1 Introduction

With the recent and prevalent utilization and development of modern engineering applications, such as the disposal of nuclear waste in underground geological media, the exploitation and utilization of geothermal resources, coal gasification and fluidized mining, as well as evaluation of bearing capacity, restoration and even reconstruction of geotechnical structures after fire hazards, the profound study and adequate understanding of the responses of both physical and mechanical properties of rocks exposed to thermal treatment are of significant theoretical and applicable value for ensuring the safety and performance of these projects (Shafirovich and Varma 2009; Tremel et al. 2012; Xie et al. 2017; Meng et al.2020; Huang et al. 2020a, b; Tao et al. 2020; Zhu et al. 2021).

To date, many indoor experimental studies have been conducted to evaluate the thermally induced changes in the physical properties of rocks, including pore structures, porosity and longitudinal wave velocity (Gautam et al. 2018; Shen et al. 2018; Yin et al. 2019; Li et al. 2021a), mineral composition, thermal expansion, cracking and microdefects (Yavuz et al. 2010; Tiskatine et al. 2016; Shi et al. 2020), permeability and transport characteristics (Yasuhara et al. 2015; Yin et al. 2019). Generally, with increasing temperature, due to gradually developed thermal damage, the pore volume increases, resulting in enhanced porosity and flow capacity but weakened P-wave velocity and thermal conductivity (Abdulagatova et al. 2020). In addition, how the temperature affects the mechanical responses of rocks has also been investigated in certain studies, including the uniaxial/triaxial compressive strength, elastic modulus, cohesion, splitting tensile resistance, fracture toughness, deformation behaviours and residual strain (Koca et al. 2006; Siegesmund et al. 2007; Su et al. 2017; Rong et al. 2018; Talukdar et al. 2018; Li et al. 2021b). The results have indicated that thermal stress has a negative effect on strength behaviours, but increases the deformation of rocks, especially in terms of plastic/ductile deformation and Poisson's ratio. Previous research results provide certain guidance for our study.

However, in actual rock projects, the shear mechanical properties and corresponding normal deformation are important issues (Jiang et al. 2004; Tang et al. 2020). The deformation and failure of surrounding rocks in chambers are always involved with the shear failure of rock masses, which is characterized by crack propagation and the extension of slipping surfaces under an applied shear load as a result of tectonic movements or human activities (Bahaaddini et al. 2016; Meng et al. 2018). Thus, it is of great significance to analyse the shear mechanical mechanisms of rock masses. Additionally, the shear resistance, deformation behaviours and failure responses of a rock mass are all restricted by the occurrence boundary conditions, including constant normal load (CNL) and constant normal stiffness (CNS) conditions (Thirukumaran and Indraratna 2016; Li et al. 2018). The former is mainly applicable to surface or shallow buried non-anchored slope engineering, and is characterized by ignoring the influences of the dilatancy effect on the normal stress of the rock mass during the shear process. The latter corresponds to deep underground projects, indicating that under an applied shear load, the rock mass cannot dilate freely due to the restriction of the surrounding rock mass, and the boundary normal stress increases continuously (Jiang et al. 2004; Mirzaghorbanali et al. 2014; Han et al. 2020; Zhang et al. 2020). Until recently, extensive works have been performed to analyse the shear properties of rocks under CNL conditions, including laboratory tests (Asadizadeh et al. 2018; Meng et al. 2018), numerical simulations (Wang et al. 2019; Zhang et al. 2020), and theoretical analysis (Lee et al. 2014; Li et al. 2017). The microcrack propagation process, shear strength properties, dilatancy deformation, and failure characteristics of rock were studied in depth. However, for most underground projects, the potential self-stability of the surrounding rock mass relies on the interaction between dilatancy deformation and normal stress. Thus, investigating the shear mechanical properties of rock masses under CNS boundary conditions is much closer to actual projects, which has to date rarely been reported (Jiang et al. 2004; Liu et al. 2020; Yin et al. 2020a, b; Wang et al. 2021), much less for rock samples exposed to high temperatures. Tang et al. (2020) performed direct shear tests on granite discontinuities after high temperature treatment to 800 °C, and investigated the influences of temperature on the shear strength, displacement, and surface degradation of rock fractures. However, their works were conducted under CNL rather than CNS boundary conditions.

Therefore, in this study, we investigate the influences of high temperature exposure (25–800 °C) on the shear mechanical responses of intact sandstone samples subjected to various initial normal stresses under CNS boundary conditions. First, the physical properties of thermally treated sandstone, including porosity, P-wave velocity, fractal dimension of pores and development of thermally induced defects, were analysed. Then, a number of direct shear tests were conducted with respect to various initial normal stresses (0.02, 2, 4, 6, 8 MPa). On the basis of the experimental results, the temperature-dependent shear mechanical behaviours, including the typical shear failure process, shear strength, normal dilation, secant peak shear stiffness, normal stress – shear stress variation paths, strength envelope, and the ultimate shear failure patterns, were respectively clarified.

2 Sample preparation and test apparatus

Medium-grained yellow sandstone, gathered from Rizhao City, Shandong Province, China, was selected for the experiment. The reasons for the choice of sandstone are as follows. First, there are abundant sedimentary sandstones in the geological structure of the Rizhao area (Zhu et al. 2019). With the development of underground resources and space utilization, disturbances occur due to excavation unloading and human activities, thus producing fracture initiation, propagation and shear slip of the chamber surrounding rock mass (Huang et al. 2020a, b). In addition, disasters from tunnel fires and the spontaneous combustion of coal exert high temperatures up to 800–1000 °C to the surrounding rock mass, which weakens the strength resistance and varies the shear responses of rocks (Zhao et al. 2019). The selected sandstone is mainly comprised of quartz, kaolinite and clinolite, occupying a mean bulk density of 2.36 g/cm3 and a uniaxial strength subjected to an axial load of 31.90 MPa. The sandstone has no visible cracks by unaided eyes in its natural state, implying an intact and dense matrix. Using an infrared laser cutting system, 45 cubic samples with a side length of 100 mm were machined. Then, the samples were subjected to high temperature treatments of T = 100, 200, 300, 400, 500, 600, 700 and 800 °C, respectively, by using a fixed temperature increasing rate of 5 °C/min (Fig. 1a) (Yin et al. 2019). After the temperature value rose to a certain predetermined level and was maintained for 2 h for achieving uniform heat treatments, the rock was then cooled until its natural state (T = 25 °C) within the furnace by using a fixed cooling speed of 1 °C/min. As T increases, the thermally treated sandstone gradually turns from yellow to brick red due to the oxidation of iron ions.

Fig. 1
figure 1

Sample preparation and shear test apparatus

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Then, the rock samples were conducted shear tests under CNS boundary conditions by applying a servo-controlled shear testing system (equipment type of MIS-233–1-55–03) at Nagasaki University, Japan (Fig. 1b). This apparatus mainly consists of five units of vertical jack, horizontal jack, shear box, data acquisition system and control panel, which can provide a loading capacity limit of 200 kN along its normal and shear directions, with a shear displacement range of 0–20 mm (Zhang et al. 2020). During the shear process, the displacement loading control mode was selected, with a loading rate of 0.2 mm/min. Both shear and normal deformations were monitored using the LVDTs with an accuracy of 0.001 mm. The CNS boundary condition was achieved by real-time feedback of shear dilation information and applying corresponding normal loads based on the designed constant normal stiffness Kn.

3 Physical properties analysis

Figure 2a presents the scanning electron microscopy (SEM) observation results of sandstone after high temperature treatment. For T = 25 °C, the sandstone exhibits a typical pore structure. For T = 100–300 °C, the pore structures gradually develop, accompanied by several thermally induced cracks that are not fully developed. For T = 400–800 °C, the internal defects develop rapidly and coalesce with each other to produce crack networks, and the rock matrix gradually breaks into smaller blocks, characterized by scale-like weathered zones. Especially for T = 800 °C, the matrix is completely decomposed, and thermal cracks filled with weathered detritus present a substantial increase in the aperture thickness. The variations in micro defects would certainly destroy the original structures of sandstone, resulting in an attenuation of both P-wave velocity v and unit weight ρ (Fig. 2b). In the T range of 25–800 °C, v and ρ show a decrease of 63.21% and 23.88%, respectively.

Fig. 2
figure 2

Variations in physical properties of sandstone after high temperature treatment

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Then, the pore porosity λ and fractal dimension of pores D of sandstone exposed to high temperature were characterized using the mercury intrusion porosimetry (MIP) method (Anovitz and Cole 2015). By referring to the Washburn equation, variations in the pore size diameter of rocks as a function of the cumulative mercury intrusion are shown in Fig. 2c:

$$r = - \frac{4\sigma \cos \theta }{{P(r)}}$$
(1)

where r is the pore diameter, P(r) is the pressure exerted by mercury, θ denotes the contact angle, which equals 140°, and σ is the interfacial surface tension (Zhang et al. 2017).

In Fig. 2c, as P increases, the accumulative injection of mercury, namely, the pore volume of rock, keeps gradually increasing, while the pore diameter that can be injectable continues declining. The increasing process of cumulative injection of mercury could be divided by four phases, including gentle growth, quick growth, slow down and basically unchanged. With increasing T from 100 to 800 °C, the accumulative injection of mercury in its steady state shows an increase of 39.87% due to gradually developed thermally induced microdefects. Then, based on the establishment thinking of algorithm of the Menger sponge (Giménez et al. 1997; Yin et al. 2019), the log–log fitting curves between dVP(r)/dP(r) and P(r) of the pore structures were achieved, as shown in Fig. 2d:

$$\lg \left[ {\frac{{{\text{d}}V_{P(r)} }}{{{\text{d}}P(r)}}} \right] \propto (D - 4)\lg P(r)$$
(2)

in which VP denotes the pore volume, and D is the fractal dimension of the pores (Qin et al. 2012).

In Fig. 2d, the variations in lg(dVP(r)/dP(r)) with respect to lgP(r) can be well described using a linear function with a negative slope of (D-4) by generating all R2 values larger than 0.975. As T increases, the absolute slope value increases, resulting in a gradual reduction in D, as displayed in Fig. 2e. With an increase in T from 100 to 800 °C, D decreases from 2.971 to 2.561, a decrease of 13.79%, which is in the theoretical bandwidth of 2–3 for three dimensional porous media, while the porosity λ increases from 18.59% to 26.49%, an increase of 42.48%.

The variations in λ with increasing temperature can be divided into two phases. In the T range of 100–400 °C, λ exhibits a slight increase of 12.96%. In this temperature range, water in the forms of free and bonded is released from the mineral grains and escapes quickly. There are some microcracks initiated, but these cracks might not be perfectly expanded, resulting in a small growth in λ of sandstone samples below 400 °C. Then, as the temperature exceeds 400 °C, thermal expansion of weak clay minerals happens, and different minerals exhibit different expansion rates, resulting in various deformations at the same temperature level. As the increasing thermal stress is higher than the internal stress of the solid particles, the stress equilibrium state is destroyed, resulting in stress redistribution and structural changes to the rock. The rock samples experience irreversible thermal damage. Microcracks initiate and extend quickly to produce micro network structures, leading to the increased connectivity of microcracks. In addition, at T = 573 °C, a phase transition of quartz from the α phase to the β phase happens, which results in the volume growth of rock and an increased number of microcracks. Therefore, the porosity λ increases sharply for T = 400–800 °C.

For the pore fractal dimension D, the main reasons for the quick decrease after T = 400 °C are as follows. With increasing T from 100 to 400 °C, D experiences a gentle reduction, implying that the loss of water in both free and bunded forms, as well as the preliminary growth of thermally induced cracks in rocks during this temperature range, might not induce remarkable effects on the micropore structures. However, when T exceeds 400 °C, due to the further development, dilation and transformation of mineral grains, an inhomogeneous thermal expansion of rocks happens, generating a significant influence on the fractal dimension of pores. The original irregular crack structures in rocks gradually change into relatively homogeneous pore structures, resulting in a decreasing D.

The change rules of λ and D for sandstone after high temperature exposure are consistent with the views in several existing reports (e.g., Yin et al. 2015; Chen et al. 2017; Zhang et al. 2017; Kumari et al. 2019; Su et al. 2020).

4 Shear mechanical responses

4.1 A typical shear failure process

Figure 3a presents a typical shear failure process for the thermally treated intact sandstone samples. In stage I, the normal displacement δv – shear displacement u curves are characterized by a slight shear contraction due to closure and compaction of initial microdefects. In stage II, variations in both shear stress τ and δv present upward concave shapes. Stage III is characterized by elastic deformation before the peak strength τmax. Afterwards, with the generation, development and coalescence of microcracks, macro rough-walled fracture surfaces that run through the whole thickness of rock samples are produced, with a normal displacement of Δδv1. Both τ and δv reach the peak strength τmax and peak dilation δvmax before experiencing a notable drop abruptly at almost the same time (Stage IV) (Fig. 3a, b).

Fig. 3
figure 3

Typical shear stress and normal displacement variation process

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Then, with a continuous increase in u, shear slipping occurs on the rough fracture surfaces. Both τ and δv increase again due to shear off and damage of the surface asperities, accompanied by a normal dilation of Δδv2 (Stage V). The normal stress σn of the fracture surfaces also increases due to the CNS boundary conditions (Jiang et al. 2004).

$$\sigma_{n} (t + \Delta t_{2} ) = \sigma_{n} \left( t \right) + K_{n} \Delta \delta_{v2}$$
(3)

where σn(t) and σn(t + △t2) denote the normal stress at t and t + △t2, respectively (Fig. 3b).

At the end stage VI of u = 10 mm, both τ and δv generally stabilize, retaining the residual strength τres and terminal normal dilation δv10, respectively. From the above analysis, the whole shear failure process of all thermally treated rock samples can be divided into two stages of the fracture surface generation process and shear slipping process, as shown in Fig. 3.

4.2 Shear stress and normal dilation

The relations between τ, δv and u with respect to various T and σn0 are displayed in Fig. 4. With increasing T, both τ – u and δv – u curves generally shift downwards, resulting in a decrease in both τmax and τres. During the test, the fracture surface generation process generally occurs at u = 2–4 mm. At a given σn0, for a higher T level, the initial shear contraction is more obvious in the δv – u curves due to gradually developed micro defects, and the shear displacement that corresponds to the peak dilation δvmax is larger, mainly as a result of mechanical response transition from brittleness to ductility of sandstone after high temperature treatment (Yang et al. 2017). In addition, the shear displacement corresponding to δvmax increases gradually with σn0 due to the enhancement of shear resistance at a high applied normal stress. After the drop of δvmax, both τ and δv show a gradual increase with u, while the extent of the increase declines, which is mainly because as shearing proceeds, an increasing number of surface asperities are destroyed and the fracture roughness coefficient declines in the shear slipping stage, resulting in weakened dilation effects after the peak strength. The above analysis is consistent with the results in some existing reports (e.g., Lee et al. 2014; Li et al. 2018).

Fig. 4
figure 4

Relations between τ, δv and u with respect to various T and σn0

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Figure 5a, b present the variations in τmax and τres as a function of T and σn0. As T increases, τmax and τres show a similar variation, which could be separated into two phases, i.e., a gentle increase or fluctuation with increasing T from 25 to 400 °C, while they decrease significantly in the T range of 400 to 800 °C. The τmax – T and τres – T variation curves could be reliably described with the following exponential function:

$$y = {\text{e}}^{{(a + bx - cx^{2} )}}$$
(4)

where a, b and c are fitting coefficients related to T and σn0.

Fig. 5
figure 5

Variations in τmax, τres, Ks and δv10

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The main reasons for the exponential variation characteristics of shear strength with T are as follows. For T = 25–400 °C, vaporization escape happens in both bound water and interlayer water in sandstone, leading to a decrease in the lubrication effects but an enhancement in the bonding strength and frictional force. The mineral lattice structure is destroyed to a certain degree but has a relatively weaker effect on the mechanical properties. Thus, thermal hardening occurs, and the overall shear resistance increases with T. However, for T = 400–800 °C, the internal defects further develop, with a richer connectivity. Under a high temperature environment, strong thermal expansion and decomposition occur to weak clay minerals. The sandstone experiences obvious thermal cracking and irreversible thermal damage. Internal thermal cracks propagate rapidly, leading to an obvious increase in porosity and sharp degradation in the shear strength. Generally, variations in τmax and τres with T are consistent with the views of some previous studies that both physical and mechanical properties significantly degrade for a T higher than 400 °C (e.g., Liu and Xu, 2015; Yin et al. 2015; Meng et al. 2020; Tang 2020). For a certain T, with an increase in σn0 from 0.02 to 8 MPa, τmax and τres increase by 36.63–170.94% and 25.04–205.22%, respectively, due to increasing shear resistance under an applied larger σn0.

The secant peak shear stiffness Ks, which has been extensively utilized in both numerical analysis and mathematical modelling, can be defined as the ratio between τmax and the corresponding shear displacement up (Eq. 5) (Usefzadeh et al. 2013; Tang et al. 2020).

$$K_{{\text{s}}} = \tau_{\max } /u_{{\text{p}}}$$
(5)

Figure 5c presents the evolution of Ks as a function of T. With an increase in T, Ks generally declines, which can be separated into two phases. For T = 25–400 °C, Ks fluctuates in a small range, while as T increases from 400 to 800 °C, Ks shows a significant reduction of 43.79%–70.48%. The degradation in Ks with T is mainly due to enhanced ductility and a decrease in the peak shear strength of thermally treated rock samples.

Variations in the terminal normal displacement δv10 at u = 10 mm with σn0 are displayed in Fig. 5d. As σn0 increases from 0.02 to 8 MPa, δv10 generally presents a decrease of 52.68%–57.37%. The dilatancy effect gradually weakens due to increasing normal stress. However, for a certain σn0, δv10 shows a first increased and then decreased variation with T, reaching a threshold value at T = 400 °C.

4.3 Normal stress and strength envelope

Variations in normal stress σn, as a function of u with respect to various T and σn0, are shown in Fig. 6a, d. During the shear process, σn first presents an increase, and the growth extent also increases. When the rough-walled fractures are generated through the intact samples, a sudden stress drop happens, and the normal stress corresponding to the stress reduction point increases with a larger σn0. Afterwards, with a continuous increase in u, shear slipping occurs on the fracture surfaces, and σn increases once again, but the increasing rate gradually declines, because the “climbing effects” along asperities on the fracture surfaces are restricted by the normal stiffness under the CNS boundary conditions. Figure 6e shows the variations in the terminal normal stress σnter at u = 10 mm. With an increase in T, σnter generally presents a decreasing variation, which can also be well fitted using the exponential function in Eq. (4), with the correlation coefficient R2 values all larger than 0.90. However, for a given T, σnter increases by 7.05–111.36% with σn0.

Fig. 6
figure 6

Variations in σn, σn–τ paths and the strength envelop

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Figure 6f–i present the τ – σn variation paths during shearing. Before the peak strength τmax, σn displays a continuous increase variation under CNS boundary conditions, which is essentially different from the results achieved in the CNL boundary conditions and exhibits an excellent agreement compared to the findings from some existing reports (e.g., Jiang et al. 2004; Li et al. 2018; Han et al. 2020). The essential reason for τ – σn variation paths during shearing is as follows. Under CNL conditions, σn of the samples is kept unchanged, and the τ – σn variation curves are perpendicular to the σn axis in Fig. 6f–i. However, under CNS conditions, variations in normal stress as a function of normal displacement can be characterized using Eq. (3). From the typical shear stress and normal displacement variation process in Fig. 3, the normal displacement δv first experiences a slight shear contraction and then presents upward concave shapes until the peak shear strength. Thus, based on Eq. (3), the normal stress σn first shows a slight decrease compared with the initial normal stress σn0, and then with an increase in δv due to shear dilation, the normal stress keeps increasing.

As σn0 increases, τmax generally presents a gradual increase. By referring to the research idea of Indraratna et al. (1998), a linear fitting through the origin point is conducted to obtain the linear envelopes between τmax and the corresponding normal stress σnp for rock samples after high temperature exposure during shearing (Eq. 6), as plotted in Fig. 6j. As T increases, the slope of the linear envelopes first increases and then decreases, reaching a maximum value of 0.9971 at T = 200 °C and a minimum value of 0.5906 at T = 800 °C, resulting in an increase in the apparent internal friction angle from 42.68° to 44.92° in the T range of 25–200 °C, and then a decrease to 30.57° for T = 800 °C.

$$\tau_{\max } { = }\sigma_{{{\text{np}}}} \tan \varphi_{{\text{e}}}$$
(6)

where σnp denotes the normal stress corresponding to τmax and φe denotes the apparent internal friction angle.

Note that the slope of the linear envelopes reaches the maximum value at T = 200 °C. The reasons are as follows. In the T range of 100–200 °C, the losses of interlayer water and bonded water destroy the crystal skeletons in minerals, resulting in an increasing number of the internal defects and attenuation of shear resistance. However, the water loss results in gradually weakened lubrication effects while enhancing the bonding strength and frictional force among mineral grains, which eventually leads to an increasing overall shear resistance. The above two effects interact with each other, and which effect plays the dominant role depends on both the pore characteristics and mineral structures. Due to the large porosity and relatively uniform distribution of mineral particles of the tested sandstone in its natural state, water loss easily occurs while the damage degree of the crystal skeleton is relatively weak, thus producing an increase in the overall shear resistance and corresponding slope of the linear envelopes for sandstone after high temperature exposure of 100–200 °C. However, with a continuous increase in the temperature level to 800 °C, the thermal damage of sandstone is enhanced and plays the principal role, resulting in a decrease in the shear resistance as well as the slope of the linear envelopes.

4.4 Ultimate shear failure modes

The ultimate shear-induced failure modes and fracture surface morphologies of the tested rock samples are shown in Fig. 7. Two representative failure patterns, including the wear characteristics of sheared asperities and the edge spalling of the rock matrix, can be identified. Generally, for a certain T, with increasing σn0, more severe surface shear slipping traces can be observed, and secondary crack initiation, propagation, and even rock block disintegration happen because a larger normal stress can be supplied under CNS boundary conditions during shearing, especially for σn0 = 6 and 8 MPa, and the failure of an “X” conjugate shape is finally produced. In addition, as T increases, due to the generally weakened shear strength, the shear-induced damage to the samples is also more serious.

Fig. 7
figure 7

Shear failure characteristics of samples after high temperature exposure

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From the typical shear process and ultimate failure modes of intact sandstone samples, the shear behaviour can be divided into two stages, including generation of rough-walled fracture surfaces through the intact block and wear of the surface asperities. During the generation of fracture surfaces, serious edge spalling occurs due to stress concentration. Thus, during the latter shear off of surface asperities, only the internal fracture surfaces play the role of shear resistance. Due to severe block spalling, digital reconstruction of the surface morphology, and the corresponding joint roughness coefficient (JRC) are difficult to achieve. Thus, the central square zones of 50 mm × 50 mm on the fracture surfaces were extracted, and binary calculations of these zones were conducted using a MATLAB procedure (Fig. 8a). By setting a relevant threshold value, the shear wear area on fracture surfaces is defined as white, and the area without shear failure is defined as black. The binary calculation results show excellent corresponding characteristics compared with the real shear failure on the fracture surfaces. Then, changes in the shear area ratio ξ were quantitatively evaluated with respect to T and σn0. In the T range of 25 to 400 °C, ξ retains volatility and then shows a rough linear increase as T increases from 400 to 800 °C. Generally, ξ increases by 38.83%–50.91% in the T range of 25 to 800 °C. For a certain T, with increasing σn0, ξ also presents an increase due to relatively strong shear dilation inhibition under an applied larger σn0.

Fig. 8
figure 8

Shear area ratio and mass loss ratio of rock samples after shear with respect to various T and σn0

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The shear-induced damage of rock samples can also be partly recognized by the mass loss ratio (Tang et al. 2020), including weight loss induced by sheared asperities and edge spalling, as shown in Fig. 8b. For a certain T, the mass loss ratio η shows an increase with σn0 by 27.36–57.54%. Additionally, at a given σn0, the changes in η with increasing T remain in line with the variations in ξ, implying a small fluctuation or increase in the T range of 25 to 400 °C and then an approximate exponential increase beyond 400 °C onward, especially for T = 800 °C.

5 Conclusions

  1. 1.

    The internal microstructure of sandstone varies as a result of exposure to high temperatures, especially for temperatures larger than 400 °C, at which the matrix is gradually decomposed, and thermal crack networks are developed, characterized by larger aperture thickness and filled with weathered detritus. In the temperature range of 25–800 °C, due to thermally induced defects, the porosity of sandstone increases by 42.48%, while the P-wave velocity, unit weight and fractal dimension of pores decline by 63.21%, 23.88% and 13.79%, respectively.

  2. 2.

    A typical shear failure process of intact sandstone after high temperature treatment is identified, characterized by a fracture surface generation process and a shear slipping process of surface asperities. Both the peak shear strength and residual shear strength show an exponentially decreasing variation with temperature, achieving a threshold temperature value of 400 °C, while they increase by 36.63–170.94% and 25.04–205.22%, respectively, with the applied initial normal stress. The secant peak shear stiffness declines by 43.79–70.48% in the temperature range of 400–800 °C due to enhanced ductility and a decrease in the peak shear strength. The terminal normal displacement decreases by 52.68–57.37% with initial normal stress due to weakened dilation effects.

  3. 3.

    Under CNS boundary conditions, the normal stress continuously increases, and due to the generation of fracture surfaces through the samples, a normal stress drop occurs. The terminal normal stress shows an exponentially decreasing variation with temperature but increases by 7.05–111.36% with increasing initial normal stress. The shear stress–normal stress variation paths are plotted for all test cases, and the linear envelopes of the peak shear strength indicate that the apparent internal friction angle generally decreases with temperature. Two representative failure patterns, including wear/shear off of surface asperities and edge spalling of the rock matrix, are identified. Generally, both the shear area and mass loss ratios of sheared rock samples show an increase with both increasing temperature and initial normal stress due to weakened shear strength and strong shear dilation inhibition effects, respectively.