics of rocks.Considering the purpose of engineering construction, and engineering disturbance strength, the effects of loading rate(Huang et al., 2016; He et al., 2019; Zhai et al., 2021) and loading mode(tensile-shear,compressive-shear,and vibration shear)(Yao et al.,2017;Huang and Zhu,2018;Okada and Naya,2019;Du et al.,2020) on the mechanical parameters of rocks have been studied.Although the shear strength parameters of intact rocks after thermal treatment have been investigated(Zhao et al.,2015,2019;Yin et al., 2021; Zhang et al., 2021), this type of test differs from the shear test of intact rocks under TM coupling, which cannot accurately reflect the rock shear strength parameters under high realtime temperatures in the field with different geological conditions.Therefore, it is necessary to further conduct shear tests of intact rocks under TM coupling.

A fracture surface with certain morphological characteristics is produced after the shear failure of an intact rock.Based on on-site experience, continuous shear sliding of a fracture surface can also cause geological disasters,such as the rockburst at the Jinping No.2 hydropower station and the earthquake at the Pohong geothermal site, China (Zhou et al., 2015; Xiao and Li, 2020; Yeo et al., 2020).Therefore, studies regarding fracture surfaces are also particularly important for underground engineering construction.Up to now,there have been significant achievements related to the shear strength of fracture surfaces(Barton,1976;Barton et al.,1985;Sanei et al., 2015; Yang et al., 2016; Tan et al., 2019; Zhao et al., 2022),damage evolution of fracture surfaces in the shear process(Bahaaddini et al.,2016;Zhao et al.,2018;Jiang et al.,2020a,2021b),anisotropic characteristics (Kumar and Verma, 2016; Jiang et al.,2020b; Jia et al., 2021), the relationship between the roughness of fracture surfaces and peak shear strength(Du et al.,2011;Hencher and Richards,2015;Wu et al.,2019a),and the influence of lithology,loading modes, and other factors affecting the shear behavior of fracture surfaces (Tang and Wong, 2016; Cui et al., 2019; Ram and Basu, 2019; Zheng et al., 2020).The morphological characteristics of fracture surfaces formed under different buried depths and mining disturbances vary.Therefore, it is necessary to obtain the morphologies of fracture surfaces under corresponding working conditions for accurately studying the fracture strength and deformation.To determine the fracture surface morphologies of intact rocks,the effects of loading rate,loading mode,and confining pressure have been examined by laboratory testing(Yin et al.,2012;Yang et al., 2020; Liu et al., 2021).However, most of these studies are based on shallow underground engineering projects.For deep engineering problems (buried depths are typically greater than 1000 m), the surrounding rock is in a complex environment coupled with high temperature and high stress.Although the morphology of a shear-formed fracture surface is closely related to the high temperature and high stress, their influence and mechanisms are unclear.

The main purpose of this study is to obtain the changes of shear strength parameters of intact granite under different TM coupling conditions and to quantitatively characterize the 3D morphologies of shear-formed fracture surfaces of intact granite under various TM coupling conditions.

After the Introduction, the test equipment and scheme are illustrated in Section 2, followed by the presentation of the MTS816.01 direct shear test equipment and the high-temperature and high-pressure sealed test box used to simulate the shear behavior of intact granite under TM coupling conditions at different buried depths in Section 3.The variations in the mechanical parameters of the intact granite with the TM coupling environment are analyzed, and shear-formed fractures are obtained under different TM coupling conditions.Furthermore, the accuracy of Grasselli’s model in characterizing the shear-formed fracture surfaces under TM coupling conditions is verified.Moreover, the differences in the morphological parameters(height of the asperities,roughness,and anisotropy)of the shearformed fracture surfaces under different TM coupling conditions are quantitatively analyzed.The macroscopic failure mode and fracture formation mechanism of intact granite at significant depths under TM coupling conditions are explained from a microscopic perspective.In Section 4, the shapes and arrangements of the asperities on the shear-formed fracture surfaces of intact granite under different TM coupling conditions are examined from a 3D perspective, and a pyramid model is proposed to characterize these asperities.The test results not only provide an important reference for the evaluation of the mechanical parameters of rocks in the process of deep underground engineering construction but also are significant for the accurate selection of fracture surfaces to study the strength and deformation under different working conditions.Finally, the main conclusions are presented in Section 5.

2.Sample preparation and test methods

2.1.Sample preparation

The granite for the tests was obtained from Weihai, Shandong,China.The granite blocks were cut, polished, and processed into standard cubic samples, each having a size of 50 mm × 50 mm ×50 mm.The main components of the granite were determined using a Rigaku Ultima IV X-ray diffractometer.The maximum output power of the equipment was 3 kW,the scanning mode used was the THERA/THERA goniometer, the sample level was not moved,and the minimum step was 0.0001°.The granite was mainly composed of quartz,mica,potash feldspar,and plagioclase,and its specific proportion of components is shown in Fig.1.

2.2.Direct shear test

In this study,the direct shear tests of granite samples under TM coupling were jointly completed using MTS 816.01 direct shear testing equipment and a high-temperature sealed test box developed by the Shandong University of Science and Technology,China,as shown in Fig.2a.

The high-temperature sealed test box is mainly composed of four parts (Fig.3): a main stressed frame, a high-temperature loading module, a sensor, and an acquisition control module.Overall uniform heating was achieved by embedding 10 ceramic heating rings on the surface of the sealed box.The maximum heating temperature of the sealed box was 400°C,and the control precision was ±1°C.The thermocouple sensor feeds back the temperature value in the sealed box in real time and automatically adjusts the temperature in it using a temperature controller.The exterior of the sealed box is equipped with a heat insulation plate composed of a nano-aerogel material, which ensures that the temperature in the sealed box is maintained.High-temperature resistant linear variable differential transformers (LVDTs) were installed adjacent to the axial and lateral loading heads torespectively monitor the displacements in the axial and shear directions during the shear process.

Fig.1.Granite samples and their mineral composition.

Fig.2.Test equipment.

The normal stresses were set to 20 MPa, 30 MPa, and 40 MPa,and the temperatures were set to 25°C,100°C,200°C,and 300°C,respectively.Cross combinations of the temperature and normal stress were obtained, and a total of 12 groups of tests were conducted.Direct shear tests of intact granite samples were conducted under TM coupling conditions as follows:

(1) An axial load was applied and increased to the target value at a loading rate of 0.5 kN/s.Subsequently,the target value was maintained and remained unchanged.

(2) The temperature was increased to the target value at a heating rate of 3°C/min.To ensure uniform heating of the samples, the target value was maintained for 2 h after reaching the target temperature(Wang et al.,2018),followed by the next operation.

Fig.3.High-temperature sealed test box.

Fig.4.Contour line and total height of the upper and lower parts of the shear-formed fracture surfaces.

(3) A force-controlled loading condition was adopted in the shear tests, and the loading rate was 0.5 kN/s until shear failure of the intact granite samples occurred.

2.3.3D laser scanning test and point cloud data processing of shear-formed fracture surfaces

A 3D-ML-130 non-point contact laser scanning system was used to scan and measure the shear-formed fracture surfaces, and the results are shown in Fig.2b.The scanning rate was 220,000 times per second, the measurement accuracy was 0.02 mm, and the measuring range was 220 mm× 180 mm.To accurately obtain the 3D morphological features of the fracture surfaces, a 0.3 mm sampling interval was employed for the scanning according to previous studies (Grasselli, 2001; Xia et al., 2014).Taking the shear-formed fractures at a normal stress of 20 MPa and a temperature of 25°C as examples (Fig.4), we compared and analyzed the coincidence between the upper and lower parts of the fracture surfaces.Both the upper and lower parts of the shear-formed fracture surfaces have a high degree of coincidence, as shown in Fig.4.Therefore, only the upper part of the fracture surface was scanned.

Point cloud data obtained by 3D laser scanning were imported into the Geomagic Studio software, packaged into surfaces, and preprocessed for noise reduction and hole filling.Subsequently,the packaged surfaces were discretized into points and imported intothe MATLAB software.Finally,the point cloud data were discretized and constructed using the Delaunay triangulation algorithm.Fig.2c presents the processing results.

Fig.5.Shear stress-shear displacement curves of intact granite samples under normal stresses of(a)20 MPa,(b)3 MPa,and(c)40 MPa.The interval from the first dashed line in the same color to the zero point of the abscissa indicates the linear growth stage,and the interval between the first and second dotted lines in the same color indicates the nonlinear growth stage.

Fig.6.Peak shear strength of intact granites.

2.4.Preparation and observation of thin section

The procedure for the preparation and observation of the thin section is illustrated as follows:

(1) Sample cutting.A rock fracture surface is cut and processed into a rectangular block with a size of 5 mm × 3 mm.

(2) Grinding of bottom surface.The flat side is considered as the bottom surface.Three processes including rough grinding,fine grinding, and high-precision fine grinding are conducted.The thickness of the rock sample is reduced to 1 mm via grinding, and the surrounding faces of the rock sample are polished.

(3) Bonding.An acrylic resin is used to adhere the rock block to a glass slide.The standing time before the next operation is required to exceed 12 h.

(4) Slicing and grinding.After the resin is hardened,the sample is placed on a thin slice cutting machine and cut to a thickness of 100 μm.The thickness of the sample is determined using a micrometer.The rock sample is fixed on a vacuum suction cup using the vacuum principle and is subsequently directly ground to a thickness of 0.03 mm on a thin grinding disk.

(5) Observing and obtaining photos.The prepared rock slice is placed on the stage of an Olympus BX53 polarizing microscope.The slice is pressed with a pressing leaf spring, the microscope light source is turned on,and the focusing knob is used to adjust the focus.Thereafter, the rock slice is observed, and images are collected and processed.

3.Results and analysis

3.1.Mechanical behavior of intact granite under TM coupling conditions

3.1.1.Shear stress-shear displacement curves

As shown in Fig.5,the shear stress-shear displacement curves of intact granite under different TM coupling conditions have similar variation trends.The curves before the peak shear strength can be divided into linear and nonlinear growth stages.

3.1.2.Peak shear strength, internal friction angle, and cohesion

Fig.6 presents the variations in the peak shear strength of intact granites under different TM coupling conditions.The peak shear strength of intact granite positively correlates with the normal stress, whereas it negatively correlates with the temperature.

With the normal stress increasing from 20 MPa to 40 MPa, the peak shear strength of granite increases from 49.94 MPa to 72.19 MPa at 25°C,indicating an increase of 44.6%.Similarly,when the temperatures are 100°C, 200°C, and 300°C, the peak shear strengths increase from 47.28 MPa to 69.39 MPa,from 42.31 MPa to 56.22 MPa, and from 37.73 MPa to 50.72 MPa, with increases of 46.8%, 32.9%, and 34.4%, respectively.

When the normal stress is 20 MPa, the peak shear strength of intact granite decreases from 49.94 MPa to 37.73 MPa (decreasing by 24.4%)as the temperature increases from 25°C to 300°C.When the normal stress is 30 MPa,the peak shear strength decreases from 59.81 MPa to 42.24 MPa (decreasing by 29.4%).When the normal stress is 40 MPa,the peak shear strength decreases from 72.19 MPa to 50.72 MPa(decreasing by 29.7%).

The cohesion and internal friction angle are important mechanical parameters for evaluating the shear-bearing capacity of intact rock (Yao et al., 2021).So far, the fitting method has been commonly used to obtain the cohesion and internal friction angle ofintact rock.Among the several shear strength criteria of rocks, the Mohr-Coulomb criterion has been extensively employed owing to its universality(Hackston and Rutter,2016;Jiang,2018;Shen et al.,2018; Yin et al., 2021; Zhao et al., 2021), which is expressed as follows:

Fig.7.Variations in the internal friction angle and cohesion of intact granite.

Fig.8.3D morphological cloud images of shear-formed fracture surfaces at different temperatures and normal stresses:(a)25 °C and 20 MPa;(b)25 °C and 30 MPa;(c)25 °C and 40 MPa; (d) 100 °C and 40 MPa; (e) 200 °C and 40 MPa; and (f) 300 °C and 40 MPa.

where τ and σnare the shear and normal stresses acting on the rock sample,respectively;and φ and c are the internal friction angle and cohesion of the rock sample, respectively.

The fitting results demonstrate that temperature has an important influence on the internal friction angle and cohesion of intact granite.As the temperature increases from 25°C to 300°C, the internal friction angle of intact granite decreases from 47.98°to 33.02°(decreasing by 31.2%), and the cohesion decreases from 27.27 MPa to 24.08 MPa (decreasing by 11.7%), as shown in Fig.7.

3.2.Morphological characteristics of shear-formed fracture surfaces

3.2.1.3D morphologies of shear-formed fracture surfaces

Fig.8 presents the variations in the 3D morphologies of shearformed fracture surfaces of intact granites under different TM coupling conditions.Shear-formed fracture surfaces have been found to have a remarkable peak-valley zoning distribution.

The height of asperities is an important index for reflecting the fluctuations of a fracture surface.To quantitatively characterize the morphological characteristics of the shear-formed fracture surfaces, their peak and valley values under different TM coupling conditions are obtained using the following equations:

where Dpand Dvrepresent the peak and valley points of the shearformed fracture surfaces,respectively;and Dnrepresents any point of the shear-formed fracture surfaces.

Thus,the height of asperities in the fracture surfaces,ΔD,can be calculated as follows:

Based on Eqs.(2)-(4), the height of asperities on the shearformed fracture surfaces at 25°C and under the normal stress of 20 MPa is 5.07 mm, as shown in Fig.9.With the increase in the normal stress at a constant temperature,the height of asperities is reduced owing to the enhancement in the restraint effect of the normal stress.When the normal stress is 40 MPa, the height of asperities is reduced to 3.17 mm, with a decrease of 37.7%.Under the constant normal stress of 40 MPa, the height of asperities increases with an increase in the temperature.When the temperatureincreases to 300°C, the height of asperities increases to 4.47 mm,with an increase of 41% compared to that at 25°C.This is because the crystal expands and deforms by different degrees along various crystal axis directions under high temperatures.Thus, high temperatures imply a severe impact.

Fig.9.Heights of asperities on the shear-formed fracture surfaces:(a)Variation in height of asperities with the normal stress;and(b)Variation in the height of asperities with the temperature.

Simultaneously, the uniformity of asperities on the shearformed fracture surfaces of intact granite under different coupling conditions is obtained using the following equations:

When the normal stress increases from 20 MPa to 40 MPa at 25°C,the variance of all the asperities on the shear-formed fracture surfaces decreases from 1.22 to 0.43, which suggests that the increase in the normal stress significantly improves the uniformity of fracture surfaces.When the temperature increases from 25°C to 300°C at a normal stress of 40 MPa, the variance of asperities on the shear-formed fracture surfaces increases from 0.42 to 0.88.This suggests that the increase in the temperature increases the unevenness of the shear-formed fracture surfaces.

3.2.2.3D roughness characteristics of shear-formed fracture surfaces

Barton and Choubey (1977) first proposed a method to quantitatively characterize the roughness characteristics of fracture surfaces.By analyzing the morphological characteristics of 136 natural rock joint surfaces,they summarized 10 classical two-dimensional(2D) roughness profiles.However, a few studies (Grasselli et al.,2002; Ban et al., 2018; Chen and Zeng, 2021) found that there are several problems in using this 2D characterization method to describe the roughness of fracture surfaces having 3D characteristics.For example, the 2D roughness characterization method has notable local characteristics and cannot reflect the rough characteristics of the overall fracture surfaces.In addition, the aforementioned 2D roughness characterization method cannot describe the anisotropy of fracture surfaces.Subsequently, a series of 3D morphological characterization methods have been proposed to accurately characterize the real 3D morphological characteristics of fracture surfaces.Among the several existing 3D morphological characterization methods(Gentier and Hopkins,1997;Lanaro et al.,1998;Belem et al.,2000;Grasselli et al.,2002),the model proposed by Grasselli et al.(2002) is the most commonly used.Considering the apparent dip angle,contact area ratio,and the fitted roughness parameter,Grasselli et al.(2002)established a mathematical model to quantitatively represent the relationship between the apparent dip angle and contact area ratio, which is expressed as follows:

where A0is the maximum possible contact area ratio in the shear direction,is the maximum apparent dip angle in the shear direction,θ*is the apparent dip angle in the shear direction,and C is the rough parameter obtained by the best-fit regression function.

The accuracy of Grasselli’s model in characterizing the 3D morphologies of fracture surfaces has been effectively verified in geotechnical field, including the characterization of shear-formed fractures developed in rock bridges (Yang et al., 2020) and the characterization of slope discontinuities (Indraratna et al., 2015).However, as engineering construction shifts to increasing depths,geological environments with high stress and high temperature coupling conditions are becoming increasingly common.Currently,whether Grasselli’s model can effectively characterize the morphological characteristics of the shear-formed fractures under TM coupling conditions has not been verified.In the next section,the Grasselli’s model is used to fit and verify the data of the shearformed fractures under the considered high-temperature and highstress coupling conditions.

(1) Relationship between the apparent dip angle and contact area ratio

Fig.10 presents the 3D spatial position of the apparent dip angle obtained using the following equations:

Fig.10.Schematic of the 3D geometric recognition of the apparent dip angle.

where α is the azimuth,θ is the angle between the triangle and the shear plane, s is the shear vector, n2is the outer normal vector of shear plane, n is the outer normal vector of triangle, and n1is the projection vector of n in the shear plane.

Fig.11 presents the relationship between the apparent dip angle and the contact area ratio of the shear-formed fractures under different TM coupling conditions and the fitting results of Grasselli’s model.To facilitate statistics, the apparent dip angle is selected at an interval of 2°.When the temperature is 25°C,the R2values(representing the fitting accuracy)under the normal stresses of 20 MPa,30 MPa,and 40 MPa are 0.99192,0.99302,and 0.99896,respectively.When the normal stress is 40 MPa,the R2values at the temperatures of 100°C, 200°C, and 300°C are 0.99804, 0.99899,and 0.99946, respectively.The fitting results demonstrate that theGrasselli’s model is also suitable for characterizing the 3D morphologies of shear-formed fractures under TM coupling conditions.

Fig.11.Relationship between the apparent dip and contact area with the respective temperatures and normal stresses:(a)25 °C and 20 MPa;(b)25 °C and 30 MPa;(c)25 °C and 40 MPa; (d) 100 °C and 40 MPa; (e) 200 °C and 40 MPa; and (f) 300 °C and 40 MPa.

Fig.12.Roughness values of shear-formed fracture surfaces.

(2) 3D roughness values of fracture surfaces

Fig.14.Micrograph of fracture surfaces developed by splitting at a temperature of 25 °C(Deng et al.,2021).Dashed lines indicate intergranular fracture paths.Ab:Albite;Qtz: Quartz; An: Anorthite; Or: Orthoclase; Phl: Phlogopite.

Tatone and Grasselli (2009) confirmed that A0/（C+1） can sufficiently describe the 3D roughness values of the fracture surfaces.Fig.12 presents the variations in the roughness values of the shear-formed fracture surfaces under different TM coupling conditions.At the same temperature,the roughness value of the fracture surfaces of the rock sample decreases with an increase in the normal stress.Under the same normal stress conditions, the roughness value of the fracture surfaces of the rock sample significantly increases with an increase in the temperature.As shown in Table 1, the maximum possible contact area ratio of the shearformed fracture surfaces under different TM coupling conditions is between 0.6 and 0.8,which is larger than that in previous studies(approximately 0.5)(Grasselli et al.,2002;Hou et al.,2016;Liu et al.,2017a; Shang et al., 2021).This is mainly because in the previous studies, most of the fracture surfaces were obtained by artificial splitting tests,and the formation mechanisms mainly included the tensile failure mode.The test results indicate that the macroscopic failure mode of intact rocks at great depths under TM coupling conditions is attributed to mixed tensile-shear failure or shear failure.

Table 1Morphological parameters of shear-formed fracture surfaces.

3.2.3.Anisotropic characteristics of fracture surfaces

Fig.13.Anisotropic characteristics of fracture surfaces: (a) Temperature of 25 °C; and (b) Normal stress of 40 MPa.

Fig.15.Thin sections of shear-formed fractures under coupling of different temperatures and normal stresses:(a)25 °C and 20 MPa;(b)25 °C and 30 MPa;(c)25 °C and 40 MPa;(d)100 °C and 40 MPa; (e) 200 °C and 40 MPa; and (f) 300 °C and 40 MPa.The red and pink arrows indicate intragranular and intergranular fractures, respectively.

Fig.13 presents the anisotropic characteristics of the shearformed fracture surfaces under different TM coupling conditions.When the temperature is 25°C and the normal stress is 20 MPa,the closed figure is irregular.Meanwhile,in the range of 160°-360°,the values of/C between the adjacent directions significantly change, multiple jumps in the/C values appear, and discontinuous characteristics are significant.These results indicate that the anisotropy of the fracture surfaces under the aforementioned conditions is prominent.With an increase in the normal stress,the values of/C in adjacent directions begin to smooth and present a good continuity, and the closed pattern is gradually rounded, as shown in Fig.13a.This suggests that an increase in the normal stress can weaken the anisotropy of the fracture surfaces.Under a constant normal stress,the discontinuity characteristics of/C values between adjacent directions significantly increase with an increase in temperature.In particular, when the temperature reaches 300°C,a jump in the/C value begins to appear between the local adjacent directions, and the closed pattern also changes from circular to gourd-like.These trends indicate that the temperature can enhance the anisotropic characteristics of the fracture surfaces.

3.3.Microscopic mechanism of shear-formed fracture surfaces

The shear strength parameters of an intact rock and the morphology of a shear-formed fracture surface are closely related to the macroscopic failure mode.The initiation, propagation, and connection of microcracks are the most fundamental causes of rock macroscopic failure.From a macroscopic perspective, the failure mode of rocks can be classified into three types: tensile, mixed tensile-shear,and shear failure.To explore the macroscopic failure mode of rocks,numerous studies have interpreted the macroscopic failure mechanisms of rocks from a microscopic perspective,and it was found that the microscopic failure under tension mainly consists of intergranular fractures (Fig.14), whereas shear failure is more inclined to intragranular and transgranular fractures (Yang et al., 2017; Cheng and Wong, 2018; Wu et al., 2019b; Deng et al.,2021).The macroscopic failure mode of intact granites under different TM coupling conditions is investigated in this section from a microscopic perspective.

Fig.16.Shear stiffness of granites under TM coupling conditions.

Fig.15a-c presents the thin sections of the shear-formed fracture surfaces of intact granites under different normal stresses.We observed that damage of different degrees occurred between different crystal minerals and inside the crystal under various normal stresses.When the normal stress was 20 MPa, the microscopic fractures were mainly intergranular and intragranular,which indicates that the macroscopic failure of intact granite is mainly a mixed tensile-shear failure.With the increase in the normal stress, the number of intragranular fractures remarkably increases and the length of the microcracks increases.Meanwhile,a transgranular phenomenon gradually begins to emerge, and the macroscopic failure of intact granite changes from mixed tensileshear failure to shear failure.The main cause of failure transformation is that the increased normal stress promotes the compressive deformation of the crystal, causing the crystal structure to reorganize and intragranular fracture to form more easily under shear stress.

Fig.15d presents the thin section of the shear-formed fracture surface under the coupling of a temperature of 100°C and a normal stress of 40 MPa.Compared to the thin section under the temperature of 25°C,the number and width of micro-fractures in the thin section significantly increase,the fractures generated in the crystal present a neural network of staggered distribution, and the distribution of the micro-fractures becomes more complex.These can be attributed to the original equilibrium of different crystal minerals,which were further disrupted by high temperatures.This disruption is caused by two ways.First, the anisotropy of the crystal makes the crystal expand and deform randomly in different directions along different crystal axes.Under an increasing shear stress, intragranular fractures are randomly generated and distributed in all directions.Second, the difference in the thermal expansions of different crystal minerals results in thermal stresses between different crystals, which aggravates the development of intragranular cracks.Intragranular fractures that are randomly distributed in all directions are more likely to fracture,expand,and connect with adjacent fractures under shear stress,forming a group of fractures with a neural network distribution.With increasing temperature, intragranular fractures further develop, the distribution of microcracks becomes more complex, and the length and width of microcracks significantly increase,as shown in Fig.15e and f.These are also the main causes of the decrease in the peak shear strength of intact granite as the temperature increases.

4.Discussion

The aforementioned results demonstrate that the shear properties of intact granites are closely related to the high temperature and normal stress.As shown in Fig.16, the peak shear strength,shear stiffness (obtained according to Gutierrez-Ch et al.(2018)),internal friction angle,and cohesion of intact granites increase with normal stress, whereas they decrease with temperature.Based on Figs.5 and 6,we found that the decreasing trend of the peak shear strength of intact granite at 100°C is not notable compared to that of intact granite at 25°C.This is attributed to the close competition between the temperature-induced reinforcement effect and the temperature-induced degradation effect.The former is caused by the intercrystalline contact compaction due to the volume expansion,and the latter is induced by the intracrystalline cracks due to the difference in the thermal expansion of the same crystal along different crystal axes.As the temperature increases, the temperature-induced degradation effect has a competitive advantage,and the peak shear strength of granite remarkably decreases.

The normal stress and temperature not only affect the mechanical parameters of intact granite but also have an important influence on the shear-formed fracture surface morphology.Based on the results obtained in this study, it was found that the roughness decreases as the normal stress increases.The main reason is that the fracture pattern of more mineral grains transforms fromintergranular to transcrystalline fracture.The roughness increases with an increase in the temperature.This can be attributed to the difference in the thermal expansion of the same crystal along different crystal axes, making the paths of intragranular fractures more complex, which leads to an increase in the fracture roughness.

Fig.17.Proportion of triangles in different angle ranges on the fracture surfaces after shear failure with the respective temperatures and normal stresses:(a)25 °C and 20 MPa;(b)25 °C and 30 MPa; and (c) 300 °C and 20 MPa.

Fig.18.3D model of asperities on the fracture surfaces.

Another notable finding is that the initial contact area ratio obtained is between 0.6 and 0.8,which is different from the results of previous studies(Hou et al.,2016;Liu et al.,2017b;Grasselli et al.,2002; Shang et al., 2021) (the initial contact area ratios of tensile and shear fracture surfaces are approximately 0.5 and 0.2-0.4,respectively, which are obtained for shallow geotechnical problems).This finding questions the applicability of the shear strength criterion of fractures, which demonstrates that tensile or shear fractures are developed in shallow depths.Therefore,it is necessary to study the asperities on the shear-formed fracture surfaces under TM coupling because it is the most direct factor affecting the morphological characteristics of fracture surfaces.

The heights and apparent dip angle are important parameters of the asperities on the fracture surfaces considering that they both determine the shape characteristics of the asperities and the consequent initial contact area ratio of the fracture surfaces.The results of this study demonstrate that the height of asperities decreases with an increase in the normal stress,whereas it increases with an increase in the temperature.Fig.17a presents the apparent dip angle (＜90°) distribution of the asperities on the fracture surfaces of a rock sample under a temperature of 25°C and a normal stress of 20 MPa(X-direction represents the shear direction,and Ydirection is perpendicular to the shear direction).The apparent dip angle ratios along the X-direction,negative X-direction,Y-direction,and negative Y-direction are 63.6%, 36.4%, 50.5%, and 49.5%,respectively.As the normal stress increases to 30 MPa, the proportions of the apparent dip along the X-direction, negative X-direction,Y-direction,and negative Y-direction are 96.2%,3.8%,50.1%and 49.9%, respectively, as shown in Fig.17b.The results demonstrate that the shape of the asperities changes with an increase in the normal stress.When the temperature is 300°C and the normal stress is 20 MPa,the proportions of the apparent dip angle in the Xdirection, negative X-direction, Y-direction, and negative Y-direction are 69.3%, 30.7%, 32.1%, and 67.9%, respectively, as shown in Fig.17c.The shape of the asperities changes with increasing temperature, which also significantly change in the Y-direction.Therefore,it is not feasible to use a 2D method to characterize the asperities on the shear-formed fracture surfaces under TM coupling conditions.

We propose a 3D conceptual model that can be used to characterize the asperities on the shear-formed fracture surfaces.The model is composed of three submodels, as shown in Fig.18.Submodel 1 is a regular pyramid in which faces A and B as well as C and D are symmetrically equal.This submodel matches the symmetrical zigzag arrangement under a 2D characterization method.Therefore, it represents the asperities on the tensile fracture surfaces.Submodel 2 is a pyramid in which faces A and B are asymmetrical(the area of face A is larger than that of face B),whereas faces C and D are symmetrically equal.This model represents the asperities on the shear fracture surfaces.Submodel 3 is a pyramid in which faces A and B(the area of face A is larger than that of face B)as well as C and D (the area of face D is larger than that of face C) are asymmetrical.This submodel represents the asperities on the shear fracture surfaces under the influence of temperature.Based on the distribution laws of height and apparent dip angle of asperities under different TM coupling conditions provided above, we determined that the asperities on the shear-formed fracture surfaces under the temperature of 25°C and normal stress of 20 MPa are composed of submodels 1 and 2.The asperities on the shearformed fracture surfaces under the temperature of 25°C and normal stress of 30 MPa are composed of submodel 2.The asperities on the shear-formed fracture surfaces under the temperature of 300°C and normal stress of 20 MPa are composed of submodels 1 and 3.The proposed model is sufficiently verified by the previous test results.For example, under the temperature of 25°C and normal stress of 20 MPa,intact granite presents macroscopic mixed tensile-shear failure, and the initial contact area ratio of the fracture surface is 0.659.The combination of submodels 1 and 2 can sufficiently explain both characteristics of the fracture surface.

In this study, we obtained the morphological characteristics of shear-formed fracture surfaces under different TM coupling conditions, laying the foundation for studies related to engineering problems,such as the secondary slip and deformation of deep rock mass.For example, in the process of enhanced geothermal development,water injection-induced shear technology can increase the opening of fractures and improve the heat transfer efficiency of geothermal reservoirs by promoting the shear expansion and sliding of fractures.In the following studies, we will continue to investigate the issues related to rock fractures under the TM coupling conditions.

5.Conclusions

In this study, the shear behavior of intact granites was investigated by direct shear tests under TM coupling conditions, and the 3D morphological characteristics of the shear-formed fracture surfaces were quantitatively analyzed.As part of a novel study,the mechanical parameters and 3D morphologies of the shear-formed fractures under different TM coupling conditions were compared and analyzed.The main conclusions are obtained as follows:

(1) The peak shear strength of intact granite positively correlates with the normal stress,whereas it negatively correlates with the temperature.The shear resistance of intact granite is affected by the temperature.With an increase in the temperature from 25°C to 300°C,the internal friction angle and the cohesion are reduced by 31.2% and 11.7%, respectively.

(2) Grasselli’s model can be used to describe the 3D morphological characteristics of the shear-formed fracture surfaces under TM coupling conditions.The test results demonstrate that the temperature and normal stress have significant effects on the 3D morphologies of the shear-formed fracture surfaces.An increase in the normal stress reduces the roughness and anisotropy of the fracture surfaces.As the normal stress increases from 20 MPa to 40 MPa, the roughness values at 25°C,100°C, 200°C, and 300°C decrease by 45.8%,42.7%,41%,and 37.3%,respectively.An increase in the temperature increases the roughness and anisotropy of the fracture surfaces.As the temperature increases from 25°C to 300°C, roughness values at 20 MPa, 30 MPa, and 40 MPa increase by 34.7%, 30.5%, and 55.5%, respectively.

(3) The main macroscopic failure modes of intact granite under TM coupling conditions include mixed tensile-shear failure and shear failure.The normal stress can promote the transformation of failure mode.As the normal stress increases,the distribution range of the intragranular and transgranular fractures in a thin section gradually increases,and the failure mode changes from mixed tensile-shear failure to shear failure.In addition, a temperature increase can increase the complexity of intragranular and transgranular fracturing paths,which is also the main cause of the roughness increase with temperature.

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 research was financially supported by the National Natural Science Foundation of China(Grant No.51974173),and the Natural Science Foundation of Shandong Province, China (Grant No.ZR2020QD122).