2.1 Preparation of samples

The samples used in this experiment were selected from gabbro samples from Shandong Province, China. The main diagenetic minerals of the selected gabbro are pyroxene and plagioclase, with a small amount of olivine and amphibole. The average density of the sample is 2.85 g/cm3. To reduce the test error, all the samples were selected as large block gabbro samples with uniform texture in the same stratum, and the original cracked straight-through Brazilian disc (CSTBD) gabbro sample model is shown in Figure 1a. Figure 1b shows the schematic diagram of the precast crack after filling cement. Figure 1c shows the side view of the sample prefabricated crack of the CSTBD sample is 30 mm in length, 2 mm in width, D = 50 mm in diameter, B = 25 mm in thickness, and β is the crack angle.

2.2 Testing equipment

In this study, the samples were heated using a BLMT-1400°C muffle furnace manufactured by Henan Luoyang Bright Test Electric Furnace Co. Ltd., with a maximum heating temperature of 1400°C and a controllable heating rate ranging from 1 to 30°C/min. Stress loading was performed using an MTS-E64.206 servo-hydraulic universal testing machine, produced by MTS Systems (China) Co., Ltd., which has a maximum load capacity of 2000 kN and a stress application rate adjustable between 1 and 30 MPa/s. The fault process was monitored using the MatchID-2D/3D measurement and simulation optimization analysis system, developed by MatchID Company in Belgium. This system utilizes MI-DIC technology to measure the three-dimensional displacement and strain fields, and to calculate the corresponding stress fields. The crack propagation process during loading was recorded in real-time with a high-speed camera operating at a frame rate of 60 frames per second.

2.3 Testing procedure

Before testing, the samples were dried in an oven at 50°C for 2 h to eliminate moisture and prevent water interference during subsequent heating. The samples were then heated in a BLMT-1400°C muffle furnace at a rate of 5°C/min to target temperatures of 25, 200, 340, 500, 600, and 800°C. Upon reaching the designated temperatures, the samples were held at the target temperature for 2 h to ensure uniform thermal equilibrium. Subsequently, prefabricated cracks in some samples were filled with cement. Portland cement, a commonly used binding material known for its hardening and strength retention in both air and water environments (Liu et al., 2019), was selected for this study. Specifically, PO 42.5 ordinary silicate cement was used to prepare the slurry with a water-to-cement ratio of 1.0:0.5. The basic physical properties of PO 42.5 ordinary silicate cement are listed in Table 1. Crack filling was performed using the grouting method proposed by Pan et al. (2019). Before grouting, the bottom of each defect was sealed to prevent slurry leakage. Cement slurry was then injected into the cracks using a specialized grouting apparatus. After an initial setting period of approximately 10 min, the filling material within the cracks was repeatedly compacted by crushing and refilling to enhance density until the defects were completely filled. Once the cement was fully cured, the specimens were subjected to water curing within the cracks for 21 days. The mechanical properties of all samples were tested under a loading rate of 0.05 MPa/s. The samples were placed at the crack angles β of 0°, 15°, 30°, 45°, 60°, 75°, and 90°, respectively. The crack expansion process was recorded in real time by using a high-speed camera. To ensure the reliability and reproducibility of the experimental results, three replicate CSTBD gabbro specimens were tested for each experimental condition. In total, 252 specimens were utilized in this study.

3.1 Load–displacement curves

The relationship between load and displacement of samples with different angles after different heat treatments is shown in Figure 2. Under the load, all samples initially exhibited compression, and the load rises slowly with the increase of displacement.; with the increase in the load, the samples entered the elastic deformation stage, and the fracture load increased linearly with the increase in the displacement. The samples failed after the peak load, and the load decreased rapidly. The variation trend of load-displacement curves of specimens with different crack inclination angles is basically the same. In Figure 2, most of the dotted lines are below the solid lines; that is, most of the load–displacement curves of the unfilled crack samples are below those of the filled crack samples. Crack filling increased the peak load of the CSTBD gabbro samples. High temperature treatment has a great influence on gabbro load strength. For 25–340°C, the peak load of samples with different angles does not change significantly. When the temperature is higher than 500°C, the peak load decreases obviously, and the peak load reaches the minimum value when the temperature is 800°C.

3.2 Peak load

The variations in the peak load with temperature for gabbro samples before and after fracture filling are shown in Figure 3. The peak load of the packed sample did not change significantly in the temperature range of 25–340°C, and the peak load increased slightly at 340°C compared with room temperature. When the temperature exceeds 340°C, the peak load of the sample decreases continuously with the increase of the treatment temperature, and reaches the minimum value at 800°C, which is only 57.65% of that of the samples at room temperature at β = 15°. For unfilled samples, the peak load did not change greatly when the temperature was below 200°C. After exceeding 200°C, the peak load started to decrease continuously and reached the minimum at 800°C, which is only 44.2% of that of the samples at room temperature at β = 90°. In addition, it can be clearly seen from the figure that the peak load of the filled sample is greater than that of the unfilled sample, especially after 340°C. The filling of cement increases the peak load of the sample.

3.3 Fracture toughness

Figure 4 shows the variation of I–II fracture toughness of unfilled CSTBD samples with the treatment temperature. The variation rules of KIC and KIIC of samples with different crack angles are different under different temperature treatments. When the crack inclination β is 0°, KIC decreases slightly with the increase of temperature at 15° and by about 40% at 800°C. When the crack inclination is greater than 30°, KIC gradually increases with the increase of temperature, and there is an obvious upward trend at 600°C and an increase of more than 40% at 800°C, while the KIC of the sample with the crack inclination of more than 30° increases gradually with the increase of temperature, and has an obvious upward trend at 600°C. When the crack inclination is 0° and 90°, the sample is pure tensile and compressive failure, so the KIIC is always 0. When the fracture inclination β is 15°, 30°, 45°, 60°, 75°, and when the temperature is lower than 600°C, the KIIC decreases slightly with the increase of temperature, and shows a significant downward trend at 600°C. In view of this, 600°C can be defined as the threshold temperature for significant changes in fracture toughness.

The variations in the fracture toughness of unfilled CSTBD gabbro type I and type II with the crack angle β are depicted in Figure 5. It can be seen that KIC increases with the increase of fracture inclination, but the decline rate decreases gradually. After β reaches 75°, KIC basically does not change. KIIC increases first and then decreases with the increase of fracture inclination, reaching the maximum of 3.34 when β = 30°. For β = 0°, the KIC is greater than zero, and the KIIC value is zero, indicating that the samples are pure tensile failure. With the increase of the crack angle β (0°–22°), the KIC decreases and the KIIC increases, indicating that the failure of the sample is in the tensile-shear mixed mode. For β was approximately 22°, KIC was zero, indicating shear damage at this crack angle. KIC and KIIC decreased with increasing crack angle, and after 22°, KIC was negative, indicating that the sample damage mode changed to mixed-mode compression-shear damage. For β = 90°, the failure was compression damage. β = 22° is the threshold crack angle for failure mode transformation of the sample. In conclusion, the crack inclination angle has a considerable effect on fracture toughness.

3.4 Fracture patterns

The failure morphology of CSTBD gabbro samples with different crack angles filled and unfilled after different heat treatments is shown in Tables 2 and 3. As can be seen from the table, crack angle has a significant effect on the fracture behavior of the CSTBD sample. For the specimen whose crack angle is 0°, the failure mode is pure tensile failure. Cracks occurred along the loading direction in both filled and unfilled samples, and secondary cracks also appeared; in addition, secondary cracks were observed. The failure mode of the specimen with a crack angle of 15° is tensile shear mixed failure. Under this condition, the failure crack starts at the two ends of the preset crack and extends to the upper and lower contact points between the sample and the press. For samples with crack angles of 30°, 45°, 60°, and 75°, the failure mode was compression-shear failure, and the main failure crack was affected by a prefabricated crack. For the sample with a crack angle of 75°, the main crack does not start at the end of the preset crack, but extends from below the end of the prefabricated crack, which is consistent with the results reported by Al-Shayea (2005). The aforementioned observations were for unfilled samples at 200, 600, and 800°C and for most filled samples. The failure mode of the specimen whose crack angle is 90° is pure compression failure. It should be noted that at this time, the failure surface of the filling sample at 600 and 800°C breaks along the loading direction, and there is no secondary crack of the unfilled sample at 600 and 800°C, which may be caused by the filling cement preventing the secondary development of the crack.

Table 2. Failure patterns of unfilled cracked straight-through Brazilian disc gabbro samples at different temperatures and crack angles.

Table 3. Failure patterns of filled cracked straight-through Brazilian disc (CSTBD) gabbro samples at different temperatures and fracture crack angles.

4.1 High-temperature thermal damage

The calculated thermal damage of samples with different crack angles is shown in Figure 6. It can be seen that at lower temperatures, the thermal damage of gabbro does not vary greatly and even appears negative due to the only binding of rock minerals and the escape of attached water and interlayer water from tiny pores (Zhang et al., 2023). The negative value is due to the expansion of mineral particles caused by heat treatment, resulting in the closure of some primary fractures, which slightly reduces the pore space of gabbro (Peng & Yang, 2018). With the gradual increase of temperature, different degrees of thermal expansion occur inside the mineral, connecting the originally isolated pores with dead-angle pores (Shang et al., 2019). At the same time, crystal particles form intergranular cracks under thermal stress and gradually expand and develop to form micro-cracks inside the sample (Hassanzadegan et al., 2014; Vidana Pathiranagei & Gratchev (2021)), resulting in increased thermal damage of the sample starts at 500°C, increasing sharply after 600°C and reaching the maximum at 800°C, which increases 4.23 times compared with 600°C. It can be considered that 600°C is the threshold temperature for the significant increase of thermal damage.

Due to the different rock types and loading disposition methods used, normalization of fracture toughness was performed to better show the effect of high temperature on rock fracture toughness. The variation trend of normalized type I and type II fracture toughness with temperature in different studies is shown in Figure 7. The normalized fracture toughness of type I and type II has no significant change when the temperature is below 200°C, but decreases with the gradual increase of temperature after 200°C, and drops sharply after 600°C. This result is consistent with the findings of Zhang et al. (2022) and Yin et al. (2020) on the influence of different heat treatments on the mixed fracture toughness of granite. In their study, the fracture toughness began to decline sharply at 200°C, while in the current study, it began to decline at around 500°C; this difference is due to the type of sample used: the internal mineral composition and structure of granite and gabbro are different.

4.2 Deformation procedure

The DIC technique is used to measure full-field deformation displacement of the target surface by an optical method (Miao et al., 2021). The basic principle is to track the same pixel points in the two digital images recorded before and after deformation. As shown in Figure 8, the correlation function is used to track the position of the subimage in the deformation image or the square subset (2 N + 1) × (2 N + 1) centered on the consideration point. The position of the sub-image and its displacement component are obtained by calculating the maximum or minimum coefficients (Gao, Yao, et al., 2015, Gao, Huang, et al. 2015).

In the loading process, cracks caused by rock failure are closely related to changes in the strain field (Zhang et al., 2022). In this study, DIC technology was used to monitor the strain during loading. The Mises strain failure evolution of typical samples at different temperatures was shown in Figure 9. Due to the small initial load, the germination, development, and propagation of microcracks were slow, and the von Mises strain did not change significantly under the initial load; however, it was insufficient to form macroscopic cracks. Subsequently, with the increase in the load, the strain energy in the sample accumulates gradually, and the microcracks develop and expand further. It was obvious that von Mises strain increased significantly, and cracks began to appear at the top and bottom of the sample. At the peak load, the direct through connection of microcracks in the samples resulted in macroscopic cracks and failure of the samples, and an obvious longitudinal high-strain band appeared in the von Mises strain diagram.

4.3 Fracture mode of the unfilled sample and the filled sample

Under different loading modes, according to the change trend of fracture toughness of the specimen and the failure characteristics of the specimen, combined with the research results of predecessors (Xing et al., 2020), Figure 10 shows the stress response and fracture characteristics of unfilled CSTBD gabbro samples under different loading modes: (1) pure type I tensile loading failure mode (β = 0°) (Figure 10a), the stress is concentrated at both ends of the precast crack, and the failure surface of the specimen is perpendicular to the horizontal direction; (2) the I–II tensile shear loading failure mode (β = 15°) (Figure 10b), The stress is also concentrated at the end of the precast crack, and the main crack expands from the end of the precast crack to the loading point, resulting in tensile shear fracture of the specimen; (3) type I–II compression shear loading failure mode (β = 30°, 45°, 60°, and 75°) (Figure 10c), the specimen ruptures under the action of compression shear; (4) the compression loading failure mode (β = 90°) (Figure 10d), the compression crack of the compressed specimen extends to the contact point between the specimen and the pressure, resulting in pure compression failure of the specimen.

Figure 11 shows the stress response and fracture characteristics of the packed CSTBD gabbro. When β = 0°, according to Figure 11a, tensile fracture occurs in the sample in this mode, and the stress is concentrated in the prefabricated crack after filling, and the crack extends from the initiation of the end point of the prefabricated crack to the loading point. At this time, the interface bonding force between cement and rock resists the tensile fracture of the sample. When β = 15°, 30°, 45°, 60°, 75°, corresponding to Figure 11b, the failure mode of the sample is tensile shear failure. The filled CSTBD gabbro sample is equivalent to a whole. In this case, the pressure on the sample is shared by the filled cement and the sample. The filled CSTBD gabbro sample is equivalent to a whole body. In this case, the pressure on the sample is shared by the filled cement and the sample, and the stress is changed from concentrating only on the tip of the prefabricated crack to concentrating on the entire prefabricated crack. The compressive stress is shared by the cement and the prefabricated crack, and the interface adhesion and friction between the cement and the rock resist the compressive shear stress of the sample and prevent the crack propagation along the direction of the prefabricated crack.

4.4 Action mechanism of filling cement

After cement filling, the peak load that the samples can bear increases significantly, and there is no transverse crack extending along the prefabricated fracture direction in some of the filled samples, and the failure modes are changed from four modes of pure tensile failure, tension-shear failure, compression-shear failure, and pure compression failure to two modes of pure tensile failure and compression-shear failure, indicating that grouting filling can significantly improve the bearing capacity of the rock mass. The mechanism of action of filling cement is to weaken the stress on the rock (Luo et al., 2021). The filled cement generates sliding friction with the crack surface of the sample and bears part of the normal stress during the loading process, which hinders the crack initiation and extension of the crack (Pan et al., 2019). In addition, the filled cement also reduces the degree of stress concentration, so that the stress originally concentrated only on the crack tip is concentrated on the entire prefabricated crack, and thus increases the peak load that the sample can bear (Cui et al., 2022; Liu et al., 2019), as shown in Figures 10 and 11.