Thermal shock effects on the mechanical behavior of granite exposed to dynamic loading


Under certain extreme conditions in rock engineering works, fast change in temperature in the load-bearing rocks can happen. Known as thermal shock (TS), such process involves rapid temperature rise or drop, which causes fracturing in the rock material and thus can pose as a threat to the stability of the rock structures. To investigate the influence of thermal shock caused by fast cooling on the mechanical property of rock, laboratory tests are performed on heated granite which are cooled with different methods, with the highest cooling rate reaching 167.4 °C/min. The dynamic loading tests are performed on the heated granite specimens utilizing the split Hopkinson pressure bar (SHPB) system. The test results show that the dynamic compressive strength drops with the increase in heating level or cooling rate. This pattern is explained by the nuclear magnetic resonance (NMR) test data that the pores inside the heated granite increase both in size and quantity as heating level or cooling rate rises. Damage patterns of the tested granite specimen fragments are analyzed based on the observation with scanning electron microscope (SEM), and the mechanisms of thermal shock in granite are also discussed.


In rock engineering projects such as deep mining, tunneling and nuclear waste disposal sites, rock structures can be subjected to extreme conditions involving high temperature and rapid temperature change. For example, in a presumable fire accident [1,2,3], the rock materials can experience sudden temperature rise as fire starts and fast temperature drop in the process of extinguishing the fire with the cooling water. Rapid change in temperature (temperature rise or drop) can cause thermal stress and thus produce fracture in rocks, which is known as thermal shock (TS) [4,5,6]. Therefore, although high temperature is widely recognized as a factor affecting the mechanical properties of rocks [7,8,9,10,11], temperature changing rate cannot be overlooked since TS may be induced in the heating or cooling process. It has been proposed that a rate ≥ 2 °C/min seems to be a lower boundary for TS to occur in rocks [4]. However, the fact that the data of temperature changing rate are not available in the thermal treatment of many tests [12,13,14,15] makes the influence of TS in rocks still largely in vague. For example, Han et al. [15] studied the effect of rapid cooling (water cooling) on the physical and static mechanical properties of sandstone. However, the action of TS cannot be confirmed since the temperature changing rate was not provided. Huang et al. [16] studied the effect of TS on the strength and fracture behavior of pre-flawed granite specimens under uniaxial compression without providing the temperature changing rate used in the test. Zhao et al. [17] performed Brazilian tensile tests on granite after thermal treatments, where the granite specimens were heated to a maximum level of 400 °C and cooled them in air or in water. However, the cooling rate was not provided. In many other studies where the value of temperature changing rate was mentioned, comparatively low rates (under 10 °C/min) were often adopted [8, 10, 18, 19]. For example, Wang et al. [20] adopted a cooling rate of 2.25 °C/min to apply cycled TS on the sandstone at the heating level of 200 °C, and the dynamic compressive properties of sandstone after TS were investigated. Low cooling rate was also adopted in the cooling process of the heated sandstone specimens performed by Li et al. [21]. For instance, according to the temperature profile, the cooling rate is about 2.4 °C/min for the water cooling method and about 5 °C/min for the liquid nitrogen cooling method. The use of comparatively low temperature changing rates in the tests makes it difficult to acknowledge the effect of TS, a phenomenon featured by rapid temperature change.

In a previous study [22], mechanical behavior of granite after TS was investigated under quasi-static loading condition, where the Mode I and Mode II fracture toughness were obtained and analyzed using the cracked straight through Brazilian disks. However, the dynamic behavior of granite after TS was not involved. In fact, scenarios involving impact on rocks after TS are also possible, such as the demolishing process of rock buildings after fire accident and the assessment of the influence of earthquake on the underground rock structures after fire hazard [23,24,25]. As a continuation of the previous paper [22], this work is extended to investigate the dynamic mechanical behavior of granite after TS. In this paper, the split Hopkinson pressure bar (SHPB) system is adopted to obtain the dynamic compressive strength of the heated granite specimens. Three cooling methods, stove cooling (no TS), air cooling (TS) and water cooling (TS), are adopted to provide different cooling rates. The scanning electron microscope (SEM) and nuclear magnetic resonance (NMR) technique are utilized to analyze the mechanisms of TS and provide explanations for the test results.

Specimen preparation

The granite is quarried from Hunan Province, China. The specimens are cored from the same rock block with no visible geological weakness. The standards of the international society for rock mechanics (ISRM) are maintained in the preparing processes of the specimens. The diameters of the specimens used in the dynamic loading test are 50 mm with the length-to-diameter ratio of 1:1 (Fig. 1a). According to the thin-section analysis (Fig. 1b), the granite is composed of quartz (46%), feldspar (44%), muscovite (6%), biotite (3%) and opaque mineral (1%).

Fig. 1

Granite specimen used in the test: a geometry of the specimen, b photomicrograph of the granite under cross-polarized light (Qtz, quartz; Pl, plagioclase; Bt, biotite; Ms, muscovite)

Thermal shock treatment

The granite specimens are divided into 10 groups, including three different heating levels (200 °C, 400 °C and 600 °C) combined with three different cooling methods (stove cooling, air cooling and water cooling) and another group of untreated specimens serving as a control group. Totally 60 specimens are used with each group comprises six specimens. The thermal treatment can be described as follows. The specimens are first heated inside a box-type electrical stove to the preset heating levels (with a heating rate of 5 °C/min). Then the temperature is kept constant for 2 h. Afterward, the specimens are cooled with one of the three methods: 1. Leave the specimens inside the unplugged stove to cool down slowly (stove cooling); 2. take the specimens out of the stove to cool down in the open air at ambient temperature (air cooling); 3. immerse the specimens into water at ambient temperature (water cooling). In the heating process, the temperature data is read from the monitor of the stove every 60 s. In the cooling process, the temperature of the specimen is measured by an infrared thermometer (Type PM6530D produced by Shenzhen Huayi Peakmeter Technology) every 60 s in stove cooling process and air cooling process, and every 30 s in water cooling process. The temperature profiles of the thermal treatments are illustrated in Fig. 2, where the average cooling rate is 0.42 °C/min for stove-cooled specimens, 30.14 °C/min for air-cooled specimens and 167.40 °C/min for water-cooled specimens. Accordingly [6], the air cooling and water cooling conditions can well be categorized into TS conditions, while the stove-cooled specimens have avoided the influence of TS.

Fig. 2

Temperature profiles of thermal treatments: a air cooling and water cooling conditions (TS), b stove cooling conditions (no TS)

Physical properties of granite after TS

The physical properties of the heated granite, including dry density, porosity and P-wave velocity, are tested to demonstrate the damaging effect of TS on the intactness of the rock matrix. The dry density and porosity are obtained with buoyancy techniques [26]. The P-wave velocity is measured by a non-destructive ultrasonic detector (SET-CWA-01 produced by Hunan Sine Electronic Technology). For each thermal treatment, the property values of the six specimens are averaged, and the data are illustrated in Fig. 3, where the properties of granite specimens free from thermal treatment are also included for reference. In general, the heated specimens have lower density and P-wave velocity and higher porosity compared with the untreated specimens. As the heating level rises, the dry density and P-wave velocity present a descending trend and the porosity presents an ascending trend. At any heating level, with rising cooling rate, the dry density and P-wave velocity decrease, and the porosity increases. For instance, at 600 °C, the lowest temperature changing rate (stove-cooled case) renders the highest density. At a higher rate (air-cooled case), the density becomes lower, and the highest rate (water-cooled case) renders the lowest density (Fig. 3).

Fig. 3

Physical properties of heated granite: a dry density, b porosity, c P-wave velocity

As porosity and P-wave velocity are important indicators of rock damage [27], the above patterns reflect the deterioration of the intactness of the rock matrix as heating level rises. In addition, the aggravated damage caused by higher cooling rate is also evident. It can be assumed that the higher temperature and temperature changing rate have resulted in microcracks which increase in the volume of the specimen and thus decrease the density. This in turn induces a higher porosity and therefore a lower P-wave velocity.

Dynamic loading test

The dynamic loading tests are performed on an improved split Hopkinson pressure bar (SHPB) system [28]. The loading device consists of a spindle-shaped punch, an incident bar, a transmitted bar and an absorbing bar, which are made of high strength 40 Cr steel with the density of 7821 kg/m3, the elastic modulus of 233 GPa and the yield strength of 800 MPa (Fig. 4). The lengths of the spindle-shaped punch, incident bar, transmitted bar and absorbing bar are 350 mm, 2000 mm, 2000 mm and 500 mm, respectively, with an identical diameter of 50 mm (same as the diameter of the granite specimens used in the test shown in Fig. 1). In the test, the incident bar is struck by the punch driven by the gas released from the gas cylinder through the gas gun, and a half-sine wave is induced in the bar. As the wave advances in the incident bar, some of the wave is reflected at the contacting faces of the bar and the specimen, and the rest of the wave is transmitted through the specimen and reaches the transmitted bar attached to the specimen. The strain gauges are attached to the surface of the incident bar and transmitted bar as shown in Fig. 4. During the test, the electric signals are transmitted through the dynamic strain test devices and recorded by the oscilloscope and are finally converted to the dynamic mechanical parameters such as stress and strain in the computer for analysis.

Fig. 4

The SHPB system

According to the one-dimensional wave principle, the relationship of stress (σ), strain (ε) and strain rate (\( \dot{\varepsilon } \)) of the specimen is listed as follows [29]:

$$ \sigma (t) = \frac{{A_{\text{e}} E_{\text{e}} }}{{2A_{\text{s}} }}\left[ {\left[ {\varepsilon_{\text{I}} (t) + \varepsilon_{\text{R}} (t) + \varepsilon_{\text{T}} (t)} \right]} \right] $$
$$ \varepsilon (t) = \frac{{C_{\text{e}} }}{{L_{\text{S}} }}\mathop \smallint \limits_{0}^{t} \left[ {\varepsilon_{\text{I}} (t) - \varepsilon_{\text{R}} (t) - \varepsilon_{\text{T}} (t)} \right]{\text{d}}t $$
$$ \dot{\varepsilon }(t) = \frac{{C_{\text{e}} }}{{L_{\text{S}} }}\left[ {\varepsilon_{\text{I}} (t) - \varepsilon_{\text{R}} (t) - \varepsilon_{\text{T}} (t)} \right] $$

where Ae, Ee and Ce denote the cross-sectional area, Young’s modulus and wave velocity of pressure bars, respectively; εI, εR and εT denote the incident strain, reflected strain and transmitted strain, respectively; AS denotes the cross-sectional area of the specimen; LS denotes the length of the specimen [30]. The forces P1 and P2 on the two sides of specimen can be calculated as:

$$ P_{1} = E_{\text{e}} A_{\text{e}} \left[ {\varepsilon_{\text{I}} (t) + \varepsilon_{\text{R}} (t)} \right] $$
$$ P_{2} = E_{\text{e}} A_{\text{e}} \varepsilon_{\text{T}} (t) $$

In the testing period, the equilibrium of stresses on the two sides of the specimen is required to avoid axial inertial effect and to render reasonable results [30]. In this case (P1 = P2), it can be deduced that εT(t) = εI(t) + εR(t). According to Eq. (1) and Eq. (3), the stress and strain rate of the specimen in the dynamic compressive loading process can be calculated as:

$$ \sigma (t) = \frac{{A_{\text{e}} }}{{A_{\text{s}} }}E_{\text{e}} \varepsilon_{\text{T}} (t) $$
$$ \dot{\varepsilon }(t) = - \frac{{2C_{\text{e}} }}{{L_{\text{S}} }}\varepsilon_{\text{R}} (t) $$

Figure 5 shows an example of the stress history of one typical test. Good coincidence can be observed between the transmitted wave (blue curve) and the sum of the incident and reflected wave (green curve), which indicates that the forces on the two sides of specimen are almost equal in the dynamic compressive testing period [11].

Fig. 5

Stress balance diagram of the loading process

Test results

Dynamic compressive properties of heated granite

In the dynamic loading test, the air pressure is set as a value between 0.4 and 0.6 MPa, where the specimens after different thermal treatments can be breached so that dynamic compressive strength can be obtained. This way, the resulted strain rates also falls into a narrow range, so that the comparison of test results for specimens after different thermal treatments is possible. In order to minimize the friction between the bars and the specimen, their contact surfaces are fully lubricated with lubricant. Examples of the failure stage of specimens in the SHPB tests are captured by the high-speed photography (Fig. 6a–d), and the corresponding specimens after the tests are shown in Fig. 6e–h, respectively, where it is clearly seen that the rock specimens are fragmented by the impact load at the aforementioned air pressure level.

Fig. 6

Fragmented granite specimens: ad failure stages of specimens in the SHPB tests, eh corresponding fragments of specimens after the tests

In the testing period of each specimen, the electric signals are transmitted through the strain gauges and are recorded by the oscilloscope, through which the incident wave, reflected wave and transmitted wave were obtained (e.g., Figure 7a). Similar to Fig. 5, the transmitted wave (blue curve) and the sum of the incident and reflected wave (green curve) almost coincide in Fig. 7a, which indicates the equilibrium of stresses on the two sides of the specimen. The stresses on the bars can be deduced from the strains on the bars reflected by the aforementioned waves. The stress on the specimen can then be deduced from the strain in the bars (Eq. 6). The strain and stain rates of the specimen can be obtained from the strain of the incident bar (induced by reflected wave) (Eq. 7). And the stress–stain curve is plotted from the stress and strain data of the specimen (Fig. 7b), where the peak value of the curve is the dynamic compressive strength. For each heating level and cooling rate, six specimens are tested, and the obtained dynamic compressive strength values are plotted against the strain rate as shown in Figs. 8 and 9, where the fitted lines of strength are also plotted. In general, the strength increases with ascending strain rate regardless of specific thermal treatment. This is in accordance with the enhanced effect of strain rate which is well acknowledged [31]. As shown in Fig. 8a–c, with the identical cooling method, higher heating level results in lower strength values. The data also indicate that higher cooling rate renders lower strength values, which holds true for all three heating levels (Fig. 9). It is noticed in Fig. 8 that the fitted line for 600 °C (blue line) has longer distance from those for 400 °C, 200 °C and ambient temperature (green line, red line and black line, respectively), which are comparatively more close to each other. This pattern is in accordance with the observation that both the quantity and size of the pores are increased tremendously at 600 °C (Fig. 11). This phenomenon is believed to be the result of the αβ transition of quartz occurring at 573 °C. When the heating level reaches 600 °C, the change in the geometry of quartz due to αβ transition encourages pores between the mineral grains, which cause additional damage, and this in turn affects the strength value [32, 33]. Therefore, the fitted strength line distances farther away from that of 400 °C than the distance between 200 and 400 °C. This pattern can also been seen in Fig. 9c, where the fitted line of 600 °C (red, green and blue lines) distances farther from that of the ambient temperature (black line) than the case of 200 °C (Fig. 9a) and 400 °C (Fig. 9b).

Fig. 7

Test results of the stove-cooled specimen after heating at 200 °C in the dynamic loading process: a half-sine waveform of the electric signals, b the deduced stress–strain curve

Fig. 8

The variation of dynamic compressive strength with different heating levels (circled data points correspond to the specimens that are used in the nuclear magnetic resonance test as shown in Figs. 10 and 11)

Fig. 9

The variation of dynamic compressive strength with different cooling methods (circled data points correspond to the specimens that are used in the nuclear magnetic resonance test as shown in Figs. 10 and 11)

Nuclear magnetic resonance test analysis

Nuclear magnetic resonance (NMR) can be used to measure the physical properties and molecular structure of materials by testing the directional rotation of hydrogen (H) nucleus in magnetic field [34]. In this section, the NMR instrument is utilized to detect the fluid media inside the fully saturated granite specimens after thermal treatments, whereby the size distribution of the internal micropores can be obtained and therefore the damage condition can be deduced. For reference, the specimens tested by NMR are also denoted by the circled data points in Figs. 8 and 9. Before test, the specimens are first vacuum saturated in air and water for 240 min and 120 min, respectively, at vacuum pressure of 0.1 MPa to guarantee the complete saturation [35]. In order to avoid the error caused by water evaporation, the saturated specimen was wrapped in a thin film before test. An important parameter obtained from NMR test is the transverse relaxation time T2, also known as the spin–spin relaxation time, which can describe the decay rate of transverse magnetization [36]. The T2 relaxation time can be expressed as [37, 38]:

$$ \frac{1}{{T_{2} }} \approx \rho_{2} \left( {\frac{S}{V}} \right)_{{\text{pore}}} $$

where T2 denotes transverse relaxation time (ms); ρ2 denotes surface relaxation strength of rock; (S/V)pore denotes the ratio of surface area to the volume of pore in rock (μm−1). Based on the approximation that the pores inside the rock have a spherical or columnar shape, Jiang et al. [39] found that (S/V)pore has a negative linear correlation with the pore radius:

$$ \left( {\frac{S}{V}} \right)_{{\text{pore}}} = \frac{{F_{\text{s}} }}{{r_{\text{c}} }} $$

where rc denotes pore radius (μm); FS denotes the pore shape factor. According to Eqs. (8) and (9), the pore radius can be expressed as:

$$ r_{\text{c}} = \rho_{2} F_{\text{S}} T_{2} $$

Equation (10) indicates a positive correlation between the T2 value and the pore size. According to [39], for spherical pores and columnar pores with a height-to-diameter ratio of 1, FS = 3, and for columnar pores where the height-to-diameter ratio is close to infinity, FS = 2. Basically, the value of FS is between 2 and 3. In this study, as a simplification, the shape of the voids is assumed to be spherical, and FS = 3 is approximated to quantify the data. For rock with high silicate mineral contents such as the granite specimens used in this study (see Sect. 2), ρ2 = 0.00426 μm/ms [40]. Therefore, the following equation can be deduced:

$$ r_{\text{c}} = 0.01368T_{2} $$

According to the above equations, smaller T2 relaxation time corresponds to higher ratio of surface to volume for the pores, i.e., smaller pores, and vice versa [41, 42]. Based on the NMR test results, the T2 spectrum distributions of the heated specimens are shown in Figs. 10a–c and 11a–c, which are transformed into pore size distributions (Figs. 10d–f, 11d–f), respectively, according to Eq. (11). It should be noted that the specimens tested to obtain the results in Figs. 10 and 11 correspond to the circled data points shown in Figs. 8 and 9.

Fig. 10

Evolution of T2 spectrum distributions (ac) and corresponding pore size distributions (df) at different heating levels with varying cooling rate (dash lines correspond to the peak of the curves)

Fig. 11

Evolution of T2 spectrum distributions (ac) and corresponding pore size distributions (df) at different cooling rates with varying heating level (dash lines correspond to the peak of the curves)

In general, the curves in Fig. 10 present a twin peak pattern, which indicates the quantitative dominance of the pores with the corresponding sizes. For instance, at heating level of 200 °C, the majority of pores have a radius of around 0.009 μm and 1.573 μm (dash lines in Fig. 10d). In this case, the curves are almost identical for heated specimens and untreated specimens, and the difference between different cooling methods is also indiscernible. This indicates the fact that the quantity and size of the pores are not affected by 200 °C of heating and the variation of cooling rate. Comparatively, more pores are induced after heating at 400 °C and 600 °C, denoted by the larger area enclosed by the curves of heated specimens (Fig. 10e, f). In addition, the size of the pores in the heated specimen also presents the trend of expansion. This can be observed by the magnified section of the curves around 0.0013 μm in Fig. 10e, where smaller pores of untreated specimens start to transform into bigger ones after heating. The larger pores are also expanding in size and increasing in quantity as cooling rate increases, which can be observed by the shifting of the dash line toward right direction, and the larger area enclosed by the respective curves. Specifically, at 600 °C, the amount of larger pores (pore radius > 1 μm) has increased tremendously compared with the untreated specimen. The expansion of smaller pores is also evident, where the lower boundary of pore radius shifts from 0.0013 to 0.006 μm (magnified curve sections in Fig. 10f).

The pattern of the curves in Fig. 11 indicates an increase in both the quantity and size of the pores as heating level rises. For all three cooling methods, the curves at 200 °C are almost identical to the unheated case, and at 400 °C, the quantity of the pores and pore size start to increase. Particularly, significant increase in the quantity of the pores can be observed at 600 °C, where the area enclosed by the curves is much larger than other temperatures. With respect to the pore sizes, all pores with radius smaller than 0.006 μm have transformed into larger ones (magnified curve sections in Fig. 11). Besides, the radii of the two majorities of pores (values of blue dash lines on the abscissa in Fig. 11) also become larger than other heating levels (values of red and green dash lines on the abscissa in Fig. 11). It is assumed that the greater gap between the curves of 600 °C and 400 °C comparing with that between 400 and 200 °C is the cause of transition of quartz from α to β at 573 °C, where the volume of quartz increases due to the transition of its form and extra microcracks are therefore induced at the grain boundary [43, 44].


The thermo-mechanical fracture caused by thermal stress can be induced by different types of thermal loading. One example is thermal fatigue which is commonly attributed to in the investigation of weathering of rocks involving temperature [45,46,47,48]. Thermal fatigue is induced by repeated thermal stress coming from cyclic variations of temperature and the cumulative damage aggravates as cycles increase. On the other hand, TS condition discussed in this study is a different type of thermal loading, where the damage in the rock matrix is caused by singular thermal stress event involving rapid changes in temperature. Although challenges exist in authenticating the alleged TS tests reported by researchers so far, as important factors of initiating TS are still unclear (such as the threshold of temperature and the threshold of temperature changing rate), the occurrence of TS can be identified by the typical patterns of fracture. Hall and Thorn proposed that TS produces two primary fracture patterns, namely orthogonal and polygonal fractures (Fig. 12a) [6]. These two fracture patterns are also observed on the specimens after heating at 400 °C and 600 °C with rapid cooling (both air-cooled and water-cooled conditions). An example is given in Fig. 12b, where orthogonal fracture pattern is shown on the left and polygonal fracture pattern is shown on the right. The observation indicates the successful performance of TS treatments in this study. It should also be noted that such fracture patterns are not found on specimens heated at 200 °C. It is assumed that at lower heating level such as 200 °C, the action of TS is not manifested. This is also supported by the fact that the physical properties at 200 °C are close to the untreated specimens.

Fig. 12

Fracture surfaces of granite specimens after TS: a orthogonal and polygonal fractures in Hall and Thorn [6], b fractures observed on the air-cooled specimen after heating at 600 °C


TS treatments with different cooling rates are successfully performed on granite specimens. The variation trends of the physical and dynamic mechanical properties are obtained. The mechanisms of TS are discussed consulting the results of the NMR technique. Particularly, the occurrence of TS is verified through the typical fracture patterns observed through SEM. Based on the scope of this study, the following conclusions can be drawn:

  1. 1.

    As heating level increases (same cooling rate) or cooling rate increases (same heating level), the dry density and P-wave velocity of the heated granite decrease, and the porosity increases.

  2. 2.

    At similar strain rates, the dynamic compressive strength of the specimen decreases with ascending heating level or cooling rate. The NMR results indicate that both the size and quantity of the pores increase with ascending heating level or cooling rate.

  3. 3.

    Primary fracture patterns reflecting the action of TS are observed through SEM. This verifies the successful application of TS treatment. Based on the observation, it is assumed that at a low heating level such as 200 °C, the action of TS (if any) is rather trivial.

  4. 4.

    In general, as heating level increases, more damage is caused which deteriorates the physical and dynamic mechanical properties of granite. Particularly, higher cooling rate further aggravates the damage. The above patterns are more excessive at heating level of 600 °C, which is believed to be caused by the additional damage due to α–β transition of quartz occurring at 573 °C.

To identify the threshold of temperature changing rate which initiates TS, more tests need to be developed where a wider range of temperature changing rates can be induced. TS test should also be applied to different rock types to elucidate the influence of the geometry and composition of minerals. The results of this study not only can provide valuable hints to the assessment of the dynamic load bearing capacity of rock structures after fire hazard, but also may inspire innovation in tunneling and mining methods with the assist of heat.


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This work was supported by the National Nature Science Foundation of China (Grant Numbers 41630642, 11972378, 51904359 and 51774325). The authors thank the anonymous reviewers and editor for their valuable hints and suggestions for the improvement of this paper.

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Correspondence to Yan Wang or Wengang Dang.

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Li, X., Li, B., Li, X. et al. Thermal shock effects on the mechanical behavior of granite exposed to dynamic loading. Archiv.Civ.Mech.Eng 20, 66 (2020).

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  • Thermal shock
  • Cooling rate
  • SHPB
  • Fracture pattern