Introduction

The effect of temperature on the rock has been widely concerned in recent years for underground geological engineering projects such as underground coal gasification, geothermal exploitation, and utilization (Fan et al. 2018, 2020). In some cases, including fracturing technology, the high-temperature rock is inevitably subjected to rapid cooling treatment. At present, hydraulic fracturing has been verified to be an effective stimulation technology to improve reservoir rock permeability and is widely used in geothermal energy industries (Olasolo et al. 2016; Sha et al. 2020). However, hydraulic fracturing has the disadvantages of wasting water resources and polluting the environment due to the attachment to water (Sha et al. 2020). Liquid nitrogen (LN2), as an environment-friendly and clean inert cryogenic liquid, has been currently confirmed to have great potential in improving the fracture network of coalbed methane. Besides, as an effective coal extinguishing agent, it can significantly reduce the fire threat to underground coal mining (Fu-Bao et al. 2015; Shao et al. 2018; Shi et al. 2018). In these cases, when relatively low-temperature fluids (such as water and LN2) contact high-temperature rocks, the sharp temperature change is accompanied by the generation of thermal stress, resulting in damage (Li et al. 2020b). Therefore, exploring the physical and mechanical properties after different cooling treatments can lay a theoretical foundation for underground coal gasification and geothermal energy mining.

Consequently, a series of studies on the mechanical behavior of rock induced by heating have been conducted (Brotons et al. 2014; Jha et al. 2016; Lu et al. 2017; Fan et al. 2017; Ersoy et al. 2019; Meng et al. 2019; Peng et al. 2019; Sirdesai et al. 2019). Some basic knowledge about the effect of temperature on rock properties was obtained. Namely, heating treatment led to the change in rock properties. Specifically, the changes in physical and mechanical properties of rocks after high temperature were attributed to mineral decomposition (Yin et al. 2018a; Wang et al. 2019) and transformation of the crystal structure (Yin et al. 2018b; Liu et al. 2019). The mechanical properties of granite under different high temperatures were studied with uniaxial compression tests through real-time loading at high temperature (25–850 ℃) and reloading after cooling at high temperature (25–1200 ℃); the results demonstrated that the uniaxial compressive strength and elastic modulus of granite continuously deteriorated and the P-wave velocity gradually decreased with the increasing heating temperature (Zhang et al. 2011). It suggested that intergranular fracture was the primary form of thermal cracking. With the increase of the thermal treatment temperature, trans-granular cracks significantly increased. Besides, micro-voids and large inter-granular cracks may become new damage sources of thermal cracking.

Regarding cooling treatments, some previous studies have focused on the effect of water quenching on high-temperature rocks. For instance, the mechanical behavior of granite after water cooling under different thermal cycles was explored by uniaxial compression experiments (Zhu et al. 2020). The results revealed that the deterioration mechanism of granite physical and mechanical properties was primarily caused by the generation and propagation of microcracks. With the increase in thermal cycles, the micro-crack density slowly increased, and the extreme quenching effect of water aggravated the energy degradation of granite’s physical and mechanical properties. Acoustic emission (AE) system was also used to study the corresponding fracture propagation mode (Kumari et al. 2017; Ge and Sun 2018). The results indicated that the failure mode of granite changed from brittle fracture to semi-brittle fracture with the increasing temperature. The rapid cooling of water led to the further development of pore cracks, which further reduced the strength. The effects of natural cooling and water cooling on granite’s physical and mechanical properties under different temperature treatments have also been compared (Kumari et al. 2017; Zhang et al. 2020a; Li et al. 2020a). It was demonstrated that with the increase in the treatment temperature, the wave velocity, uniaxial compressive strength, and elastic modulus of granite gradually decreased while the failure strain gradually increased. Compared with natural cooling, the wave velocity decreased more extensively, and the strength and elastic modulus were lower after water cooling. Wang et al. (2017) investigated the dynamic characteristics of red sandstone under repeated thermal shock caused by cyclic heating and water cooling treatment, revealing that the trans-crystalline fracture accompanied the high strain rate in cooling samples. Rathnaweera et al. (2018) analyzed the thermal degradation of Hawkesbury sandstone and discussed the mechanical weakening effect of sandstone cooled by water from a mineralogical perspective.

Besides, LN2 has been used as a potential fire extinguishing agent and fracturing fluid. Some pioneering studies on the characteristics of LN2 treatment rocks were carried out. Wu et al. (2018) studied the effect of LN2 freezing treatment on high-temperature shale (25–260 °C) through experiments, discovering that LN2 freezing treatment significantly damaged shale and produced apparent cracks on the surface of shale. The size and number of these cracks increased with the temperature increase; the noticeable cracks induced by LN2 freezing treatment led to the increase in permeability, the decrease in uniaxial compressive strength and wave velocity; the effect of high cooling rate on thermal stress was confirmed through numerical simulation. In the previous studies (Zhang et al. 2018a, b; Qin et al. 2018; Wu et al. 2019b), the physical and mechanical properties were explored in high-temperature granite specimens sprayed with LN2. The experiments indicated that LN2 significantly reduced the strength characteristics and improved the permeability of granite specimens. Zhang et al. (2018a, b) analyzed rock’s thermal characteristics during LN2 fracturing based on the three-dimensional numerical model. The simulation results illustrated that the thermal stress was concentrated near the solid–liquid interface in tensile stress, contributing to the generation of thermal cracks in the rock. Considerable studies have been carried out on the effects of water and LN2 cooling on the physical and mechanical properties of rocks from the quasi-static perspective. At the same time, there were few reports about the effect of dynamic load. However, underground projects are inevitably disturbed by dynamic loads such as underground coal seam explosions caused by fire and construction vibration.

Generally, underground coal gasification occurs in very deep coal seams, mainly surrounded by sandstone and siltstone (Rathnaweera et al. 2018). Some studies have focused on the physical and mechanical properties of sandstones, including the influence of the length–width ratio on the stress–strain characteristics of the sandstones (Munoz and Taheri 2017) and the deterioration of static and dynamic physical and mechanical properties after the freeze–thaw cycle (Zhang et al. 2018a, b; Zhang et al. 2019). In addition, the failure behaviors of sandstone under cyclic loading were investigated. The results illustrated that when the cyclic loading stress was lower than the fatigue threshold stress, the sandstone sample did not fail. Contrary, when the loading stress exceeded the fatigue threshold stress, the brittleness of the sample increased with the increase of applied stress (Faradonbeh et al. 2021).

In some cases, sandstones suffer high-temperature and cooling shock and dynamic load at the same time (Fan et al. 2013, 2021). Considering these situations, the physical and dynamic mechanical properties of high-temperature sandstone under natural, water, and LN2 cooling were investigated in this study through a series of mechanical tests. Besides, the evolution of P-wave velocity, dynamic strength, strain, and elastic modulus was analyzed. The average fragmentation size was defined by the screening experiment. Under different cooling treatments (natural cooling, water cooling, and LN2 cooling), the fragmentation degree of high-temperature sandstone was discussed, and the damage mechanism of thermal-treated sandstone was analyzed. The experimental results are expected to provide a sufficient theoretical basis for the development and utilization of geothermal resources and underground coal gasification.

Materials and methods

Specimen preparation

In this study, the sandstone samples were selected from Yunnan Province, China, a typical sedimentary rock with a uniform red surface (Fig. 1b). X-ray diffraction (XRD) results illustrated that the sandstone is composed of 63% quartz, 12.8% calcite, 10% plagioclase, 8.5% clay minerals, and 3.2% potash feldspar, 1.7% hematite, and 0.8% mica (Fig. 2). Samples with similar wave velocities were selected for testing to reduce the difference between the specimens. All specimens were processed into standard rock samples with a diameter of 50 mm and a height of 25 mm (a length-diameter ratio of 0.5) to satisfy the hypothesis of stress uniformity (Dai et al. 2010; Wang and Hao 2017; Zhang et al. 2020b). Both ends were carefully polished to ensure that the surface flatness was within 0.05 mm according to the previous study (Fan et al. 2017), as illustrated in Fig. 1a.

Fig. 1
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Sandstone specimens. a Geometric dimension. b Cross section

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Fig. 2
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XRD results of the sandstone. a Percentage of minerals of the sandstone. b Content of minerals of the sandstone

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Heating and cooling treatment

In the present study, five target temperature levels were set as 25 ℃, 200 ℃, 400 ℃, 600 ℃, and 800 ℃, and three specimens for each expected temperature were used to study the effect of heating and cooling treatments on the dynamic mechanical properties of sandstone.

The thermal treatment was accomplished by a high-temperature furnace, as exhibited in Fig. 3. It has a maximum of 1200 ℃ and an accuracy of 1.0 ℃. In addition, the high-temperature furnace is also equipped with a cooling water tank, which is used to cool the sealing rubber ring of the furnace door so that the high-temperature box has a good sealing performance, thereby ensuring the stability of the temperature. Besides, 2.5 ℃/min was chosen as the heating rate to avoid the possible thermal shock during rapid heating (Fan et al. 2017). Then, specimens were kept for 2 h under the predetermined temperature in the furnace to uniformly distribute the designed temperature (Yin et al. 2019). Subsequently, the specimens were removed from the furnace. Three different cooling treatments were applied immediately to the specimens, including rapid cooling of water and LN2 for 1 h (Wu et al. 2019a; Yu et al. 2020) and natural cooling in an open atmosphere for 6 h. For water cooling, the sample was fully immersed in a 20 L water tank. In addition, due to the high temperature of 600 °C and 800 °C, the heated hot water was also replaced by water circulation to ensure the cooling effect. Since the gasification temperature of LN2 is extremely low, to prevent excessive volatilization of LN2, a foam box with good thermal insulation was used for LN2 cooling, and LN2 was replenished in time, so that the sample was completely immersed in LN2 during the cooling process. The average cooling rate of water cooling is about 71.4–156.2 ℃/min, that of LN2 cooling is about 133.3–188.8 ℃/min, and that of natural cooling is about 5.1–14.3 ℃/min. With the purpose of reducing the impact of moisture content when all samples were cooled to room temperature, they were put into a high-temperature box, dried at 60 ℃ for 3 h, and then cooled to room temperature again for further testing, as illustrated in Fig. 4.

Fig. 3
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High-temperature heating furnace

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Fig. 4
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Procedure of heating and cooling

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The appearance of the samples under different cooling methods after thermal treatment was observed, as presented in Fig. 5. Specifically, different cooling methods after heating significantly affect the generation and development of the micro-cracks on the surface of the samples. Before 400 ℃, the surface of all sandstone samples remains intact irrespective of the cooling methods. Subsequently, some visible micro-cracks first appear on the surface of the water-cooled samples when the temperature reaches 600 ℃. Afterward, apparent thermal cracks appear on the surface of both water-cooled and LN2-cooled specimens at 800 ℃. This suggests that higher heating and cooling rates cause more thermal shock damage to the sandstone samples. Moreover, the micro-cracks on the surface of the water-cooled samples show distinct connectivity at 800 ℃, which is not observed in the natural cooled and LN2-cooled samples. Through the enlarged view of the cracks at the same magnification, it can be distinctly seen that the crack of the 800 ℃ water-cooled sample is more significant than that of the LN2-cooled sample.

Fig. 5
figure 5

Specimens before and after heating and cooling

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Test procedure

Ultrasonic detector

The P-wave velocity of the specimens before heating and after cooling was measured using the HS-YS2A rock acoustic velocimeter (Fig. 6a) based on the ultrasonic pulse transmission technology. The sample was placed in the center of the exciter and receiver, with both ends of the sample coated with vaseline to reduce the attenuation of the wave velocity. Additionally, a certain force was also applied to the two sensors to make them in close contact with the sample, as displayed in Fig. 6b. Besides, the average P-wave velocity of three samples under each heating and cooling treatment was calculated as the final measurement result to ensure the reliability of the result.

Fig. 6
figure 6

Wave velocity measurement. a Wave velocity analyzer. b Sandstone sample

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SHPB test system

The uniaxial dynamic impact compression test was conducted by using the SHPB device (Fig. 7). The length of the impact bar, incident bar, and transmission bar was 600 mm, 2500 mm, and 2500 mm, respectively, and the diameters of them were all 50 mm. In the test, a copper plate with a diameter of 30 mm and a thickness of 1.0 mm was used as the pulse shaper to eliminate the influence of high-frequency oscillation (Li et al. 2016).

Fig. 7
figure 7

SHPB test system

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Based on the one-dimensional wave propagation theory, the dynamic constitutive relation can be derived using the incident signal and the reflection signal recorded by the strain gauge on the incident bar and the transmission signal recorded by the strain gauge on the transmitted bar (Xi et al. 2021). The stress–strain \(\varepsilon \left(t\right)\) and strain rate \(\varepsilon \left(t\right)\) can be calculated by the formula (1).

$$\left\{\begin{array}{c}\;\;\;\;\sigma\left(t\right)=\frac A{2A_S}E\left(\varepsilon_I+\varepsilon_R+\varepsilon_T\right)\\\;\;\;\;\;\;\varepsilon\left(t\right)=\frac C{L_s}\int\limits_0^t\left(\varepsilon_I+\varepsilon_R+\varepsilon_T\right)dt\\\varepsilon\left(t\right)=\frac C{L_s}\left(\varepsilon_I-\varepsilon_R-\varepsilon_T\right)\end{array}\right.$$
(1)

where A and As denote the cross section of the bar and specimen, mm2, respectively; Ls represents the length of the specimen, m; E indicates Young’s modulus, GPa, and C illustrates the elastic wave speed of the bar, m/s, respectively.

Results

Effect of heating and different cooling on P-wave velocity

The wave velocity of the ultrasonic wave propagating in different media was different. Based on this characteristic, the decrease of P-wave velocity could be used to reflect the propagation of micro-cracks in rock. In this study, the P-wave velocity of thermal-treated sandstone cooled by nature, water, and LN2 was measured, as illustrated in Fig. 8. The detailed values are listed in Table 1.

Fig. 8
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Effect of different cooling treatments on P-wave velocity

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Table 1 P-wave velocity of thermal treatment sandstone after different cooling treatments
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As observed in Fig. 8 and Table 1, it can be seen that the P-wave velocity of sandstone decreases as the thermal treatment temperature increases. Due to the influence of cooling methods, there is a significant difference in the reduction trend. Before the treatment temperature is 400 ℃, the average P-wave velocity decreases slightly under the three cooling treatments. When the sandstone is heated to 600 ℃, the average P-wave velocity decreases sharply because of the irreversible chemical change of quartz in sandstone and the uneven expansion of minerals (Li et al. 2020b).

Compared with natural cooling, the P-wave velocity attenuations caused by water cooling and LN2 cooling are more prominent when the treatment temperature is the same. For example, when the treatment temperatures are 400 ℃, 600 ℃, and 800 ℃, compared with room temperature, the average P-wave velocities of samples under natural cooling, water cooling, and LN2 cooling decrease by 0.69%, 11.92%, and 9.45%; 36.87%, 50.92%, and 37.67%; 54.87%, 59.10%, and 58.04%, respectively.

Based on the above comparison, it can be seen that the average P-wave velocity of water-cooled samples is the lowest at any heating temperature, further confirming that water cooling causes the most severe damage to the internal structure of the rock. It is worth noting that the average P-wave velocity of natural cooling is slightly higher than that of the original sample when the treatment temperature is 200 ℃. This is mainly because the thermal expansion coefficient of different minerals causes less uneven thermal expansion deformation among minerals when the thermal treatment temperature is low. At this time, the temperature mainly leads to the expansion of some minerals including quartz, feldspar, and mica (Sirdesai et al. 2019; Wang et al. 2019), making some initial micro-cracks close and improving the compactness of the sample (Liu and Xu 2015a; Wang et al. 2019).

SHPB test results

In the split Hopkinson pressure bar (SHPB) test, the air pressure was set to 0.25 MPa consistently, and the bullet was launched from the same position each time to avoid the influence of strain rate difference. The waveform recorded during the impact test and the stress equilibrium were showed in Fig. 9. It could be observed that the difference between the transmitted wave (TR) and the reflected wave (RE) is equal to the incident wave, demonstrating that the dynamic stress of the sample has reached equilibrium. Furthermore, the dynamic stress equilibrium of all samples was checked.

Fig. 9
figure 9

Eight hundred degree Celsius natural cooling dynamic force balance check for a typical specimen. a Typical SHPB wave (800 ℃ natural cooling). b Stress equilibrium (800 ℃ natural cooling)

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Effect of heating and cooling treatments on the dynamic stress–strain curve

The dynamic stress–strain curves of the specimens under different treatment temperatures and methods were exhibited in Fig. 10. From the figures, it can be seen that the dynamic stress–strain curves show a similar characteristic, which can be approximately divided into three stages (Fig. 10d) according to the previous study (Yang et al. 2020): (1) Stage I (elastic stage): the stress increases linearly with the strain, with a certain degree of linear elasticity. (2) Stage II (yield stage): the extension and propagation of micro-cracks; the stress increases nonlinearly as the strain increases to the peak. (3) Stage III (destroyed stage): the decline stage of the stress–strain curve; the stress decreases with the further increase in strain, and the rock breaks at this stage.

Fig. 10
figure 10

Dynamic stress–strain curves under different cooling treatments: a natural cooling; b water cooling; c LN2 cooling; d typical curve (200 ℃ water cooling)

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Interestingly, a significant compaction stage appears in the stress–strain curves when the thermal treatment temperature reaches 600 ℃ and 800 ℃ due to severe thermal damage in rocks under the three different cooling methods. Additionally, as the thermal treatment temperature increases, the dynamic peak strength decreases while the peak strain increases under the three cooling treatments. Thus, the increase in temperature can lead to an increase in plasticity and a decrease in rock brittleness. The results are consistent with the previous research (Fan et al. 2017; Yang et al. 2020).

Effect of heating and different cooling treatments on dynamic properties

The variations of dynamic peak stress of red sandstone with the treatment temperature under the three cooling treatments are illustrated in Fig. 11. The dynamic strength significantly decreases with the increase in the thermal treatment temperature. Under the condition of natural cooling, the strength increases slightly in the interval of 25 ~ 200 ℃ and then decreases as temperature rises, especially when the temperature is 400 ~ 800 ℃, the strength decreases sharply. This is principally because the non-uniform thermal expansion deformations among different minerals before 200 ℃ are small. In this temperature range, the increase of the temperature causes the expansion of some minerals in the granite and improves the compactness of the sample. With the temperature further increasing to 400 ℃, the uneven expansion of minerals significantly increases, resulting in the decrease of peak stress. When the temperature reaches 573 ℃, the quartz in the sample undergoes an irreversible phase transition, leading to a rapid reduction in the peak strength (Wang et al. 2019; Li et al. 2020b).

Fig. 11
figure 11

Effect of different cooling methods on dynamic peak stress

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The dynamic peak stress decreases linearly for the rapid cooling of water and LN2 as the temperature increases. As revealed from the fitting curve, the strength decreases much faster under these two cooling modes than under natural cooling, suggesting that rapid cooling causes significant damage to the rocks. When the treatment temperature is 200 ℃, the corresponding dynamic strengths of the specimens under water and LN2 cooling are 98.18 MPa and 109.08 MPa, which decreases by 12.34% and 2.61%, respectively, compared that at the room temperature. When the temperature rises to 800 ℃, the strength under three cooling treatments decreases to 81.41 MPa and 91.02 MPa, 27.32%, and 18.73% lower than that at the room temperature, respectively.

From the above analysis, it can be concluded that the dynamic peak stress is always the lowest under the water cooling treatment, which indicates that after the same high-temperature treatment, water cooling has the most significant effect on the dynamic peak stress of the sandstone.

Figure 12 shows the peak strain of the sandstone with thermal treatment under three different cooling therapies. The peak strain under the three cooling treatments exhibits a similar pattern, representing a growing trend with the rising thermal treatment temperature.

Fig. 12
figure 12

Effect of different cooling methods on dynamic peak strain

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When the temperature is lower than 400 ℃, the peak strain marginally changes, slightly increasing with the rising temperature. When the temperature is higher than 400 ℃ and lower than 600 ℃, the mineral composition in the rock qualitatively varies, and the micro-cracks rapidly expand, leading to a rapid increase in the strain. The peak strains of specimens under the conditions of natural, water, and LN2 cooling are 1.85%, 1.74%, and 1.61%, respectively, increasing by 62.57%, 52.90%, and 41.48%, compared with that in the room temperature.

When the treatment temperature exceeds 600 ℃, the peak strain of rock is enormous due to the further metamorphism of the rock. And when the treatment temperature is 800 ℃, the strain under the natural, water, and LN2 cooling reaches 2.48%, 2.45%, and 2.11%, respectively. Compared with the strain at room temperature, the increment under different cooling treatments is 118.19%, 115.64%, and 85.59%, respectively.

This is mainly because the rapid cooling of water and LN2 makes the temperature of sandstone sharply decrease compared with slow cooling (natural cooling). Then, the cold quenching effect increases the brittleness of sandstone and reduces the ability of plastic deformation, resulting in a slight reduction of peak strain compared with natural cooling (Liu et al. 2020).

The secant slope of the two-point line with 40% and 60% peak stress in the rising section of the stress–strain curve was selected as the elastic modulus of the sample (Liu and Xu 2015b). The calculation formula is

$${E}_{S}=\frac{{\sigma }_{1}-{\sigma }_{2}}{{\varepsilon }_{1}-{\varepsilon }_{2}}$$
(2)

where \({E}_{S}\) represents the secant modulus of elasticity, GPa; \({\sigma }_{1},{\sigma }_{2}\) indicates the 40% and 60% of the peak stress, Mpa, respectively; \({\varepsilon }_{1},{\varepsilon }_{2}\) denote the corresponding strains.

The elastic modulus of the thermal-treated samples under natural, water, and LN2 cooling was presented in Fig. 13. It can be observed from the trend of the curve before 400 ℃ that the elastic modulus slightly decreases with the increase in temperature, and the amplitude is pretty tiny. When the treatment temperature is 400 ℃, the elastic modulus under the cooling of nature, water, and LN2 decreases by 5.36%, 8.47%, and 19.41%, respectively, compared with that in the room temperature.

Fig. 13
figure 13

Effect of different cooling methods on Young’s modulus

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When the temperature exceeds 400 ℃, the elastic modulus decreases rapidly. Especially the temperature is 800 ℃, the elastic modulus decreases to 4.36 GPa, 3.81 GPa, and 2.98 GPa, respectively, compared with that in the room temperature, with a decrease rate of 68.43%, 72.41%, and 78.42% under the natural, water, and LN2 cooling treatments. It can be seen that under water cooling, the elastic modulus decreases the fastest, followed by LN2 and natural cooling. This is because the damage evolution effect resulting from the rapid cooling of water and LN2 reduces the ability of sandstone to resist deformation and thus declines the elastic modulus.

Effect of heating and different cooling treatments on crushing morphology characteristics

The rock fragments in this study after dynamic impact were collected, as displayed in Fig. 14. It illustrates that the impact fragmentation degree of sandstone increases with the rising thermal treatment temperature, changing from large block at room temperature to small block even powder at 800 ℃.

Fig. 14
figure 14

Effect of different cooling methods on crushing morphology characteristics

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When the thermal treatment temperature is low, the failure of the specimens is accompanied by the phenomenon of axial splitting corresponding to 25 ~ 400 ℃ under natural and LN2 cooling, or 25 ~ 200 ℃ under water cooling. With the increase of the treatment temperature, the fragmentation degree of the sample gradually intensifies. When the temperature reaches 600 ℃, the sample is broken into considerable small pieces under three cooling treatments, accompanied by powder generation. As the temperature continues to rise to 800 ℃, the fragmentation degree of the sample reaches the maximum under their respective cooling, the number of fragments is the largest, the size of fragments is the most minor, and the peripheral powder increases. It is worth noting that when the treatment temperature is the same, the degree of fragmentation of water-cooled samples is significantly greater than that of natural and LN2 cooling pieces.

Additionally, the rock fragments after the dynamic impact test were collected for standard sieving with different pore sizes (1.0, 2.0, 5.0, 10.0, 20.0 mm). Then, the average fragment size \(\overline{d }\) was defined to evaluate the degree of rock fragmentation. Specifically, the smaller the average fragment size, the greater the degree of rock fragmentation.

$$\overline{d }=\sum \left({r}_{i}{d}_{i}\right)/\sum {r}_{i}$$
(3)

where \({d}_{i}\) represents the average fragment size in the standard sieves of different volumes, mm; \({r}_{i}\) denotes the mass percentage corresponding to \({d}_{i}\) fragment. The calculated values are listed in Table 2.

Table 2 Average fragment size of thermal treatment sandstone after different cooling treatments
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The average fragment size with heating and cooling is illustrated in Fig. 15. With the increase of the treatment temperature, the average fragment size decreases, suggesting that the degree of rock fragmentation gradually enlarges under three cooling treatments.

Fig. 15
figure 15

Effect of different cooling methods on average fragmentation

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Under natural and LN2 cooling conditions, the average fragment size slightly decreases, and the rock splits into  several large blocks before 400 ℃. When the treatment temperature was at the interval of 400 ~ 800 ℃, the average fragment size rapidly decreases, and the degree of rock fragmentation sharply increases. Compared with that in the room temperature, the average fragment size under natural and LN2 cooling reduces by 50.45% and 71.08%, respectively, when the treatment temperature is 800 ℃.

For water cooling, the average fragment size decreases linearly with the increase in temperature. When the treatment temperature is 800 ℃, the average fragment size is only 18.66% of that at room temperature, indicating that water cooling has a significant effect on the deterioration of the mechanical properties of sandstone.

In Fig. 15, at the same temperature, the average fragment size of the rock is the smallest, and the degree of fragmentation is maximal under water cooling; the degree of fragmentation is the minimum under natural cooling. That is because some minerals of sandstone are soluble in water. Not only can the rapid cooling of water cause secondary temperature damage, but the softening effect of water can also deteriorate the mechanical properties of sandstone. For ultra-low temperature LN2, the thermal damage caused by the vast temperature difference makes the fragmentation degree greater than natural cooling.

Discussions

Thermal shock damage evolution

As described in the previous section, heating and different cooling treatments could cause significant thermal shock damage to the rock samples, which deteriorates the physical and mechanical properties of the pieces. Therefore, a damage factor related to P-wave velocity was defined to evaluate the damage degree of rock (Sha et al. 2020). The formula is

$${D}_{v}\left(T\right)=1-{\left(\frac{{v}_{post}}{{v}_{pre}}\right)}^{2}$$
(4)

where \({D}_{v}\left(T\right)\) indicates the damage factor calculated by P-wave velocity; \({v}_{post},{v}_{pre}\) represents the P-wave velocity of heated and cooled samples and untreated samples, respectively, m/s. The detailed calculation results \({D}_{v}\left(T\right)\) are listed in Table 3.

Table 3 Damage factor of thermal-treated sandstone after different cooling treatments
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The evolution of damage factors \({D}_{v}\left(T\right)\) of thermal-treated sandstone subjected to different cooling treatments is presented in Fig. 16 and Table 3. The results demonstrate that different cooling treatments have a considerable effect on the damage of sandstone. The damage factor increases with the rising temperature. Especially for water cooling, it increases linearly with the increase in temperature.

Fig. 16
figure 16

Damage factor of sandstone after different cooling treatments

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When the treatment temperature is 200 ℃, the damage factor of samples after natural, water, and LN2 cooling is − 0.089, 0.167, and 0.109, respectively. At this stage, the decrease in damage factor during natural cooling is mainly caused by the expansion of some mineral particles, which improves the compactness of the sandstone mentioned above.

When the treatment temperature is in the interval of 25 ~ 400 ℃, the growth of the damage factor is relatively slow under natural and LN2 cooling treatment, owing to the loss of free water and bound water in sandstone, as well as the propagation of initial micro-cracks induced by uneven deformation of mineral particles.

When the temperature continues to increase from 400 to 800 ℃, the damage factor significantly increases under the three cooling conditions. The reason for the rapid increase in damage factor in this stage is that the quartz transforms from α to β, and the minerals in the sandstone undergo irreversible chemical changes when the temperature reaches 573 ℃ (Wang et al. 2019; Li et al. 2020b). Simultaneously, the micro-structure of rock exhibits thermal expansion imbalance ascribed to the anisotropy of mineral particles and different expansibility at high temperatures, leading to the significant increase in micro-cracks of sandstone samples (Hartlieb et al. 2016). When the temperature is 800 ℃, the damage factor reaches the maximum value of 0.796, 0.832, and 0.824, respectively.

Besides, the damage of samples cooled by water and LN2 is much more significant than that of samples cooled by air because of the high cooling rate. The softening effect of water causes the most significant damage to water-cooled samples. Generally, the damage factor can reflect the internal damage of rock specimens with temperature and different cooling treatments, consistent with the experimental results.

Damage mechanism of heating and different cooling

The experiment results demonstrated that the higher treatment temperature and cooling rate could cause more severe damage to the sandstone, manifested in the apparent deterioration of physical and mechanical properties. The mechanisms of thermal cracking induced by both heating and cooling are illustrated in Fig. 17.

Fig. 17
figure 17

Damage mechanism of sandstone in heating and cooling process

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The sandstone interior contains minerals such as quartz, feldspar, and mica, with different thermal expansion coefficients. After the sample undergoes heat treatment, the thermal stress caused by incompatible deformation between different minerals and the evaporation of free water and bound water results in the generation and propagation of cracks (Sirdesa et al. 2017; Li et al. 2020b). The rise of temperature gradually increases the thermal stress in the rock and provides the energy for micro-crack propagation. Therefore, more significant physical and mechanical degradation is observed in the samples heated at higher temperatures.

Besides, as the main mineral of sandstone used in this study, quartz undergoes a phase transition from α to β at 573 ℃, and the volume of quartz increases by 5% in this process (Wang et al. 2019; Li et al. 2020b). Therefore, increasing the heating temperature enhances the thermal stress caused by incompatible deformation of minerals and changes the structure of minerals, causing significant damage to the sample. Meanwhile, the original pores in the rock are further developed and connected, severely reducing the physical and mechanical properties.

Moreover, when the sandstone undergoes rapid cooling, the strong cold shock produces a considerable temperature gradient, leading to the increase of thermal stress. The temperature gradient near the sample surface is much higher than that near the center of the sample because the outside of the sample contacts with the coolant first, resulting in the tensile stress on the rock surface and the compressive stress in the center (Kim et al. 2014; Sha et al. 2020). Mainly, rock, as a typical brittle material, is more prone to failure under tensile stress. Therefore, the propagation crack induced by tensile stress is a significant cause for the deterioration of rock properties for rapid cooling.

To accurately evaluate the effect of thermal shock on high-temperature sandstone, according to the results of Collin and Rowcliffe (2000), the tensile stress of rock caused by thermal shock can be calculated by the formula (5).

$${\sigma }_{t}=\frac{E\alpha \Delta T}{1-\upsilon }{f}_{\beta }$$
(5)
$${f}_{\beta }=\frac{1}{\frac{ak}{hr}+b-{ce}^{\frac{-dk}{hr}}}$$
(6)

where k, E, μ, α, and r present the thermal conductivity (W/(m K)); elastic modulus (GPa); Poisson’s ratio, thermal expansion coefficient (/K); the radius of the sample (mm), respectively; ΔT and m represent the temperature difference (℃) and heat transfer coefficient (W/m2 K) between the rock and the coolant, respectively; a, b, c, and d represent the fitting coefficients of rock.

Parameters including k, E, μ, α, and r are constant for sandstone samples heated to a specified temperature. Therefore, the tensile stress due to thermal shock is governed by ΔT and m. The heat transfer coefficient m of cylindrical sandstone sample is in the range of 200–1400 W/m2 K and 3000–39,000 W/m2 K under water-cooled and LN2-cooled conditions, respectively (Li et al. 2020a, b). fm can be calculated by the formula (6). Li et al. (2020a, b) pointed out that fm increased monotonically with the increase of heat transfer coefficient m, and the fm of sandstone samples cooled by LN2 is about 1.1–1.5 times that cooled by water. At the same time, due to the extremely low temperature of LN2 (− 196 ℃), the temperature difference ΔT between heated sandstone and LN2 is significantly higher than that between heated sandstone and water. For example, when the thermal treatment temperature is 200 ℃, the temperature difference between sandstone and LN2 reaches 396 ℃, while the temperature difference between sandstone and water is about 190 ℃, when the temperature rises to 800 ℃, the temperature difference between sandstone and LN2 up to 996 ℃, and the temperature difference between heated sandstone and water is about 790 ℃. Therefore, the tensile stress in a sandstone sample caused by LN2 cooling is more notable than that by water cooling. Moreover, through the calculation from formula (5), the tensile stress in a sample cooled by LN2 is about 2.2–4.2 times that by water-cooled at 200 ℃, and 1.4–2.5 times at 800 ℃.

Although LN2 cooling causes a more intense thermal shock to the sample than water cooling at the same thermal treatment temperature, the XRD analysis results from the above section demonstrate that the red sandstone mainly contains quartz, calcite, plagioclase, and clay minerals, and the different particles are mostly cemented together by carbonate. After the red sandstone is soaked in water, the soluble particles calcite composed of calcium carbonate minerals and carbonate will dissolve and react with water, the chemical reaction process is as formula (7). Meanwhile, a small number of clay minerals expand in volume after being soaked in water, resulting in expansion force. With the hydrolysis of calcite and carbonate and the expansion and deformation of clay minerals, the cementation of quartz and feldspar particles loses, resulting in a large number of micropores and micro-fissures in the rock. Therefore, the deterioration of mechanical properties of heat-treated sandstone after water cooling is more severe than that of LN2 cooling.

$$CaC{O}_{3}+{H}_{2}O\to {Ca}^{2+}+HC{O}_{3}^{-}+{OH}^{-}$$
(7)

Conclusion

In this study, the dynamic mechanical properties of thermal-treated sandstone under different cooling treatments (nature cooling, water cooling, and LN2 cooling) were investigated using the SHPB tests. Besides, the P-wave velocity, dynamic peak strength, peak strain, and elastic modulus were analyzed. The degree of sandstone fragmentation under dynamic compression impact was discussed. Moreover, the relationship between P-wave velocity and mechanical properties was analyzed, and the damage mechanisms of different temperatures and cooling treatments. The main conclusions are obtained as follows.

  1. 1.

    Heating and cooling treatments have a significant effect on the P-wave velocity. Under the three cooling treatments, the P-wave velocities all present a nonlinear downward trend with the increasing temperature and decrease sharply at 400 ~ 800 ℃. At each temperature level, the P-wave velocity of water-cooled sandstone is the lowest, followed by LN2 cooling and natural cooling.

  2. 2.

    With the increasing temperature, the dynamic peak stress and elastic modulus of sandstone after three cooling treatments decrease during the peak strain, and the fragmentation degree increase. Mainly, the mechanical properties of sandstone significantly decrease when the temperature is higher than 600 ℃. Besides, the rapid cooling of water and LN2 induces more pores, and the invasion of water weakens the connection between mineral particles, resulting in a further decrease in strength. Consequently, the strength of water-cooled high-temperature sandstone is lower than that of natural and LN2-cooled sandstone. And also, the strain of sandstone after water cooling and LN2 cooling is smaller than that after natural cooling.

  3. 3.

    The damage caused by thermal treatment can be attributed to the loss of water, the uneven deformation of mineral particles, and the transformation of the crystal structure. The damage induced by rapid cooling (water cooling and LN2 cooling) results from the tensile stress caused by the high-temperature gradient. Besides, the softening effect of water causes further damage to the sample.