Deep geothermal energy is of great strategic importance for the development of the energy industry. In the process of geothermal energy extraction, temperature changes will significantly affect the physical and mechanical properties of the rock mass. To investigate the influence of temperature on the physical and mechanical properties of red sandstones and marbles, the uniaxial compression test, variable-angle shear test, mercury intrusion porosimetry (MIP) test, and SEM test were conducted on the red sandstone and marble specimens treated by 9 temperature levels (from 25°C to 800°C). The results show that the porosity is positively correlated with the temperature regardless of rock types. The peak strength of red sandstones during uniaxial compression increases first when temperature increases from 25°C to 400°C and then decreases when temperature increases from 400°C to 800°C, whereas the peak strength of marbles exhibits a first decreasing (from 25°C to 300°C), then increasing (from 300°C to 600°C) and finally decreasing (from 600°C to 800°C) trend. Similarly, the shear strength and cohesion of red sandstones increase first and then decrease as temperature rises from 25°C to 800°C, despite of the predesigned shearing angle, which is opposite to the variation in frictional angle. The variations in physical and mechanical behavior are closely related to the expansion of the constituent grains or groundmass which make up the rock composition and closure of pores. Additionally, the temperature in the range from 400°C to 600°C plays an important role to evaluate the variations in the physical and mechanical characteristics of red sandstones and marbles after high-temperature exposure, because of the stress, strain, and porosity change dramatically.

During underground geothermal energy extraction, the complex geological conditions such as high temperature and high stress are commonly encountered [1]. As the temperature in underground geothermal reservoirs is relatively high (i.e., larger than 200°C), the mechanical behavior and heat transport properties of rocks under such conditions are different from those in shallow conditions. [2]. In the process of geothermal energy extraction, the change in temperature will significantly affect the physical and mechanical properties of the rock mass [39].

In recent years, the contributions have been made to the stability analysis of rock engineering such as tunnels after fire, the reuse of abandoned mines, and energy extraction from enhanced geothermal systems in the international community [1015]. High temperature would induce variations in the physical and mechanical characteristics of rocks [1619]. Thus, it is very significant to fundamentally understand the physical and mechanical behaviors of rocks after thermal treatment.

The physical and mechanical characteristics of rocks after high-temperature exposure have been diffusely studied [2029]. For red sandstones, a fracture evolution process was conducted by Yang et al. [30] on a specimen containing a single fissure and two parallel cracks under uniaxial compression, which was heated by thermal treatment from 25°C to 900°C. They found that the uniaxial compressive strength increases with increasing the temperature from 25°C to 300°C, which however decreases with continuously increasing the temperature from 300°C to 900°C, despite of the number of fissures. Yu et al. [31] conduced triaxial compression tests on red sandstones after thermal treatment. The analysis showed that the differential stress increases from 69.35 MPa to 78.06 MPa as temperature increases from 20°C to 200°C due to the closures of pores and cracks while it decreases from 78.06 MPa to 33.44 MPa as temperature increases from 200°C to 600°C due to the high temperature-induced degradation effect. To study the mechanical behaviors and hydraulic properties of red sandstones under different temperature levels, Zhang et al. [32] carried out seepage tests under hydrostatic pressure conditions and triaxial compression conditions. The results indicated that the initial, peak and postpeak permeability, and the strength increase first when the temperature is between 25°C and 50°C because the thermal stress can accommodate deformation and crack closure and then decrease with the increment of temperature from 100°C to 150°C because of the thermal stress-induced crack initiation and propagation.

For marbles, to investigate the influence of temperature on the physical properties and microstructure, Yavuz et al. [33] measured the density, effective porosity, and P-wave velocity by multiple testing means. They found that the compaction of rock structures occurs for temperatures up to 150°C through microscopic analyses and P-wave velocity measurements. The influence of temperature on the physical and mechanical properties of marbles was investigated by Ozguven and Ozcelik [34]. The results showed that the marbles suffered destructive damage when temperature reaches 600°C ~800°C, because the natural stones’ structure becomes damaged and/or changes, brakes down, pours, or cracks. The similar conclusions are also reported by Castagna et al. [20]. The uniaxial compression and acoustic wave experiments were performed on the marbles after heating under natural cooling or water cooling conditions by Huang et al. [35]. They found that the peak strength, peak strain, and P-wave velocity of heated marbles under water cooling condition exhibited a decreasing trend as a whole with increasing the temperature. Tiskatine et al. [36] studied the hardness and structure of thirteen marbles collected from diverse places in Morocco in a high temperature thermal storage following different heating-cooling cycles between 20°C and 650°C. They reported that the quartz and calcite are the principal minerals that control rock physical properties. The conventional triaxial compression experiment was carried out on the veined marbles that contain either horizontal or vertical veins after thermal treatment by Su et al. [37]. They found that the strength and strain of the veined marble specimens changed with the temperature presenting a critical temperature of 600°C, at which the strength, stain, and damage factor change dramatically. To study the thermal-induced damage on the fracture behaviors of marbles that are heat-treated with different temperature levels, Guo et al. [38] conducted the three-point bending tests. The results indicated that the fracture toughness and elasticity modulus diminished gradually with the increment of treated temperature.

The present study is aimed at investigating the physical and mechanical characteristics of red sandstones and marbles treated by different temperatures. First, mercury intrusion porosimetry (MIP) tests are carried out to address the pore-related physical properties. Then, uniaxial compression tests and variable shear tests are carried out to investigate the peak strength, cohesion, and frictional angle of the samples. Finally, the failure mode and scanning electron microscope (SEM) images are utilized to interpret the variations in both micro and macromechanical properties induced by temperature treatment.

2.1. Testing Procedure

To investigate the influence of temperature on the pore-related physical properties of red sandstones and marbles, 9 red sandstones and 9 marbles were heated to different temperature levels (T=25, 100, 200, 300, 400, 500, 600, 700, and 800°C). Concretely, the specimens were heated to the designed temperature level with a constant heating rate of 5°C/min first and then kept 2 hours, which were naturally cooled down to the room temperature finally [37].

The MIP tests were conducted on the two kinds of specimens after thermal treatment, as shown in Figure 1, using AutoPore IV 9500 Version 2.03.00 that can provide a maximum pressure of 228 MPa and the pores between 0.05 μm and 1000 μm can be detected and measured. Since the MIP tests do not have strict requirement on the shape of samples, some blocks are artificially selected. The MIP tests start with an initial pressure of 0.49 Pa and end when the cumulative intrusion does not increase with increasing the pressure. The pore diameter can be calculated according to the intrusion pressure, and the variations in cumulative intrusion with a unit of mL/g versus pore diameter with a unit of nm, as well as the average pore diameter with a unit of nm and porosity versus temperature, can be obtained.

The uniaxial compression tests on the red sandstones and marbles were carried out using the MTS816 testing system, in which the normal load is automatically controlled by the electrohydraulic servo system, as shown in Figure 2. The normal load capacity of the MTS816 testing system is 1500 kN, and the normal stroke is 100 mm.

2.2. Sample Preparation

A total of 72 sandstone specimens with a diameter of 50 mm and a height of 50 mm were prepared. They were divided in to 8 groups on the average and then heated at 8 temperature levels (T=100°C, 200°C, 300°C, 400°C, 500°C, 600°C, 700°C, and 800°C), and other 8 specimens were not heated as the reference specimens (25°C). The details of heating procedure were the same as the above heating procedure for MIP tests.

2.3. Testing Apparatus

The DDT-500 loading system with a maximum load capacity of 500 kN and the variable-angle shear device with the variable-angle range of 0~70° were utilized to test the shear behavior of the specimens, as shown in Figure 3. The axial force was imposed to both ends of the variable-angle shear device with a constant loading rate of 0.2 mm/min until failure occurred. The load and displacement applied on the frame of the DDT-500 testing system were recorded synchronously at a sampling frequency of 10 HZ. The preapplied pressure was 0.5 kN. The shear angle (α) equals to 40°, 50°, 60°, and 70°, as shown in Table 1.

To characterize the evolutions of microstructures of samples treated by high temperatures, the Quanta™ 250 SEM system is used. The maximum scanning range is 50 mm in both directions of the horizontal plane. The accelerating voltage is within 200 V and 30 kV, and the sample chamber pressure can be up to 2.6 kPa. The SEM tests can be carried out under high vacuum, low vacuum, and environmental vacuum conditions, according to the requirements needed.

3.1. Pore-Related Physical Properties

Figure 4 displays the MIP test results for red sandstones. From Figure 4(a), regardless of T, the cumulative intrusion displays an increasing trend with a decreasing pore diameter. The variations in cumulative intrusion versus pore diameter can be divided into 3 stages. In the first stage, when pore diameter exceeds 104 nm, the cumulative intrusion slightly increases with the decrement of pore diameter. In the second stage, the cumulative intrusion rapidly increases as pore diameter increases from 104 nm to 103 nm. In the third stage, as pore diameter is less than 103 nm, the increasing rate of cumulative intrusion becomes slower again. These variations preliminarily indicate that the diameter of pores of red sandstones with different temperature levels is mostly between 103~104 nm. For a given pore diameter, the cumulative intrusion is smaller in the range of 100~400°C than that at the room temperature, but it is larger in the range of 500~800°C. This indicates that the pore volume of red sandstones is negatively correlated with temperature when T400°C, whereas it is positively with temperature when T>400°C. The variations in dVp/dlogD versus pore diameter of red sandstones are shown in Figure 4(b). It can be obviously known that the pore diameter of red sandstones after thermal treatment fastens on 103~104 nm as well.

The relationships between average pore diameter of red sandstones and T can be divided into 2 stages (see Figure 4(c)). First, as T increases from 25°C to 200°C, the average pore diameter exhibits a decreasing trend from 107.09 nm to 48.22 nm. Second, in the T range of 200 ~800°C, average pore diameter mainly increases from 48.22 nm to 135.19 nm with the increment of T except it slightly decreases at 700°C. Figure 4(d) depicts the relationships between porosity of red sandstones and T, which is divided into ascent, descent, and steady stages. In the ascent stage, the porosity slowly decreases from 0.093 to 0.068 as T increases from 25°C to 400°C. In the descent stage, when T increases from 400°C to 600°C, the porosity sharply increases from 0.068 to 0.144. In the steady stage, the porosity fluctuates between 0.144 and 0.133 when T exceeds 600°C. The increment of T induces the closure of pores of red sandstones in lower temperature range (T400°C) while it leads to the expansion of pores in higher temperature range (T>400°C). The results imply that 400 ~600°C can be regarded as the critical temperature range to evaluate the variation in pore characteristics of red sandstones.

The MIP test results for marbles are shown in Figure 5. From the variation in cumulative intrusion versus pore diameter (see Figure 5(a)), in the T range of 25 ~700°C, the cumulative intrusion slowly increases as pore diameter decreases from 106 nm to 102 nm, whereas it significantly increases when pore diameter is less than 102 nm. Specifically, 103 nm is the threshold value to decide the sudden increment of cumulative intrusion with a decrease in pore diameter when T=800°C. Under a specific pore diameter, the cumulative intrusion generally is larger with the higher T. It tentatively shows that high temperature causes the increment of pore diameter of marbles. Figure 5(b) presents the variations in dVp/dlogD versus pore diameter. The variations show that the pore diameter of marbles with different temperature levels mostly fasten on 101 ~103 nm and it mainly enlarges with an increase in T. It can be also known that the temperature is positively with the pore diameter of marbles.

The relationships between average pore diameter of marbles and T can be divided into 2 stages as shown in Figure 5(c). As T rises from 25°C to 500°C, the average pore diameter slightly enlarges from 23.96 nm to 43.36 nm at a rate of 0.04 nm/°C in general. However, it suddenly increases from 42.67 nm to 107.51 nm at a rate of 0.22 nm/°C as T increases from 500°C to 800°C. Similarly, the relationships between porosity of marbles and T fall into steady and ascent stages as shown in Figure 5(d). In the steady stage, the porosity is near 0.04 when T500°C; in the ascent stage, the porosity increases from 0.037 to 0.104 as T rises from 500°C to 800°C. Therefore, 500 ~600°C can be treated as the critical range to assess the variation in pore characteristics of marbles.

3.2. Mechanical Behaviors under Uniaxial Compression Tests

Figure 6 plots the stress-strain curves for red sandstones and marbles under uniaxial compression tests. From Figure 6(a), regardless of T, the failure mode of red sandstones under uniaxial compression conditions displays obvious brittle characteristics. The shapes of strain-stress curves after thermal treatment of 25 ~400°C are similar to each other, which can be mainly divided into initial compaction stage, linear elasticity stage, and failure stage. However, different from the shape of curves corresponding to 25 ~400°C, the curves corresponding to 500 ~800°C include initial compaction, linear elasticity, elastic-plastic, and failure stages. The above results indicate that high temperature leads to an increase in plasticity of red sandstones. As shown in Figure 6(b), the failure mode of marbles under uniaxial compression condition also displays brittle properties. But different from red sandstones, the stress-strain curve of marbles with different temperature levels includes more than one peaks, which is on account of many relatively obvious weak surfaces of marbles after thermal treatment.

The variations in peak strength and peak strain of red sandstones and marbles under uniaxial compression conditions versus T are as shown in Figure 7. The peak strength of red sandstones under uniaxial compression conditions substantially increases first and then decreases with the increment of T. In the range of 25 ~400°C, peak strength slowly increases from 50.84 MPa to 75.37 MPa due to the closure of pores of red sandstones with the increment of T, which is proven by the relationships between porosity of red sandstones and T. Peak strength decreases from 75.37 MPa to 36.41 MPa when T rises from 400°C to 700°C while it suddenly enlarges from 36.41 MPa to 58.75 MPa as T increases from 700°C to 800°C. This descent trend is attributed to the generation of cracks of red sandstones under the high temperature conditions, which is related with the uneven expansion of material compositions of rocks. It can be known that 400 ~600°C is a critical T range to determine the variations in uniaxial compression strength of red sandstones. The peak strength of marbles under uniaxial compression conditions exhibits a first decreasing, then increasing and decreasing again trend. When T300°C, peak strength slowly decreases from 60.61 MPa to 29.96 MPa at a rate of 0.11 MPa/°C. In the range of 300 ~600°C, peak strength slowly increases from 29.96 MPa to 115.52 MPa at a rate of 0.29 MPa/°C with the increment of T. As T rises from 600°C to 800°C, peak strength decreases again from 115.52 MPa to 34.24 MPa at a rate of 0.41 MPa/°C. From the results, 300°C and 600°C can be regarded as the turning temperatures for the variations in peak strength of marbles under uniaxial compression conditions. Figure 7(b) shows the variations in peak strain of red sandstones and marbles under uniaxial compression conditions. The peak strain of red sandstones mainly exhibits a slowly increasing trend as T rises from 25°C to 800°C. With a larger T, the peak strain of marbles diminishes first and then enlarges. Concretely, peak strain decreases from 0.00995 to 0.00411 as T increases from 25°C to 300°C while it increases from 0.00411 to 0.01293 as T increases from 300°C to 800°C. These indicate that the ductility of red sandstones gradually enhances while the ductility of marbles weakens first and then enhances with the increment of T.

3.3. Evolutions of Cohesion and Frictional Angle during Variable-Angle Shearing Tests

Figure 8 displays the shear-axial displacement curves of red sandstones for different α during variable shearing tests. Similar with the failure mode under uniaxial compression conditions, the failure mode of red sandstones under variable shearing conditions substantially exhibits obvious brittle characters. Regardless of T, the shear-axial displacement curves are of multipeaks when α=60° and 70° while the curves are of one peak as a whole when α=40° and 50°. The axial displacement gradually decreases because the shear stress increases with the increment of α.

The relationship between shear strength (τ) and T falls into 3 stages (see Figure 9(a)). In the range of 25 ~400°C, the shear strength mainly displays an increasing trend with an increase in T. When 400°C<T<700°C, the shear strength gradually decreases with an increasing T. However, as T increases from 700°C to 800°C, the shear strength increases again. The cohesion (C) and frictional angle (φ) can be calculated using the Coulomb criterion, as written in the following equation.
(1)τ=C+σtanφ.

The variations in C and φ can be divided into 3 stages as shown in Figure 9(b). As T rises from 25°C to 400°C, C increases first and then tends towards stability while φ decreases first and then stabilizes. In the range of 400 ~700°C, C gradually decreases but φ mainly increases with the increment of T. However, as T increases from 700°C to 800°C, C suddenly increases and φ decreases. Based on the MIP tests results for red sandstones with different T, the variations in the τ, C, and φ in the range of 25 ~400°C are mainly attributed to the closure of pores of sandstones with an increasing T. The fractures of red sandstones generating under the high temperature condition result in the variations in the τ, C, and φ as T rises from 400°C to 700°C. And the τ, C, and φ change again as T rises from 700°C to 800°C probably because of the increasing average pore diameter. Hence, 400 ~600°C can be treated as the critical range to describe the shear properties of red sandstones with different temperature levels.

3.4. Failure Modes before and after Uniaxial Compression Tests and SEM Analysis

As shown in Figure 10, the surface of red sandstones gradually brightens with the increment of T, preliminarily indicating that the material compositions of red sandstones change as T increases. From the sketches in Figure 10, there are mainly vertical cracks occurring when T200°C, which result from the tensile failure. However, in the range of 300 ~800°C, the surface cracks are composed of the broken-line cracks which result from the tensile and shear damages. The variations in rock failure mode are closely related to the pore structure of red sandstones after thermal treatment. Similarly, the surface of marbles gradually brightens because of the variations in compositions of rocks as T increases (see Figure 11). From the sketches in Figure 11, the failure mode of marbles after heating is obvious tensile failure. When T100°C, there are several tiny cracks existing on the surfaces, whereas no crack occurs when T100°C, before tests. After tests, the opening of surface cracks gradually enlarges with an increasing T.

On the basis of marble fragments after uniaxial compression tests (see Figure 12), the SEM tests were conducted to investigate microscopically the cracks of marbles after thermal treatment. As shown in Figure 13, the surfaces of marble fragments according to the different temperature levels are relatively coarse. Concretely, in the range of 25 ~400°C, there are a large number of micro pores but no obvious microcracks exist. However, for T500°C, several microcracks can be observed in the SEM images. These SEM images indicate that the pore and crack structure of marbles are gradually developed with the increment of T, which is consistent with the MIP tests results of marbles with different T.

The mechanical characteristics of red sandstones and marbles after thermal treatment are closely related to variations in the pore and crack structures, material compositions, and grain expansion of rocks with different temperature levels. For red sandstones, in the range of 25 ~400°C, the grain expansion induces the closure of pores and the thermal stress can accommodate deformation with an increasing temperature, leading to the increase in the strength [4, 5, 8, 32]. However, as T increases from 400°C to 600°C, the quartz of red sandstones becomes from α-phase to β-phase [39], resulting in the developed the pore and crack structures and weakened mechanical behaviors. When T>600°C, the ductility of sandstones increases and the strength increases, too. For marbles, as T rises from 25°C to 400°C, the microcracks induce by unevenness grain expansion result in the closure of pores, fluctuant porosity variation, and decrease in strength [4, 7, 20]. As T increases from 400°C to 600°C, the increasing ductility of marbles causes the strengthened mechanical properties with the increment of T. When T increases from 600°C to 800°C, with the decreasing Ca and increasing Si, marbles probably transform from stable crystalline state to unstable amorphous state expanding the volume of the sample, leading to the increase in porosity and decrease in strength.

Comparing with the red sandstones and marbles at a room temperature, the red sandstones and marbles after high-temperature exposure exhibit reductions in strength and elastic characteristics on account of thermally-induced damage. Therefore, the thermomechanical behaviors of surrounding rocks should be investigated when designing geological applications such as reconstruction after fire, deep mining projects, deep nuclear waste disposal facilities, and enhanced geothermal system. As temperature increases, there are some obvious variations in the physical and mechanical behaviors of red sandstones and marbles, inducing severe structural failures. Besides, the failure modes of red sandstones and marbles would change between brittleness and ductility because of high temperature. Most of the current experimental tests are carried out in laboratory, and the effect of confining pressure on the thermal treatment–induced evolutions of mechanical properties is not taken into account, which however is commonly encountered in deep mining and/or geothermal applications. Thus, there are some considerations about the proper criteria when applying to the engineering design and/or numerical simulations.

The influence of temperature on the physical and mechanical behaviors of red sandstones and marbles was experimentally investigated in this study. The MIP and SEM tests were conducted to evaluate the thermal-induced damage of micro pores and crack structures of red sandstones and marbles, which were used to interpret the macro mechanical characteristics.

The results show that with the increment of temperature, the porosity of red sandstones decreases first and then increases, whereas porosity of marbles keeps stable first and then increases. As the temperature rises from 25°C to 800°C, the uniaxial compression strength of red sandstones enlarges first and then diminishes while the peak strain gradually enlarges. The compression strength of marbles exhibits a first decreasing, then increasing, and finally decreasing trend while peak strain exhibits a first decreasing and then increasing trend with an increase in temperature. The high temperature induces the shear strength of red sandstones to increase first and then decrease. As temperature rises, the cohesion of red sandstones increases first and then decreases. However, the frictional angle of red sandstones decreases first and then increases. The failure pattern of red sandstones under uniaxial compression conditions transforms from tensile failure to tensile-shear failure, whereas the failure mode of marbles mainly is typical tensile failure. From SEM images of marbles, there are obvious microcracks occurring when temperature comes up to 500°C.

The data are available by contacting the corresponding author.

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.

This study has been partially funded by Natural Science Foundation of China, China (Grant nos. 51979272, 41907251, and 52179098), International Science and Technology Cooperation Plan of Jiangsu Province, China (Grant no. BZ2020066), and Natural Science Foundation of Fujian Province of China (2019J05030). These supports are gratefully acknowledged.

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