1 Introduction

The growing energy demand and the worsening environmental pollution are two major challenges facing the world today. Exploring renewable and environmentally friendly energy resource is an effective way to address such issues. In recent decades, a special interest has been devoted to hot dry rock (HDR) geothermal energy due to its great potential in industrial and residential applications (Wyborn 2005). In general, the HDR reservoirs are composed of the compact granite or other crystalline rocks at depths in the order of 5–6 km, with a temperature variation of 150–500 °C (Potter et al. 1974; Gallup 2009; Breede et al. 2013). At present, the exploitation of HDR geothermal energy is mainly by virtue of Enhanced Geothermal System (EGS), which circularly pumps the working fluid through the doublet well configurations to achieve heat exchange (Olasolo et al. 2016; Barla 2017; Rybach 2014). Due to the ultra-low permeability of reservoir matrices, the permeability enhancement technology has to be taken to improve the thermodynamic efficiency and productivity of EGSs.

In terms of the current field applications, hydraulic fracturing is a common means to enhance the permeability of unconventional reservoirs. It is reported that more than 90% of shale gas wells and 70% of oil wells in the world are required to carry out large-scale hydraulic fracturing for effective exploitation (Brannon 2010). However, due to the high reliance on water, hydraulic fracturing cannot avoid the disadvantages of waste of water resources, clay hydration swelling and environmental pollution (Sinal and Lancaster 1987; Jackson et al. 2013; Bahrami et al. 2012; Boudet et al. 2014). To solve these problems, a novel waterless fracturing technology, liquid nitrogen (LN2) fracturing, is proposed and gradually developed during the past decades (Li et al. 2016). As the fracturing fluid, LN2 is a colorless, tasteless, and inert liquid with an extremely low temperature of about -196 °C at normal atmospheric pressure (Jacobsen et al. 1986). Unlike the traditional hydraulic fracturing processes, LN2 fracturing does not cause the issues associated with the use of water-based fracturing fluids, as well as has the advantages of cleanliness, low price and high construction safety (Wang et al. 2016).

LN2 fracturing is first proposed by Shouldice (1964) to assist drilling and completion operations. In the 1990s, it was also successfully applied in coalbed methane and shale gas extraction (McDaniel et al. 1997; Grundmann et al. 1998), which verifies the feasibility of cryogenic fracturing with LN2 for reservoir stimulation. In recent years, a great deal of experimental works has been conducted to investigate the effect of LN2 freezing on the physico-mechanical properties and microstructure of rocks at room temperature (Finnie et al. 1979; Inada and Yokota 1984; McDaniel et al. 1997; Cai et al. 2014a, b, 2015; Qin et al. 2016, 2017; Yang et al. 2017b; Han et al. 2018; Wu et al. 2018; Gao et al. 2018). The results from these studies revealed that the cryogenic LN2 had outstanding performance in enhancing the connectivity of pore structure, promoting the expansion of thermal cracks, and reducing mechanical strength of rocks. To systematically study the damage characteristics and mechanisms of cryogenic fracturing, Cha et al. (2017) developed a laboratory system for cryogenic fracturing under true-triaxial loading conditions, which can perform LN2 fracturing on 20 cm cubic rock blocks. On this basis, Alqatahni et al. (2016) conducted a series of LN2 cryogenic fracturing experiments on concrete, sandstone and shale samples under different stress conditions. The results showed that the fracturing effect could be improved by increasing the injection of LN2, and the expansion direction of fracturing fractures was obviously controlled by the magnitude and anisotropy of confining pressure. Wu et al. (2019) performed a transient fluid-thermo-structural coupling simulation to investigate the cooling effect during LN2 jet impingement. According to the results, LN2 jet induced higher tensile and shear stresses in rocks, thus could achieve better rock-breaking performances than water jet. Qin et al. (2018a, b) conducted a comparative study on the heat and mass transfer process and fracture propagation behaviors of coal samples under single and cyclic LN2 injection conditions. They pointed out that the fracturing efficiency of the cyclic LN2 injection is far higher than that of single LN2 injection. From their results, the damage of coal sample after a single LN2 injection treatment was mainly concentrated in the area adjacent to the injection tube, while cyclic injection method notably expanded damage area and form a propagated fracture network in rocks.

In comparison, cryogenic fracturing is a relatively novel fracturing technology that has not been well investigated in either laboratory or field. According to the literature review, most previous studies were mainly focused on the oil and gas reservoir rocks at room temperature (e.g., coal, shale and sandstone), and few researches have been done on high-temperature crystalline rocks in HDR reservoirs. In addition, although LN2 has been demonstrated to have great potential for reservoir stimulation, the feasibility and effectiveness of cyclic LN2 fracturing in HDR reservoir are still unclear. The aim of this paper is to investigate the influence of cyclic heating––LN2 cooling on the physico-mechanical behaviors of granite. The granite samples were subjected to 0–24 heating–cooling cycles in two ways, i.e., slow heating to 300 °C followed by air cooling or LN2 cooling. A comparative analysis was conducted to studied the variations in the physico-mechanical behavior of granite after different heating–cooling cycles. In addition, the development of microcracks within the sample was evaluated based on acoustic emission (AE) monitoring and microscopic observations. Meanwhile, the damage evolution and mechanisms of the granite under cyclic heating–cooling cycles were revealed. It is expected that the results of the present study would provide some new insights for extracting geothermal energy assisted by cyclic LN2 fracturing.

2 Materials and Methodology

2.1 Rock Sample Characterization

Granite is an igneous crystalline rock that form by crystallization of certain slow-cooling magma invading the upper formation. It is reported that more than 60% of the EGSs are performed on granite formations (Potter et al. 1974; Breede et al. 2013; Vidal and Genter 2018). Therefore, the granite is selected in this study to carry out relevant experiments. The rock material was collected from a mine located in Macheng City, Hubei Province, China. The mineral composition of the granite is obtained by X-ray diffraction analysis, as presented in Table 1. It is seen that the main mineral compositions of the granite sample are feldspathic minerals and quartz. Figure 1a presents the microstructure of the granite observed from thin slice. From the figure, the internal structure of the rock is intact in natural state, and the minerals are tightly bound together.

Table 1 Mineral composition of the granite sample
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Fig. 1
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a Microstructure of granite observed from the thin slice, and b photograph of the prepared standard cylindrical and disk samples

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To conduct uniaxial compression tests and Brazilian splitting tests, the cylindrical samples (Φ50 × 100 mm) and disk samples (Φ50 × 25 mm) were prepared in strict accordance with the specifications recommended by ISRM (Ulusay and Hudson 2007), as shown in Fig. 1b. The ends of all samples were carefully grind and polished to ensure flatness at both ends of less than 0.02 mm. Visual inspection reveals that the granite sample has a uniform texture and no visible defects. Prior to conduct thermal treatments, the physico-mechanical properties of granite samples subjected to 7 days of air drying were measured and tested, and the main results are summarized in Table 2.

Table 2 Summary of physico-mechanical properties of granite sample before treatment (mean ± standard deviation)
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2.2 Cyclic Heating–Cooling Treatment and Nomenclature

The heating processes of rock samples were carried out in a SX3-10-12 box-type resistance furnace. Since the temperature of geothermal reservoirs currently exploited is generally lower than 350 °C (Bertani 2005; Breede et al. 2013), 300 °C was selected as the predetermined thermal treatment temperature in this study. A slow heating rate of 5 °C/min was employed during heating to ensure that the microcracks within the rock are not a result of thermal shock (Dwivedi et al. 2008; Yavuz et al. 2010). After attaining the target temperature, the rock samples were held thermostatically in the furnace for 4 h to sufficiently heat. Subsequently, the samples were cooled to room temperature in two different ways: (1) rapid cooling by LN2 immersion (i.e., LN2 cooling), and (2) slow cooling in the atmospheric environment (i.e., air cooling). At this point, one heating–cooling cycle was complete. A total of seven heating–cooling cycles were set in the present study, i.e., 0 (no heating–cooling treatment), 1, 3, 6, 12, 18 and 24. Figure 2 shows the schematic of these two types of heating–cooling cycles. To improve the reliability of the experimental results, three repeated experiment were carried out on the cylindrical and disk samples under each cycle cooling condition. For the sake of convenience, the granite sample after LN2 cooling is referred to as “LG” in this study, and the sample after air cooling is referred to as “AG”.

Fig. 2
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Schematic o of cyclic heating–cooling process

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2.3 Instrument and Test Procedure

Prior to mechanical testing, the physical properties of the sample, such as mass (M), bulk volume (V), porosity (n) and P-wave velocity (Vp), were first measured before heating and after cooling. The M and size (i.e., height and diameter) of the rock were measured separately using electronic balance and vernier caliper, both with an accuracy of 0.01. To reduce the measurement errors, the height and diameter were measured three times at different positions of the sample and then averaged. The V and density (ρ) of the granite can be easily obtained based on the above measurement results.

As per ISRM-recommended method (Ulusay and Hudson 2007), n of the granite sample was measured utilizing a ZK-270 vacuum saturation device. First, the rock sample was immersed in water under the vacuum pressure of 0.1 MPa for 24 h to reach saturation. After drying surface, the sample was weighted to determine the saturated-surface-dry mass. Thereafter, the saturated sample was dried at 105 °C for 24 h by virtue of an air-dry oven, then weighted again to obtain the grain mass. The porosity of the specimen can be determined as

$$n = \frac{{100V_{v} }}{V}\% ,$$
(1)

where Vv is the pore volume, and V is the bulk volume. Vv can be calculated by the following equation:

$$V_{v} = \frac{{M_{{{\text{sat}}}} - M_{s} }}{{\rho_{w} }},$$
(2)

where Msat is the saturated-surface-dry mass, Ms is the grain mass, and ρw is the density of water.

Vp is highly sensitive to the growth of micro-defects within the tested material (Homandetienne and Troalen, 1984; Chaki et al. 2008), therefore, it can be used to qualitatively evaluate the level of microstructural damage of the samples after different heating–cooling treatments. In this study, Vp of the granite sample was measured utilizing an RSM-SY5(T) acoustic detector based on the ultrasonic pulse transmission technique. The sample was placed between the two transducers, and a constant pressure was applied to bring them into close contact. In the meantime, the interfaces between the sample and the transducers were coated with a layer of Vaseline film to ensure energy effectively transfer. Under each heating–cooling cycle, Vp measurement was performed on three cylindrical samples, and repeated five times for each sample. The average Vp was then calculated as the final measurement result.

In this study, the mechanical properties of the granite sample were tested employing a hydraulic servo-controlled compression system (TAW-3000), which has a maximum loading capacity of 3000 kN and an accuracy of 0.01% (see Fig. 3a). The Brazilian splitting method was utilized to determine the tensile strength of rock sample because of its convenience in preparing samples and conducting tests (Perras and Diederichs 2014; Sha et al. 2019). Figure 3b shows the loading configuration used in the Brazilian splitting test, which consists of two loading platens and two small-diameter steel rods. This configuration enables the line load to pass through the tested sample along the diameter. Throughout the test, a constant loading rate of 200 N/s was applied on the disk sample until failure according to the suggestions of ISRM (Ulusay and Hudson 2007). The axial load and axial displacement were automatically recorded by the load control software. Three disk samples were tested under each cycle condition. The Brazilian tensile strength (BTS) can be calculated by the following equation:

$$\sigma_{t} = \frac{2P}{{\pi dt}},$$
(3)
Fig. 3
figure 3

Photographs of a TAW-3000 hydraulic servo-controlled compression system; b Brazilian splitting test loading configuration; and c cylindrical specimen assembled with two LVDT and eight AE transducers

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where σt is BTS of the sample, P is the load at failure, d is the diameter of the sample, and t is the thickness of the sample.

The unconfined compression tests were conducted to determine the uniaxial compressive strength (UCS) and deformation behavior of the granite samples subjected to different heating–cooling cycles, and three cylindrical samples were tested for each treatment condition. As shown in Fig. 3c, the axial and lateral linear variable differential transformers (LVDT) were used to measure the deformation in the corresponding direction during compression. The measurement ranges of axial and lateral LVDTs are 2.5 and 6.5 mm, respectively, and both have an accuracy of 0.01%. Before conducting the compression tests, the two LVDTs were carefully calibrated to ensure the veracity of deformation data. Under the load controlled by axial deformation, the rock sample was compressed at a rate of 0.02 mm/min until failure.

In addition, AE technology was also employed in this study to monitor the microcrack activity of rocks during compression in real time. As pointed out by Mansurov (1994), AE is a phenomenon in which the strain energy is suddenly released in the form of transient elastic waves since the structure of a material changes under external force. It can reflect the initial damage and the progressive failure processes of rocks, thereby is widely used in the field of rock mechanics (Hardy 1994; Kim et al. 2015). In the present study, the AE parameters of the granite sample during compression test were recorded by a DS2 series full information AE signal analyzer. For purpose of covering the volume of the rock sample as completely as possible, eight AE piezo ceramic transducer were symmetrically mounted approximately 25 mm away from both ends of the sample by means of the conversion devices (see Fig. 3c). Moreover, the interfaces between the AE transducers and the conversion devices were coated with Vaseline film to achieve a good acoustic coupling (Zhang et al. 2015; Zhao et al. 2013). The coupling effect between them was checked through the pencil lead fracture tests, in which the amplitude of the AE signals caused by the pencil leads fracturing should be not less than 95 dB. To reduce the effect of environment noise and ensure the reliability of AE signals, the gain value of the pre-amplifier and he threshold for AE detection were set to 40 dB and 50 dB, respectively (Rong et al. 2018).

3 Experimental Results and Analysis

3.1 Changes in Physical Properties

3.1.1 Mass, Volume and Density

Figure 4 shows the changes in M, V and ρ of granite samples after different heating–cooling treatments. It can be seen that as the number of cycles increases, the decline magnitude of M gradually increases, while the reduction rate shows a downward trend (see Fig. 4a). Actually, the dehydration of minerals one of the primary factors leading to the reduction in M of the sample. Previous researches have shown that minerals in the rock generally undergo different dehydration reactions at different temperature intervals (Sun et al. 2015). For instance, the absorption water will escape from the surface of the mineral or the pores between minerals at around 100 °C, and the crystal water can get rid of the constraint of the mineral lattice before 400 °C (Zhang et al. 2016; Hu et al. 2018). The repeated heating treatments gradually enhance the dehydration effect of minerals, thereby resulting in a continuous reduction in M of the granite sample. In addition, fine surface grains on the sample may flake in the process of cyclic heating–cooling, which is also the reason for the decrease of M.

Fig. 4
figure 4

Changes in a mass b volume and c density of granite samples after different heating–cooling cycles

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As shown in Fig. 4b, V of the sample gradually increases with increasing heating–cooling cycles, but the increment rate of V exhibits reducing trend. The generation of thermal stresses during heating will cause the initiation and growth of micro-defects in the granite, which expand the void space of the rock. Such the microstructural damage is continuously accumulated as the number of cycles increase, thus leading to a gradual expansion in volume of the granite samples. On the other hand, the increase in pore space will in turn affect the level of thermal stress and slow down the volume expansion of the rock. The relevant mechanism is stated in detail in Sect. 4.1. Due to the decrease of M and the increase of V, ρ of the sample naturally presents a decreasing trend as the number of cycles increase (see Fig. 4c).

It is found from Fig. 4 that LN2 cooling has a more significant impact on the above physical properties of high-temperature granite. The change magnitudes of M, V and ρ of the LG sample are dramatically greater than that of the AG sample at each cycle condition. When the high-temperature sample are subjected to LN2 quenching, the intense thermal shock will be induced in the rock because of the rapid thermal exchange between cryogenic LN2 and high-temperature granite (Cai et al. 2014a; Han et al. 2018). This leads to a more severe deterioration of these physical properties of the LG sample. In addition, it is found that there is a distinct appearance damage of the LG sample after exposure to LN2 cooling. Taking the samples subjected to 12–24 heating–cooling cycles as the examples, the appearance characteristics of these samples were carefully inspected by a high-definition camera, as shown in Fig. 5. It is seen that the visible macro-defects appear on the surface of the LG sample after 12 cyclic treatments (see Fig. 5a–c), whereas not observed on the surface of the AG sample under the same cycle number (see Fig. 5d–f). This can well explain why the reduction in M of the LG sample is obviously larger than that of the AG sample.

Fig. 5
figure 5

Appearance photographs of granite samples after different heating–cooling cycles (arrows and ellipses indicate the location of flaking points)

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3.1.2 Porosity and P-Wave Velocity

Porosity and P-wave velocity are two important physical properties of rock materials and are widely used to characterize the structural integrity of the rock (Reuschlé et al. 2006). Figure 6 presents the magnitude and corresponding change rate of P and Vp of the granite samples after different heating–cooling cycles. The detailed measurement values of the two parameters are listed in Table 3.

Fig. 6
figure 6

Variations and change rate of a porosity and b P-wave velocity of granite samples after different heating–cooling cycles

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Table 3 Summary of average values of physico-mechanical properties of granite samples after cyclic heating–cooling treatments
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As shown in Fig. 6, for the intact granite sample (i.e., no heating–cooling treatments), the average values of P and Vp are about 0.82% and 4430 m/s, with the standard deviation of 0.01 and 26, respectively. This implies that the granite samples tested in this study are intact in nature state and similar in pore development. Generally, no matter what cooling method is adopted, P of the granite gradually increases as the increase in cycles (see Fig. 6a), while the variation in Vp with cycles is reverse (see Fig. 6b). From 0 to 12th cycles, the average P values increase by 32.93% and 57.32%, and the average Vp values decrease by 35.20% and 42.56% for the AG and LG samples, respectively. After that, the P and Vp of the granite samples nearly almost constant irrespective of the cooling method. This indicates that the influence of heating–cooling treatments on internal structures of the rock become weaker after 12 cycles. In addition, it is found no matter the increase in P or decrease in Vp of the LG sample under each cyclic condition, when compared to that of the AG sample, are of larger magnitude (see Fig. 6).

Apparently, an increase in P or decrease in Vp is an indication of micro-defects growth in the rock. As explained earlier, high-temperature treatment causes the generation of thermal stresses between adjacent minerals. The grain boundary or intragranular microcracks are induced inside the granite sample once the thermal stress destroys the cementation between minerals (see Sect. 3.4), which subsequently leads to a change in P and Vp of rocks. The repeated cyclic treatments provide the required energy for the propagation of the microcracks. Therefore, a more significant microstructural damage is found in the sample after more heating–cooling cycles. Moreover, compared with air cooling, the rapid cooling treatment with cryogenic LN2 induces additional thermal shock microcracks, thus aggravating the damage to the pore structure of the rock sample.

3.2 Changes in Mechanical Properties

3.2.1 Stress–Strain Curve

The stress–strain curve provides a fundamental understanding for the mechanical behavior of rocks during compressive loading. It is generally accepted that the axial stress–axial strain curve of the rock under unconfined condition can be divided into five stages (see Fig. 7), i.e., (1) crack closure, (2) elastic deformation, (3) stable crack growth, (4) unstable crack growth, and (5) post-peak deformation stages (Martin and Chandler 1994; Brace et al. 1966; Cai et al. 2004; Peng et al. 2015; Rong et al. 2018).

Fig. 7
figure 7

A stress–strain diagram of rock in uniaxial compression test (modified from Martin and Chandler 1994 and Peng et al. 2015). a Various deformation and stress thresholds are identified from the stress–strain curves; b a schematic representation showing different crack behaviors

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The representative axial stress–strain curves of the granite samples after different cyclic heating–cooling are illustrated in Fig. 8. As shown in Fig. 8a, c, the axial stress–axial strain curves of the samples exhibit a concave upward shape during initial loading. Many studies have pointed out that this nonlinear deformation of the rock is associated with the closure of pre-existing microcracks inside rocks during loading (Bieniawski 1967; Yang et al. 2017a). In general, the nonlinear behavior of the rock at this stage becomes more prominent as the number of cycles increases, especially for the sample cooled by cryogenic LN2. In addition, it is seen from Fig. 8b, d that the sample subjected to more heating–cooling cycles usually has more distinct volumetric compression. These phenomena indicate that more thermal cracks are induced in the rock due to the increased heating treatments and cooling rate. After the stage of crack closure, the granite sample shows a linear elastic deformation, that is, the axial stress increases approximately linearly with the axial strain. It is generally believed that no new microcracks are generated at this stage. The Young’s modulus (E) of the rock can be determined based on the linear variation of the curve. As the further increase of axial load, the axial stress–axial strain curve gradually deviates from the linear behavior due to the initiation, extension and coalescence of microcracks. Thereafter, the sample reach the peak strength and enter the post-peak deformation stage. As seen from Fig. 8, the influence of the number of cycles or cooling rate on the post-peak deformation of the sample seem to be not remarkable. A sudden stress drop following the peak stress can be found at this stage for almost all granite samples, implying that they all failed in a form of brittle failure (Siratovich et al. 2016).

Fig. 8
figure 8

Stress–strain curves of granite samples after different heating–cooling cycles. a, b Air cooling, and c, d LN2 cooling

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3.2.2 Strength Characteristic of Rock

Changes in UCS and BTS of the granite sample with the number of heating–cooling cycles are plotted in Fig. 9. The average values of UCS and BTS of the rock for each cycle are listed in Table 3. It is found that the mechanical properties of the sample greatly depend on the number of cycles and cooling methods. From Fig. 9, both the compressive and tensile strength of the sample gradually decline as the number of cycles increase. However, the decrease magnitudes in these two mechanical parameters of the LG sample at each heating–cooling cycle are more remarkable than that of the AG sample. For instance, the average UCS of LG sample is reduced by 24.8% after 24 cyclic treatments, whereas only 16.0% for AG sample (Fig. 9a). In like manner, the attenuation rate of BTS for the LG and AG samples subjected to 24 heating–cooling cycles are 53.5% and 40.6%, respectively (Fig. 9b). Such cases can be attributed to the fact that far more severe damage are caused in the rock during LN2 rapid cooling. In contrast, the attenuation amplitude of BTS of the sample is more remarkable than that of UCS. The results of Kim et al. (2013) and Shao et al. (2014) indicate that the transient thermal stress caused by rapid cooling is normally tensile at the surface of the rock. Generally, the granite has the lower resistance to the tensile stress than any other kind of stress, making it more prone to failure under tensile conditions. In addition, it is also found from Fig. 9 that the reduction in UCS and BTS of the sample mainly occurs within the initial 12 cycles, which is consistent with the variations of porosity and P-wave velocity described in Sect. 3.1.2.

Fig. 9
figure 9

Variations and change rate of a compressive strength and b tensile strength of granite samples after different heating–cooling cycles

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As presented in Fig. 7a, several stress thresholds, which are termed as the crack closure stress σcc, the crack initiation stress σci, the crack damage stress σcd and the peak strength σp (i.e., UCS), can be identified from the progressive failure process of rocks during axial loading (Martin and Chandler 1994; Cai et al. 2004). Although various methods have been proposed by researchers based on stress–strain curve or AE parameter to determine the stress thresholds, they are different in terms of applicability, conveniences and subjectivity. In the present study, the σcc, σci and σcd of the rock sample were determined using axial strain response (ASR) method (Peng et al. 2015), lateral strain response (LSR) method (Nicksiar and Martin 2012) and volumetric strain method (Brace et al. 1966; Bieniawski 1967), respectively.

The stress thresholds and their ratios to σp for the granite samples subjected to different heating–cooling treatments are summarized in Table 4. It is seen that σcc, σci and σcd of the sample without thermal damage (i.e., 0 cycle) were 32.8, 55.15 and 111.02 MPa, respectively. Figure 10 presents the changes of the stress thresholds with the number of heating–cooling cycles. As the figure shows, the magnitude of σci and σcd generally show a trend of decrease with the increasing cycles, regardless of the cooling method. The variation in σcd is found to be more sensitive to the number of the cycles than σci. However, there is only slight fluctuation for σcc as the number of cycles increases. In addition, it is seen from Fig. 10 that σcc and σci show similar change amplitude with cycles for the AG and LG samples, while σcd observed under the LN2 cooling condition is distinctly lower.

Table 4 Stress thresholds and normalized ratios of granite samples after different heating–cooling cycles
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Fig. 10
figure 10

Changes of stress thresholds of granite samples after different heating–cooling cycles

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The ratios of stress thresholds to σp of the granite samples after exposure to different heating–cooling cycles are illustrated in Fig. 11. It is seen that no matter which cooling method is adopted, the value of σcc/σp gradually increase with the increase in the number of cycles, but is opposite for the values of σci/σp and σcd/σp. Correspondingly, the crack damage presents different variation tendencies with the increase in cycle number, that is, increase of the crack closure region and the unstable crack propagation region, decreases of the elastic deformation region and the stable crack propagation region. The results are basically consistent with those of Kumari et al. (2017). The increase in crack closure region indicates that more severe initial damage has occurred in the rock sample undergone more cyclic treatments. The progressive decrease of the elastic deformation region is probably related to that the brittle characteristic of the rock sample is weakened as the number of cycles increases. In contrast, the amplitude of the decrease of stable crack propagation region and the increase of unstable crack propagation region for the LG sample are more remarkable than the AG sample, especially after more cycles. This implies that increasing number of cycles and cooling rate will accelerate the development of microcracks during loading.

Fig. 11
figure 11

Stress threshold ratios of a air cooled samples and b LN2-cooled samples after different heating–cooling cycles

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3.2.3 Deformation Characteristic of Rock

Figure 12a shows the changes of E of the granite sample with respect to the number of cycles, and the detailed test data are presented in Table 3. As with the mechanical strength, the number of cycle and cooling method have significant influence on E of the rock. As shown in Fig. 12a, E presents a decreasing trend as the number of cycles increase. After 24 heating–cooling cycles, the E values of the AG and LG samples are 50.98 and 43.90 GPa, respectively, which attenuates by 27.29% and 37.38% compared to that of intact granite sample. In the same way, the decline magnitude of E gradually becomes smaller with the increasing cycles. When the heating–cooling treatment exceeds 12 cycles, the reduction rate of E is not remarkable. In addition, it is seen that E of the LG sample is distinctly lower than that of the AG sample at all cyclic conditions.

Fig. 12
figure 12

Variations and change rate of a Young’s modulus and b failure strain of granite samples after different heating–cooling cycles

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The failure strain (εp) is defined as the axial strain that corresponds the peak strength, which can reflect the deformation behavior of rock to some extents. The variation in εp with increasing heating–cooling cycles is shown in Fig. 12b. The results reveal that εp of the sample varies greatly due to the difference in cycle number and cooling method. From Fig. 12b, the value of εp gradually increases as the increase in the number of cycles, which is particularly prominent in the first several cycles. After 24 heating–cooling cycles, the average εp of the AG sample has risen to 4.12 × 10–3, which is 1.25 times of that for the intact sample. Compared with the AG sample, the LG sample usually has a larger εp for each cycle condition. The variations in εp indicates that the increase in the number of cycles and cooling rate leads to a greater ductility of the granite.

3.3 AE Characteristics

AE count rate and accumulative AE hit are two typical AE time-series parameters. They are selected to characterize the progressive failure process and microcrack behavior of the granite sample during loading in the current study. When an AE activity occurs, the oscillation number of a pulse signal crossing the threshold in unit time is termed as AE count rate (Peng et al. 2018). It is generally considered to be an effective indicator reflecting the intensity of the AE activity. The accumulative AE hit is defined as the accumulated value of the signal received by a transducer exceeding the threshold, which is on behalf of the number of AE activities (Eberhardt et al. 1998).

The variations in axial stress, AE count rate and accumulative AE hits with axial strain of the intact granite sample are illustrated in Fig. 13. It is evident that there is a good correlation between the evolution in the AE parameters and the stress–strain curve. Generally, the AE activity occurs in the initial deformation stage is related to the closure of the pre-existing microcracks inside the rock (Yang et al. 2017a). As shown in Fig. 13, almost no AE activity is monitored at the initial loading stage for the granite sample without treatment, indicating that only very few micro-defects exist inside the natural granite sample. Afterwards, the number of AE hit presents an obvious increasing trend with the axial load increases, while the AE count rate still remain a low level. This implies that a great number of tiny fractures are generated in the rock during this process. With the further increases of axial stress, the AE count rate with a larger magnitude begin to appear intensively, and is strongest near the peak strength. But at the same time, the increment rate of accumulative AE hits becomes slower. These phenomena indicate that the cracks induced in the rock are larger in scale than before, but relatively less in number. In addition, it is also seen that the “sudden stress drop” on the stress–strain curve corresponds to a sharp increase in the AE count rate. It can be attributed to the fact that the transient stress relaxation induced by dislocation or breakage of minerals or grain boundary movement in the rock during loading (Peng and Yang 2018).

Fig. 13
figure 13

Evolution of AE count rate and accumulative AE hits with axial strain for the intact granite sample

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Figures 14, 15 show the evolution in AE parameters of AG and LG samples during uniaxial compression for different cyclic heating–cooling conditions, respectively. In general, the overall variation trends of AE count rate and accumulative AE hits of the granite samples after different cyclic treatments are basically similar with that of the intact sample, except during the initial loading stage. Compared with the intact granite sample, both the AE count rate and accumulative AE hits of the AG and LG samples are stronger at the initial loading stage, and gradually enhanced as the number of cycles increases (see Figs. 14 and 15). It can be concluded that the number of thermal cracks in the rock greatly increases when more heating–cooling treatment is applied, that is, more severe initial damage is induced in the rock. At the same number of heating–cooling cycles, the AE count rate of LG samples at initial deformation stage is generally denser and higher than that of the AG samples. This further demonstrates that the rapid LN2 quenching can exacerbate the microstructural damage to the high-temperature rocks.

Fig. 14
figure 14

Evolution of AE count rate and accumulative AE hits with axial strain for AG samples after different heating–cooling cycles. a 1 cycle, b 3 cycles, c 6 cycles, d 12 cycles, e 18 cycles, f 24 cycles

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Fig. 15
figure 15

Evolution of AE count rate and accumulative AE hits with axial strain for LG samples after different heating–cooling cycles. a 1 cycle, b 3 cycles, c 6 cycles, d 12 cycles, e 18 cycles, f 24 cycles

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The final number of AE hits of the granite samples versus different heating–cooling conditions is plotted in Fig. 16. It is seen that, with the increase in the number of cycles, the accumulative AE hits of AG and LG samples generally show an increasing trend, which is mainly associated with the initial microcracks induced by thermal shock inside the rock sample. Furthermore, for each heating–cooling cycle, the final number of accumulative AE hits of LG sample after failure is greatly far higher than that of AG samples. This indicates that more microscopic fractures occur in the sample experienced LN2 cooling treatment during loading.

Fig. 16
figure 16

Accumulative AE hits with of granite samples for different heating–cooling cycles

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3.4 Microstructural Alterations

In the current study, the microstructure of the granite samples after exposure to different heating–cooling cycles was observed with the aid of an Olympus BX53M polarizing microscope. Under each pretreatment condition, the thin slice with a side length of 2.5 mm and a thickness of about 0.03 mm was prepared. The microstructure of the rock sample was uniformly magnified by 50 times for the purpose of effectively identifying the development of grain boundary microcracks and intragranular microcracks.

Figures 17, 18 show the microphotographs of AG and LG samples after different heating–cooling cycles. As seen from Figs.17a and 18a, the internal structure of the granite sample after 1 cycle has undergone some visible changes compared with that of the intact sample (see Fig. 1a). Although most of mineral grains in the granite sample are well cemented with each other, several grain boundary microcracks around quartz grains are identified. Under high-temperature condition, the uncoordinated thermal expansion behaviors between mineral grains lead to the generation of thermal stresses within the rock matrix. Once the maximum thermal stress exceeds the cementation strength of mineral grains, the new thermal cracks are induced. In addition, the anisotropic expansion of mineral grains along various crystallographic axes can also result in the microstructural damage upon heating (Hall 1999; Sirdesa et al. 2017). Quartz is the major diagenetic mineral of the granite used in this study, which has a larger thermal expansion coefficient than other minerals (Simmons and Cooper 1978; Kranz 1983). Hence, the grain boundary microcrack is more likely occurs near quartz grain boundary, which is consists with the observations of Fredrich and Wong (1986).

Fig. 17
figure 17

Identification microcracks of AG samples after different heating–cooling cycles (GB–grain boundary microcrack, IG–Intragranular microcrack). a 1 cycle, b 3 cycles, c 6 cycles, d 12 cycles, e 18 cycles, f 24 cycles

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Fig. 18
figure 18

Identification microcracks of LG samples after different heating–cooling cycles (GB–grain boundary microcrack, IG–Intragranular microcrack). a 1 cycle, b 3 cycles, c 6 cycles, d 12 cycles, e 18 cycles, f 24 cycles

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After three cycles, the grain boundary microcrack in the granite begin to develop gradually (see Figs. 17b and 18b). It is worth mentioning that the intragranular microcrack is observed in the LG sample after three heating–cooling cycles (see Fig. 18b), but that is found in the AG sample until six cycles (see Fig. 17c). Compared with air cooling, the repeated LN2 cooling treatments cause more severe thermal shock damage to the high-temperature granite sample and provide more energy for the growth of the intragranular microcracks. It is clear from Figs. 17 and 18 that the microcracks in both AG and LG samples become denser as the number of cycles further increases, and the intragranular microcracks are easier identified, especially in the range of 12–24 cycles.

In addition, it is found that the width of microcrack is significantly affected by the number of cycles and cooling rate. As shown in Figs. 17 and 18, the microcrack in the rock after exposure to more cyclic treatments distinctly becomes wider. In contrast, the LG sample generally has a larger width of microcrack than that of the AG sample under the same treatment condition. Taking 24 cyclic treatments as an example, the average width of microcrack in the AG sample measured by virtue of the image processing software is about 32 μm, while that in the LG sample achieve 48 μm.

4 Discussion

4.1 Analysis of Damage Evolution and Mechanism

According to the analysis in the previous sections, the cyclic heating–cooling treatment leads to distinct damage to the granite sample. In general, the exponential function is able to well describe the relationship between the physico-mechanical properties of rocks and the number of cycles. Taking advantages from these correlations, the damage variables can be expressed as a function of UCS, BTS, E and Vp based on elastic strain theory. The damage variable can be calculated by Eq. (4) (Hueckel et al. 1994; Hu et al. 2018; Qin et al. 2020), and the calculated values of damage variables are given in Table 5.

$$D\left( I \right) = 1 - \frac{{I_{N} }}{{I_{0} }}$$
(4)
Table 5 Damage variables of granite samples determined by different parameters
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where I denotes the physical and mechanical parameters of rock (i.e., UCS, BTS, E and Vp), the subscript N denotes data obtained from the granite sample subjected to N heating–cooling cycles, and the subscript 0 denotes data obtained from the intact granite sample.

The relationship of different damage variables of AG and LG samples and the number of cycles is plotted in Fig. 19. As seen from the figure, regardless of the cooling method, the evolution of the four types of damage variable with the number of cycles basically follows an exponential law. The best fitting function of each damage variable is also given in Fig. 19, which all have a high correlation coefficient. In contrast, the damage extent of the AG and LG samples evaluated by BTS is the most significant, and followed by the damage evaluated by Vp, E and UCS (see Fig. 19). This is mainly related to the lower resistance of granite to tensile stress and the tensile failure generated during cooling. It is also clear from Fig. 19 that the damage variables increase rapidly in the first few cycles, while the growth rate of them gradually declines with the increasing cycles. In general, there is only a slight change in the damage variable after about 12 cycles, indicating that the internal damage of the rock sample almost reaches a stable state after that.

Fig. 19
figure 19

Damage variables of a AG sample and b LG sample versus the number of heating–cooling cycles

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According to the microscopic observations in Sect. 3.4, the macroscopic damage of granite sample is the result of the initiation, propagation and coalescence of microcracks within the rock. In the first few heating–cooling cycles, the alternating thermal stress destroys the cementation between adjacent minerals and induces the growth of microcracks between or within the grains. This caused a distinct deterioration in the physico-mechanical properties of the rock. However, with a further increase in the number of heating–cooling cycles, the development of micro-defects provides sufficient deformation space for mineral expansion, which reduce the level of thermal stress within the rock (Wu et al. 2019). Therefore, the degradation of the physico-mechanical behaviors of the granite is basically no longer aggravated after the threshold of cycles is reached.

In addition, it is seen that the damage extent of the LG sample is obviously larger than that of the AG sample. As listed in Table 5, the maximum values of the damage variables of the AG sample vary from about 0.164 and 0.406, while that of the LG sample is in the range of about 0.248–0.585. Different with the AG sample, the LG sample experienced an instantaneous, extreme temperature change during cooling. The temperature gradient during cooling process directly determines the magnitude of the thermal stresses generated in the rock (Wong and Brace, 1979). Unquestionably, the thermal stress induced by LN2 cooling is far greater than that by air-cooling. Hence, a more significant number of thermal cracks, that is, more severe damage, can be observed in the LG sample.

4.2 Correlation of P-Wave Velocity with Porosity and Strength Behavior

According to the above research results, it can be seen that the variation of Vp under different heating–cooling cycles correlates well with that of n and strength behavior of the rock. Since Vp is sensitive to the microstructure damage, it can indirectly reflect the change of pore structure of the rock. Meanwhile, the mechanical behaviors of rocks, including UCS and BTS, are significantly affected by the development of micro-defects. With that in mind, the correlation between n, UCS, BTS and Vp for the granite was investigated in this study. The relationships between them are shown in Fig. 20. As shown in the figure, n, UCS and BTS of the granite have a good linear relationship with Vp (R2 = 0.84, 0.80 and 0.84). Compared with Vp, the determination of n, UCS and BTS is time-consuming, cumbersome, and expensive. Therefore, the porosity and mechanical strength of the rock can be quickly evaluated by the non-destructive Vp measurements.

Fig. 20
figure 20

Relationship between a n, b UCS, c BTS and Vp of granite sample

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4.3 Enlightenment of Current Work on Geothermal Exploitation

The experimental results in this study suggest that LN2 has great potential in the field of geothermal reservoir stimulation. Actually, LN2 fracturing utilizes the intense thermal shock induced by cryogen to break reservoir rocks, rather than merely relying on increasing fracturing pressure. With the injection of cryogenic LN2 into HDR reservoir, the high-temperature rock experiences a rapid quenching process. The extreme thermal gradient results in considerable thermal shock damage to the rock and promote the generation and propagation of microcracks. Meanwhile, rapid cooling likely to cause tensile shrinkage cracking on the rock surface, which provides a passage for LN2 to penetrate into the rock. The cyclic injection of LN2 can not only further extends the pre-existing fracture channels, but also open up more new fractures inside the reservoir (Li et al. 2016; Elwegaa and Emadi 2018). In the meantime, a large number of secondary fractures are formed in the rock around the main fracture due to the repeated thermal shock (Cai et al. 2016). Compared with the single LN2 fracturing, the cyclic LN2 fracturing is more likely to induce larger scale and more complex fracture networks (Wu et al. 2019). The formation of the desired complex fracture networks increases the contact area between the heat exchange medium and the HDR, which is great significant for improving the efficiency of geothermal energy exploitation. However, the current research work indicates that the damage of granite is not infinitely enhanced with the increase of LN2 cooling cycles. After a certain number of cycles, the mechanical strength of the rock basically decayed to a stable value in this study. Therefore, when using LN2 fracturing for reservoir stimulation, the permeability of the reservoir rock cannot be improved by blindly increasing the number of LN2 injections. The optimal number of cyclic LN2 fracturing should be reasonably determined based on the on-site geological conditions, construction operating costs and fracture connectivity.

In addition, it can also be considered to use the cryogenic LN2 to assist in drilling operations, which is one of the critical processes for the exploitation of HDR geothermal energy through EGSs. As pointed by Huang and Meng (2018), the traditional drilling fluid under a relative higher temperature is difficult to perform the normal functions, such as protecting well walls and carrying cutting. According to the current experimental results, the cryogenic LN2 can significantly reduce the threshold of crack initiation and damage stress. This is quite beneficial for reducing the broken initiation pressure of rock and improving the drilling efficiency. At present, a method of high-pressure LN2 jet assisted drilling, which combines the double shock effect of the cryogenic LN2 and high-speed jet, has been proposed by some researchers (Huang et al. 2015, 2019). Along with the high efficiency in breaking rock, this method is also considered to have an excellent performance in cleaning the bottom hole and carrying cuttings. Unfortunately, due to the lack of a comprehensive understanding of the influencing factors and damage mechanisms of rock breaking with LN2, it has not been practically used in HDR drilling operations. This will be a significant issue to investigate the fracture initiation stress and fracture characteristics of high-temperature rocks under different stress states and jet pressures in the further work.

It has to be acknowledged that there are still many fundamental and technical issues still need to be solved before the widespread adoption of the LN2 fracturing technology. The development of a dedicated large-scale cryogenic fluid pumping equipment is a prerequisite for on-site LN2 fracturing. Besides that, the vaporization of LN2 is also an obstacle that must be addressed. During the injection of LN2, some effective measures must be taken to keep its cryogenic state, so as to maximize the thermal shock damage to the reservoir rock. Considering the cryogenic characteristic of LN2, the transport pipelines should be able to maintain the original strength for a long time in an ultra-low temperature environment. In addition, it is hard for LN2 to carry sufficient proppant into the crack due to its low viscosity (Han et al. 2018). Although some scholars suggested that the delivery efficiency of proppant can be improved by increasing the injection rate of LN2 (Gupta and Bobier, 1998; Wang et al. 2016), it is still urgent to develop a new a new proppant suitable for carrying by LN2.

5 Conclusions

In this paper, the effects of cyclic LN2 cooling and air cooling on the physico-mechanical properties of high-temperature granite are comparatively studied. The damage mechanism of LN2 cooling cycles on high-temperature rocks and its potential engineering applications are discussed. The major conclusions can be drawn from the study include:

  1. (1)

    Irrespective of the cooling method, the increasing number of heating–cooling cycles leads to a continuous deterioration of the physico-mechanical properties of granite, manifested by the increase in porosity, and the decay of P-wave velocity, strength and deformation properties. The variation of rock properties with the number of cycles can be well described by exponential functions.

  2. (2)

    The intense thermal shock induced by LN2 quenching further exacerbates the degradation of the macroscopic properties of the granite compared to that with air cooling. Microscopic observations reveal that LG samples exhibits more severe microstructural damage than AG samples, as evidenced by more pronounced crack growth and larger crack widths.

  3. (3)

    The deterioration rate of physico-mechanical properties of granite gradually reduces with the increase in cycle number. After about 12 cycles, the damage to granite induced by the heating–cooling cycle is less prominent. This is attributed to the fact that the growing micro-defects provide sufficient space for thermal deformation of the minerals, thus reducing the level of thermal stress in the rock.