Spatial gradient distributions of thermal shock-induced damage to granite

Lifeng Fn, Jingwei Go, Xiuli Du, Zhijun Wu

a College of Architecture and Civil Engineering, Beijing University of Technology, Beijing,100124, China

b School of Civil Engineering, Wuhan University, Wuhan, 430072, China

Keywords:Rock properties Thermal shock High temperature Thermally induced damage Computed tomography (CT) technique

ABSTRACT In this study, we attempted to investigate the spatial gradient distributions of thermal shock-induced damage to granite with respect to associated deterioration mechanisms. First, thermal shock experiments were conducted on granite specimens by slowly preheating the specimens to high temperatures,followed by rapid cooling in tap water.Then,the spatial gradient distributions of thermal shock-induced damage were investigated by computed tomography (CT) and image analysis techniques. Finally, the influence of the preheating temperature on the spatial gradients of the damage was discussed. The results show that the thermal shock induced by rapid cooling can cause more damage to granite than that induced by slow cooling. The thermal shock induced by rapid cooling can cause spatial gradient distributions of the damage to granite. The damage near the specimen surface was at a maximum, while the damage inside the specimen was at a minimum.In addition,the preheating temperature can significantly influence the spatial gradient distributions of the thermal shock-induced damage. The spatial gradient distribution of damage increased as the preheating temperature increased and then decreased significantly over 600 °C.When the preheating temperature was sufficiently high(e.g.800 °C),the gradient can be ignored.

1. Introduction

Thermal shock can induce spatial gradient distributions of the damage inside materials characterized by small thermal conduction,such as granite.More thermal damage can be induced near the boundary surfaces, whereas less thermal damage can be found inside the material (Kim et al., 2013; Li et al., 2020). The spatial distribution characteristics of thermal shock-induced damage can significantly infulence the macroscopic physico-mechanical properties of granite (Fan et al., 2017; Zhang et al., 2018a; Isaka et al.,2019), which further influences the safety of engineering. Therefore, studying the spatial gradient distributions of thermal shockinduced damage can facilitate our understanding of the deterioration mechanisms of the macroscopic properties of granite and thermal engineering applications.

The effects of thermal shock on the macroscopic physicomechanical properties of granite have been extensively studied over the last decade(e.g.Ge and Sun 2018;Zhao et al.,2018;Xu and Sun 2018; Zhang et al., 2018b; Zhou et al., 2018; Zhu et al., 2018;Kumari et al., 2019; Liu et al., 2019). Thermal shock to granite is generally achieved by preheating granite to high temperatures,followed by rapid cooling in water.Kumari et al.(2017)studied the rapid cooling effects on the uniaxial compressive behavior of granite. Their results reveal that rapid cooling results in a larger decrease in the strength and elastic characteristics than slow cooling does.Wu et al.(2019)evaluated the effects of thermal shock on the tensile strength.Their results suggested that granite cooling in water exhibits the lowest tensile strength compared with granite cooling in an oven or air when the preheating temperature is larger than 600°C. Kumari et al. (2018) studied the effects of thermal shock on the permeability of granite subjected to different stresses and temperatures. Their results showed that thermal shock can increase the porosity and crack density in granite, which further enhances the permeability of granite. Previous studies concentrated on the macroscopic behaviors of granite show that thermal shock can significantly deteriorate the physico-mechanical properties of granite.

Alternatively, the thermal shock-induced deterioration mechanisms of granite have been investigated microscopically(e.g. Zhao 2016; Isaka et al., 2018). Based on surface micro-observation techniques, Jin et al. (2019) investigated the effects of thermal shock on the development of microcracks by optical microscopy.Their results illustrated that thermal shock-induced microcracks can significantly deteriorate the macroscopic properties,e.g.the Pwave velocity, strength, and permeability. The surface microobservation technique can successfully explain the thermal shock-induced deterioration mechanisms (Rathnaweera et al.,2018; Wu et al., 2019). Nevertheless, a three-dimensional (3D)spatial micro-observation technique is essential for the micromechanism analysis of rock engineering (Jing et al., 2017; Zhang et al., 2018a; Wang et al., 2019), and 3D computed tomography(CT)is one of such techniques(Yang et al.,2017;Zhao et al.,2017).The internal structure and cracking of the region of interest inside the specimen can be analyzed quantitatively using CT and image analysis techniques.Although the field of view of the CT technique is larger than that of a microscope,the CT imaging magnification is smaller. These advantages of the CT technique can facilitate our analysis of the 3D spatial distributions of damage and our understanding of thermal shock-induced deterioration mechanisms.

For an analysis of the effects of thermal shock on 3D spatial distributions of damage,Isaka et al.(2019)studied the thermal shock on the spatial connectivity of pores in granite using CT. Their results showed that the thermal shock-induced interconnected pores can significantly enhance the permeability of granite. Additionally, the thermal shock-induced damage emerges from the outer circumferential edge of the specimen when the preheating temperature reaches 300°C after rapid cooling treatments. The spatial gradient distributions of thermal shock-induced damage are introduced to reveal the thermal shock-induced deterioration mechanisms of granite based on the ultrasonic imaging and acoustic emission monitoring techniques by Jansen and Carlson(1993).Previous results on the gradient distribution of thermal damage mainly involved twodimensional (2D) cross-sectional images and acoustic imaging images. However, applications of 3D spatial micro-observation techniques (such as CT) to quantitatively describe the spatial gradient distributions of thermal shock-induced damage have rarely been reported. The CT technique, with the capability of accurate spatial positioning and quantification analysis of thermal damage, can be used to quantitatively investigate the spatial gradient distributions of thermal shock-induced damage.

In this study,we quantitatively investigated the spatial gradient distributions of thermal shock-induced damage to granite based on the X-ray CT technique. The spatial gradient of the damage was generated by a series of thermal shocks induced by preheating to high temperature and then rapid cooling. The spatial gradient of the damage was described by the CT technique and visually reconstructed by a 3D image reconstruction method. Finally, the influence of the preheating temperature on the spatial gradients of the thermal shock-induced damage was discussed.

2. Experimental setup

2.1. Specimen preparation

The granite was sampled in Rizhao City, Shandong Province,China. The average uniaxial compressive strength (UCS) of the initial granite specimens with a diameter of 50 mm and height of 100 mm was 180 MPa, and the average Young’s modulus was 31.7 GPa. Fig.1a shows the granite specimen used in the CT tests.The granite specimens for the CT tests and the specimens for the uniaxial compression tests were processed from a large single block. The CT image resolution increased as the dimensions of the specimen decreased. According to the CT user manual and the reference (Fan et al., 2018), the specimens for CT tests were processed with dimensions of 10 mm × 10 mm × 20 mm(length × width × height). Three specimens were prepared under the same experimental conditions to avoid the contingency of the experimental phenomenon caused by small specimens.The surface of the specimen was smoothed with sandpaper to meet the CT test requirements (Nasseri et al., 2011).

Fig.1. (a) Granite specimen and (b) Mineral components.

Fig. 1b shows the granite mineral composition tested at the Research Institute of Petroleum Exploration and Development,China,by the D8-ADVANCE X-ray Diffractometer manufactured by Bruker AXS in Karlsruhe, Germany. The main minerals of the granite were quartz (37%), plagioclase (36.2%), K-feldspar (20.6%),mica (2.7%), calcite (2.5%), and clay minerals (1%). By using a microscope with an amplification of 50 times, different minerals in the initial specimen were observed to be tightly bonded with each other without visible microcracks on the surface of the specimen.

2.2. Thermal shock treatment

In this study,a total of 33 granite specimens were prepared,and they were divided into six groups according to the preheating temperatures of 25°C, 200°C, 400°C,500°C,600°C,and 800°C.

Table 1 shows the experimental grouping. Three specimens were prepared at 25°C (room temperature), and six specimens were heated at each temperature level. First, each group of specimens was heated to the target temperature at a heating rate of 2.5°C/min to avoid possible thermal shock influence during the heating phase(Chen et al.,2017;Yang et al.,2019)and was kept at the target temperature for 3 h.Then,three of these specimens wereremoved from the oven and immediately immersed in tap water to achieve rapid cooling. During the rapid cooling phase, the specimens were subjected to thermal shock. The remaining three specimens were slowly cooled to room temperature (25°C) in a turned off oven, which was used for comparison purposes.

Table 1Experimental grouping.

Fig. 2 shows the color change in the granite specimens with increasing preheating temperature after different cooling treatments. For both rapid and slow cooling, the color of specimens changed from white-gray to reddish with increasing preheating temperature, possibly due to the dehydration and oxidation of the minerals (Kumari et al., 2018).

2.3. CT scanning

Granite specimens after cooling treatments were scanned at Beijing University of Technology, China, by the Nano Voxel-2200 series high-resolution CT scanning system manufactured by Sanying Precision Instruments Co.,Ltd.in Tianjin,China.Fig.3 shows the scanning view in the shield room. A cone-shaped X-ray beam was emitted from the X-ray source and penetrated the specimen during scanning. The specimen stage was rotated at 360°. The flat panel detector captured the X-rays that penetrated specimens and converted the X-rays into digital radiographs (Obara et al., 2016; Fan et al., 2020). The digital radiographs were then processed to generate 2D slice images of the specimen.The scanning voltage was 130 kV,and the current was 80 μA.The voxel dimensions of the CT image were 16 μm × 16 μm × 16 μm.

Fig.4 shows the 3D reconstruction and the analyzed region of the selected cube after CT scanning. The 3D image reconstruction was performed by overlying 2D sliced images based on professional image analysis software of Voxel Studio Recon, which was provided by Sanying Precision Instruments Co.,Ltd.in Tianjin,China(see Fig.4a).Fig. 4b shows the 3D volume data of the whole specimen after 3D image reconstruction. The 3D volume data of the whole specimen with dimensions of 10 mm × 10 mm × 20 mm (length ×width×height)included 625,625 and 1250 layers of 2D images in x-,y- and z-direction, respectively. The thickness of each layer of the image was 16 μm. During the process of CT scanning, the beam hardening effect caused the same material in the specimen to show different gray values on the 2D slice images. The edge hardening phenomenon was one of the beam hardening effects.The gray values near the surface of the specimens were higher,which influenced the experimental data analysis(Cao et al.,2018).Therefore,a reasonable region needs to be selected.In addition, the analyzed region should include the region near the surface of specimens as possible for accurate analysis of the influence of rapid cooling on the specimen surface.After consideration,the location of the analyzed region of the selected cube inside the granite specimen ranged from the 12th layer to the 611th layer in x-and y-direction and from the 325th layer to the 924th layer in z-direction. Fig. 4c shows the details of the analyzed region of the selected cube inside the specimen. Fig. 4d shows the dimensions of the analyzed region of the selected cube. The dimensions of the selected cube analyzed region were 9.6 mm ×9.6 mm × 9.6 mm (length × width × height), which included 600 layers of 2D images in each direction.

Fig.2. Color change of granite specimens with increasing preheating temperature:(a)Rapid cooling, and (b) Slow cooling.

Fig. 3. View of scan in the shield room.

Fig. 4. 3D reconstruction and selected cube analyzed region after CT scanning: (a)Overlaying the sliced images, (b) 3D volume data made by overlaying the sliced images, (c) Location of selected cube analyzed region, and (d) Selected cube analyzed region.

To show the results clearly, the typical CT results from a single specimen in each group are shown in this study.

3. Results

3.1. Thermal shock-induced damage in the analyzed region of the cube

Fig. 5. 2D cross-sectional images of the cube analyzed region in z-direction after cooling treatments.Note:RC 200 °C denotes that the preheating temperature is 200 °C with the rapid cooling treatment.SC 200 °C denotes that the preheating temperature is 200 °C with slow cooling treatment.

Fig.6. 3D reconstruction images of the cube analyzed region after cooling treatments.

Fig.5 shows the 2D cross-sectional images of the analyzed region of the cube in z-direction after cooling treatments. The X-rays had different attenuation degrees passing through the minerals with different densities,thus leading to different gray levels in the CT images,as shownin Fig. 5.The lighter color regions indicate high-densityminerals, and the gray color regions indicate low-density minerals.Mica minerals are shown in white, feldspars in dark gray and quartzminerals in light gray shades. The pores and cracks were clearlyvisible, as illustratedinblack. Fig.5a shows that the grainswere tightlybonded with each other, and no microcracks were observed beforethermal treatments. After rapid cooling treatments, no obviousmicrocracks were observed when the preheating temperatureincreased from 25°C to 200°C (see Fig. 5b). However, new microcracks were generated in the feldspar minerals of granite after 400°C(Fig.5d).The microcracks then widened and were mainly generated at the outer boundaryas the preheating temperature increasedto500°C(Fig.5f).Microcracks increased significantly in the feldspar minerals with lower density when the preheating temperature reached 600°C(Fig.5h).Many intragranular microcracks were observed in the quartz minerals with a higher density,and microcracks were connected with each other to form a network at 800°C (Fig. 5j). After slow cooling treatments,new microcracks were observed at 500°C(Fig.5g).As the preheating temperature further increased to 600°C,the number of microcracks significantly increased. This change trend is similar to that after rapidcooling treatments.However,rapid cooling can induce more microcracks in the analyzed region of the cube than slowcooling does because of the intense thermal shock(Wong et al.,2017).

Fig.6 shows the 3D reconstruction images of the cube analyzed region after cooling treatments. 3D images were reconstructed by overlying 2D images using CT image analysis software. In the 3D images,the minerals or microcracks were separated by appointing grayscale values to the separation points of the minerals according to the CT user manual and the work of Isaka et al.(2019)and were given a specific color,as shown in Fig.6.The green regions denote damage.The change trend of thermally induced damage in the 3D images was similar to that in the 2D images (see Fig. 5). Fig. 6a shows that only a few pre-existing pores were observed in the specimens before thermal treatments. After the rapid cooling treatments, the thermal shock-induced damage changed slightly from 25°C to 200°C(Fig.6b).New thermal shock-induced damage was generated at 400°C and further increased as the preheating temperature increased to 500°C (Fig. 6d and f). Thermal shockinduced damage increased significantly as the preheating temperature increased from 500°C to 600°C (Fig. 6h). Thermal shockinduced cracks coalesced and developed macroscopic damage at 800°C (Fig. 6j). On the other hand, Fig. 6g shows that after slow cooling treatments,new thermally induced damage was generated at 500°C. Subsequently, the thermally induced damage increased significantly as the preheating temperature further increased over 500°C, which was similar to that after rapid cooling treatments.

Fig. 7. Porosity of the cube analyzed region after cooling treatments.

Table 2Division of local regions.

In this context, more spatial information of thermally induced damage was presented in 3D images compared with 2D images.Fig.6 shows that after rapid or slow cooling treatments,the spatial distribution of thermally induced damage was relatively scattered when the preheating temperature reached 600°C.The distribution of the thermally induced damage in the whole space of the analyzed region of the cube tended to be homogeneous when the preheating temperature was 800°C.

The thermal shock-induced damage can be quantitatively evaluated by the porosity(P)based on the 3D image analysis technique.The porosity (P) is calculated by

where VPoreand VTotalare the volume of thermal shock-induced damage and the total volume of the cube analyzed region,respectively.

Fig.7 shows the relationship between the porosity and preheating temperature. The porosity after both rapid and slow cooling treatments increased slowly before a preheating temperature of 500°Cand then increased sharply. However, the porosity induced by rapid cooling was larger than that induced by slow cooling.In addition,the differences in the porosities induced by rapid and slow cooling treatments increased when the preheating temperature increased.

3.2. Spatial distributions of thermal shock-induced damage

The thermally induced damage was not visible below 200°C in the CT images. Therefore, this study mainly analyzed the spatial distribution characteristics of thermally induced damage at 400°C,500°C, 600°C and 800°C.

Fig. 9. Distribution characteristics of the porosities of five local regions.

Fig. 8 shows the division of local regions for analyzing the thermally induced damage of different local regions from the surface of the specimen inwards.First,the analyzed region of the cube having a volume of 884.7 mm3was divided into three local regions by equal volume from inside to outside,which was denoted as local regions 1,3 and 5,respectively.The volume of each local region was equal to 294.9 mm3. Subsequently, local regions 2 and 4 were added to refine the division of the local regions.Both of the volumes of local regions 2 and 4 were also equal to 294.9 mm3.Local region 2 was the transition between regions 1 and 3.It was appropriate that local region 2 was located in the middle of local regions 1 and 3.Therefore, the method of dividing local region 2 was that the overlapping volume of local regions 2 and 1 was equal to the overlapping volume of local regions 2 and 3.The method of division of region 4 was the same as that of local region 2.The overlapping volume of local regions 4 and 3 was equal to the overlapping volume of local regions 4 and 5.Fig.8a shows the location of five local regions. The height of all five local regions in z-direction was 9.6 mm.Fig.8b shows the detailed dimensions of the cross-section of five local regions in z-direction.Fig.8c-g shows the local regions 1 to 5, respectively. The cross-section of local region 1 in the z-direction was a square with a side length of 5.543 mm.Fig.8d shows that the cross-section of local region 2 in z-direction was a hollow square with an inner side length of 3.919 mm and an outer side length of 6.788 mm.Fig.8e illustrates that the cross-section of local region 3 in z-direction was a hollow square with an inner side length of 5.543 mm and an outer side length of 7.838 mm. Fig. 8f displays that the cross-section of local region 4 in z-direction was a hollow square with an inner side length of 6.788 mm and an outer side length of 8.764 mm. Fig. 8g shows that the cross-section of local region 5 in z-direction was a hollow square with an inner side length of 7.838 mm and an outer side length of 9.6 mm.The division dimensions of local regions are shown in Table 2.

The damage induced by thermal shock could be inhomogeneous in z-direction. Therefore, the average damage degree of the entire local region should be calculated to avoid the effects of inhomogeneous damage along z-direction on the analysis of the results.The average damage degree of each local region i can be described by porosity(Pi),which is a percentage of the damage volume to the total volume of local region i.

Fig.9a-d shows the spatial distributions of the porosities of the five local regions after cooling treatments when preheating temperatures were 400°C, 500°C, 600°C and 800°C, respectively.Different spatial distributions with increasing preheating temperatures after rapid and slow cooling treatments were observed.After rapid cooling treatments, it is seen from Fig. 9a-c that the increasing tendency was obvious in the distribution of the porosities of the five local regions at 400°C, 500°C and 600°C,respectively (see red lines). The porosity of local region 1 was the minimum and that of local region 5 was the maximum in the distribution of the porosities of the five local regions.Interestingly,as the preheating temperature further increased (e.g. 800°C, see Fig. 9d), a slight change in the porosities can be noticed in the distribution of the porosities of the five local regions.On the other hand,Fig.9a-d shows that the distribution of the porosities of the five local regions after slow cooling treatments,which was different from that after the rapid cooling treatments at 400°C, 500°C,600°C and 800°C, respectively(see black lines).

4. Discussion

4.1. Spatial gradient distributions of thermal shock-induced damage

The parameter kiwas introduced to describe the change tendency of the porosity as the local regions change from i to i+1.The parameter kiis the slope of the relationship between the porosity and the distance as the local regions change from i to i+1:

Fig.10. Distribution characteristics of the parameter ki after rapid and slow cooling treatments.

where Piand Pi+1(i = 1, 2, 3 and 4) denote the porosities of local regions i and i+1,respectively;and didenotes the distance between local regions i and i+1.

In Eq. (2), the kivalues larger than zero indicate an increase in the porosity as the local regions change from i to i+1. The kivalue less than zero indicates a decrease in the porosity as the local regions change from i to i+1.The k1,k2,k3and k4values greater than zero indicate the existence of the spatial gradient distribution characteristics of thermal induced damage. This was a scenario in which the damage increased monotonically as the distance from the center of the specimen increased.

Fig.10 shows the positive and negative distribution characteristics of the parameters ki(i = 1, 2, 3 and 4) after rapid and slow cooling treatments under four preheating temperatures(i.e.400°C,500°C, 600°C and 800°C). The different distributions of the parameter kivalues after rapid and slow cooling treatments were observed.After rapid cooling treatments,Fig.10a-c shows that the k1,k2,k3and k4values were all greater than zero at 400°C,500°C and 600°C, which suggested the existence of the spatial gradient distribution characteristics of thermal shock-induced damage.When the preheating temperature increased to 800°C (see Fig.10d),some of the k1,k2,k3and k4values were greater than zero and some were less than zero.The porosity differences between the five local regions were small at 800°C. The normal experimental error can induce fluctuations in the porosity values of the five local regions.This effect can be used to explain the positive and negative changes in the calculated kivalue. In practice, the spatial gradient distribution characteristics of thermal damage induced by rapid cooling treatments can be ignored at 800°C.

After slow cooling treatments, Fig. 10a-d shows that some of the k1, k2, k3and k4values were greater than zero and some were less than zero at each preheating temperature level(400°C,500°C,600°C and 800°C).This phenomenon was different from that after rapid cooling treatments. The spatial gradient distribution characteristics were mainly induced by significant thermal shock.

4.2. Effect of preheating temperature on the spatial gradients of thermal shock-induced damage

Fig. 11 shows the relationship between the porosity and the distance from the center of the specimen after rapid cooling treatments under four preheating temperatures(i.e.400°C,500°C,600°C and 800°C).It can be seen from Fig.11a-d that the porosity of the local region increased approximately linearly as the distance from the center of the specimen increased at each preheating temperature level. The slope of the fitting line was then used to evaluate the gradient of the spatial distribution of thermal shockinduced damage at temperatures of 400°C, 500°C, 600°C and 800°C. The differences in damage between the inside and the surface of the granite specimens increased as the gradient increased.

Fig.12 shows the effects of the preheating temperature on the gradient of the spatial distribution of the thermal shock-induced

Fig.11. Relationship between porosity and distance from the center of specimen after rapid cooling treatments.

Fig. 12. Effects of preheating temperature on the gradient of spatial distribution of thermal shock induced damage.

(1) The thermal shock induced by rapid cooling can cause more damage to granite than slow cooling does.

(2) The thermal shock induced by rapid cooling can cause the spatial gradient distribution of the damage.The damage near the surface of the specimen was the maximum, while the damage inside the specimen was the minimum.

(3) The preheating temperature can significantly influence the spatial gradient distribution characteristics of thermal shockinduced damage. The gradient of the spatial distribution of thermal shock-induced damage increased as the preheating temperature increased. Subsequently, the gradient decreased significantly when the preheating temperature further increased over 600°C.When the preheating temperature was sufficiently high(e.g.800°C),the gradient can be ignored.damage. The gradient of the spatial distribution of the thermal shock-induced damage increased with increasing preheating temperature and then decreased significantly at temperatures over 600°C. When the preheating temperature was sufficiently high(e.g.800°C),the spatial gradient was approximately zero and could be ignored.

Fig.12 also shows the 3D reconstruction images of the thermal shock-induced damage of local regions 1,3 and 5 at each preheating temperature level.It was observed that the thermal shock-induced damage of each local region increased as the preheating temperature increased and then connected with each other at temperatures over 600°C.

Granite exhibits small thermal conduction (Zhao et al., 2019).The greatest thermal shock stresses are generated on the surface of the specimen and decrease with increasing specimen depth when cold water is suddenly applied to the specimen at 400°C(Kim et al.,2013;Shao et al.,2014;Kumari et al.,2017).This effect can be used to explain the spatial gradient distribution of thermal shockinduced damage at 400°C, with the maximum damage near the surface of the specimen and the minimum damage inside the specimen.The greatest thermal shock stresses on the surface of the specimen increase with increasing preheating temperature (Wu et al., 2019), which can be used to explain the increase in the gradient of the spatial distribution of damage. However, when the preheating temperature is sufficiently high (e.g. 800°C), the thermal shock stresses are sufficiently high causing severe cracking throughout the specimen (Isaka et al.,2019). The damage tends to be homogeneous in the specimen at 800°C. Therefore, the spatial gradient can be ignored at 800°C.

According to thermal shock-induced damage characteristics,thermal shock can be adopted to induce more microcracks to improve the efficiency of the energy extraction and engineering excavation.On the other hand,thermal shock-induced microcracks should be avoided to prevent the leakage of nuclear waste and decrease the stability of rock.

5. Conclusions

In this study, the spatial gradient distribution characteristics of thermal shock-induced damage were quantitatively studied using CT and image analysis techniques. The conclusions were drawn as follows:

The present study mainly focused on the spatial gradient distribution characteristics of thermal shock-induced damage to granite. More microproperties and micromechanisms of thermal shock-induced cracking shall be further studied, e.g. the quantitative analysis of thermally induced cracks in different minerals and the mechanism analysis of thermal shock-induced cracking by numerical simulation.

Declaration of competing interest

The authors confirm that there are no known confilcts of interest associated with this publication, and there has been no signifciant fniancialsupportforthisworkthatcouldhaveinfluenceditsoutcome.

Acknowledgments

The research was funded by the National Natural Science Foundation of China, China (Grant Nos. 51778021, 51627812 and 51678403).