EVALUATION OF THE THERMAL INDUCED DAMAGE OF ROCKS

*D. S. Cheon, J. G. Kim, E.S. Park, and B.G. Chae Korea Institute of Geoscience and Mineral Resources 124 Gwahang-no Daejeon, Korea (*Corresponding author: [email protected]) EVALUATION OF THE THERMAL INDUCED DAMAGE OF ROCKS

ABSTRACT

The underground structures such as high-level radioactive waste disposal thermal energy storage should be designed and constructed considering thermal-mechanical characterization because of long term and/or cyclic thermal stress. High temperature changes in these structures can extend the existing cracks and generate new cracks in surrounding rock mass. In case of long term and/or cyclic thermal stress conditions, it is possible to lose the function of structures caused by the significant cracks and fracture growth in the rock mass. In this study, the critical thermal crack temperature of the granite, limestone and thermal Kaiser effect were evaluated. Experiments were carried out with the heating speed of 1.5 ℃ /min. To avoid thermal shock and target temperatures were set at 150 ℃ and 250 ℃ . In order to verify the thermal Kaiser effect, the samples were heated by 150 ℃ after 2-3 repetition to 250 ℃ . The generation and growth of cracks were observed through an acoustic emission measuring system. The variation of the physical rock properties was measured before and after thermal experiments. After compared with the thermal experiments using PFC2D, numerical simulations were carried out at higher temperatures (400℃ ). The experiments showed that the initial thermal crack temperature of granite and limestone is about 35 ℃ , 32 ℃ and the critical thermal crack temperature were about 69 ℃ , and 49 ℃, respectively. The experiments confirmed the thermal Kaiser effect of experimented granite and limestone due to thermal cyclic loading. From the numerical analysis, the critical crack temperature showed the same tendency as the thermal experiments. The P and S wave velocity of the sample after the experiment were reduced. Therefore, when heat is applied in long-term and repetitive conditions, these cracks may affect the function and stability of the underground structure. Therefore, further studies of thermal stress effects should be performed.

KEYWORDS

Heating, Critical thermal crack temperature, Thermal Kaiser effect, Acoustic emission, PFC

INTRODUCTION

High-level radioactive waste disposal sites and thermal energy storage facilities in the underground are repeatedly applied by heat. The thermal stress which is caused by heat loading can generate micro-cracks and propagate the existing micro-cracks of the rock mass surrounding these structures. The failures of underground structures by thermal stress can be divided into two kinds depending on the mechanism (Lee, 1993).

One of them is a thermal shock failure, which can be caused by temperature gradient in the rock. It is sometimes called as thermal spalling. The phenomenon in this kind of failure can be shown as a progressive splitting. The other occurred under no temperature gradient in the rock or even if the temperature gradient exists the thermal stress caused by thermal gradient is very small, therefore it cannot affect rock failure. It is called as a thermal cracking which is caused by the thermal expansion difference between the minerals or by the thermal expansion anisotropy between the mineral itself. Therefore, in order to ensure the long-term stability of underground structures subjected to thermal load, the studies on the microscopic thermal failure are required. In relation to this, some previous researchers have been studying as follows. Mahmutoglu (1998) carried out the uniaxial compressive tests for sandstone after heating to 600 °C and showed the reduction of the uniaxial compressive strength and Young's modulus as increasing the number of heating. According to Chaki (2008), micro-crack occurred in granite at 105 ℃ and the change of Young's modulus, uniaxial compressive strength and tensile strength were shown at 500 ℃ ~ 600 ℃ which was induced by increasing porosity and permeability and decreasing wave velocity due to the increment of micro-cracks and propagation and coalescence of existing micro-cracks.

Yang and Wang (1980) performed repeated heating experiments for granite, diabase and the limestone at various temperatures. They reported the thermal Kaiser effect that it does not occur acoustic emission (AE) to previous maximum heating temperature during reheating. Potyondy and Cundall (2004) suggested the behavior of the rock from a microscopic point of view through the binding of distinct element method and bonded-particle model of a circular or spherical shape. The biggest advantage of this model is that the behavior of the model can be defined only the binding force between the particles and the stress-displacement relationship. It can reproduce directly the progressive failure process of the rock through the loss of particles.

Wanne and Young (2008) simulated the experimental results that Jasen et al.(1993) has been executed using the bonded-particle model. They showed that the amount of acoustic emission signals and the patterns of crack occurrence are similar to those of the laboratory experiments.

In this paper, we performed the thermal experiments to evaluate the thermal induced damage of granite and limestone. We used an initial thermal crack temperature, where a crack is firstly detected from AE measurement, and critical thermal crack temperature, where cracks are continuously detected from AE as damage index. We also examined the thermal Kaiser effect through a repeated heating and the changes of the properties through the X-ray CT and the wave velocity at the before and after the thermal experiments. By numerical experiments using the particle-bound model, we assessed the trend of crack occurrences and failure mechanism as well as critical thermal crack temperature and thermal Kaiser effect.

SAMPLE, EXPERIMENTAL APPARATUS AND METHOD

The samples used in this study are Hwangdeung granite and Danyang limestone, which are Korea's representative rocks. These were classified into two groups depending on whether these are vertical to the texture considering the transversely anisotropy. However, according to the results of preliminary experiments, there is rarely relationship between thermally induced damage and anisotropy. Therefore, in this paper, we only describe the samples which are vertical to the texture. Table 1 shows physical, mechanical and thermal properties of Hwangdeung granite and Danyang limestone used in the experiments.

Table 1 – Physical, mechanical and thermal properties of samples Granite Limestone Properties Value Value Density (g/cm3) 2.65 2.71 P-wave velocity (m/Sec) 3,490 4,470 S-wave velocity (m/Sec) 2,400 2,900 Compressive strength (MPa) 178 155 Tensile strength (MPa) 7.4 8.2 Young’s modulus (GPa) 42.2 58.7 Thermal conductivity (W/m-K) 2.51 3.37 Volumetric heat capacity (106 J/m3-K) 2.18 2.43

In order to evaluate the mineralogical characteristics of the samples, XRD (X-ray diffractometer) quantitative analysis were carried out (Table 2). An executed method in which it was applied is that the powder of the samples was coated on polyethylene film to an aluminum disk-shaped holder with holes of 1 cm in diameter and then the weight of sample after passing through X-rays was analyzed. The range of analytical error is about 1-2%.

Table 2 - Results of XRD analysis Granite Limestone Minerals Composition, % Minerals Composition, % Albite 45.0 Calcite 1 69.4 Quartz 25.5 Quartz 19.5 Orthoclase 1 18.8 Muscovite 4.4 Biotite, 1M 7.7 Dolomite 3.4 Magnetite 3.0 Chlorite 3.3

The environmental chamber of Interlaken Inc. was used in order to implement high-temperature conditions. This chamber can be set up to 300 ℃ and the inner temperature can be controlled by a manual and automatic method. Two kinds of AE sensors were used to measure thermal induced cracks. The S9215 AE sensor is for low and high temperature, can be used up to 540 ℃. The WD AE sensor is used in wideband and can be measured up to 177 ℃. Both of them are manufactured by PAC. Duraseal 1531 was used as a couplant for high temperature in order to transmit smoothly the signals between the sample and the AE sensor. This couplant can be used up to 340 ℃. Some parts of the S9215 are covered with a metal to enable the application to cryogenic or high temperature environments, which increase the weight of the sensor. It sometimes causes contact problems, so high-temperature tape was used for rigid contacting.

The AE measurement system, including PCI/DSP-4 of PAC was used and the signals were pre- amplified by 60 dB since the energy from thermal cracking is expected to be very small. Also, the threshold is set to 45 dB, which is the lowest value as possible considering background noise. Figure 1 shows samples with AE sensor within the chamber for thermal cracking experiments.

Figure - 1 Core samples of thermal cracking experiments (Left: granite, right: limestone)

In addition, the X-ray CT scan was taken to observe the existing cracks and occurred cracks after the experiment. The feature of used micro-focus X-ray CT apparatus (SMX-225CT by Shimadzu Corporation) is the maximum power of 225 kV, maximum current of 1 mA, maximum resolution of 4 micron. This CT system can non-destructively analyze the image and inspect the interior of the sample in 2D/3D conditions. The voltage, current and resolution was set to 140 kV, 140 uA and 27 micron respectively. The images were saved as an interval of 0.6 °. Thermal experiments were carried out at two different target temperatures; 150 ℃ and 250 ℃. This is because the WD sensor, which is 100 times more sensitive than S9215, is only available up to 177 ℃. When the WD sensor is used, the AE from thermally induced crack can be detected as well. In order to assess the thermal Kaiser effect, experiments were carried out in a sequential order of heating up to 250℃ after twice repeating heating up to 150 ℃ and then cooling down to 25 ℃. If the target temperature of experiments is 150℃, both of two S9215 sensors and one WD sensor were used. However, in the case of 250 ℃, only two S9215 sensors were used in the same location as the case of 150 ℃. To avoid thermal shock, experiments were performed at the heating rate of 1.5 ℃/min. Until a target temperature was reached. Therefore, the most of cracks maybe be generated not from the entire whole sample, but from the surface of the sample. P and S wave velocity were measured after repeated heating and cooling for checking the change in physical properties. These changes are indirectly used for investigating the occurrence of cracks.

RESULTS OF THERMAL CRACKING EXPERIMENTS

The crack was firstly detected by the WD sensor as expected in the thermal experiments. The detected numbers of cracks by the WD were about 50 to 100 times higher than the S9215. This is reasonable considering the sensitivity difference between both sensors. From the AE measurement, the initial thermal crack temperature and critical thermal crack temperature of granite are 35 ± 7 ℃ and 69 ± 10 ℃, respectively. In the case of limestone, each temperature is 32 ± 4 ℃ and 49 ± 9 ℃. In addition, the cumulative crack numbers of granite were three times more than those of limestone granite. Figure 2 shows the generated AE pattern and distribution of amplitudes of granite with temperature. After passing critical thermal crack temperature, the AE were continuously generated and the lower energy of cracks was more generated. The additional detected AE from the interval of 150 ℃ to 250 ℃ was small since those were measured by the low sensitive sensor, S9215 and amplitude of AE were relatively low compared to those of the WD.

Figure– 2 Measured AE signals of granite (left: cumulative cracks, right: amplitude distribution)

The amount of AE was very small when it cooled to room temperature after heating up to 150 ℃. There was rarely detected AE during secondly heating up to previous maximum temperature and after passing that temperature AE was being detected. From these results, it was confirmed that the thermal Kaiser effect.

P and S wave velocity of granite before heating test was 3490 ± 100 m/Sec and 2400 ± 30 m/Sec, respectively. After first heating and cooling, these were reduced to 3450 ± 80 m/Sec and, 2330 ± 20 m/Sec. After the third experiment which was heated to 250 ℃, the reduction of P and S wave velocity was 200 m/s and 100 m/s. It was found that the changes in the physical properties due to repeated heating and cooling, although the amount of reduction is not large. In the case of limestone, the first P-wave and S- wave velocity were 4470 ± 50 m/Sec and 2900 ± 10 m/Sec, they were reduced to 4360 ± 10 m/Sec and 2810 ± 10 m/Sec after first heating and cooling. After the third heating to 250 ℃, P-wave was reduced to 3910 ± 10 m/Sec and 2700 ± 10 m/Sec. The reduction of limestone is larger than granite.

NUMERICAL ANALYSIS USING BONDED-PARTICLE MODEL

Numerical analysis was performed using a PFC2D program which is based on a discrete element method. In order to evaluate the cracking and damage of the rock under heating conditions. It is possible to simulate the progress of displacement and force induced by heat as well as gradual heat transfer and heat storage of the material consisting of particles in the PFC2D thermal module. In the PFC2D thermo- mechanical coupling is only applied to the calculation of thermal stress by temperature change through thermal expansion coefficient of the rock. In the opposite case, PFC does not take into account temperature changes due to stress changes and it can be ignored for the rock (Itasca, 1995).

In order to determine the micro-parameters of the PFC model used for thermal cracking analysis, mechanical properties modeling was firstly conducted. This modeling is based on the mechanical properties of the used rock samples (Table1). Micro-parameters were determined when the tensile strength of the model is very close to that of samples used in laboratory experiments through trial & error method (Table 3 and Table 4).

The identified minerals and their composition from XRD analysis were used in a numerical model for close to the actual simulation. The size of the model (height 10cm and width 5cm) is the same used in the laboratory experiments. The cracks does not exist in the initial conditions of the model, the total number of balls in the model is 4450 for granite and 5037 for limestone.

Table 3 - Micro parameters used in PFC2D model Micro parameters Granite Limestone

Rmin (mm) 0.5 0.5 Rmin / Rmax 1.66 1.5 Particle density (kg/㎥) 2,650 2,710 Particle contact modulus (GPa) 28.97 38.55 Particle normal/shear stiffness 2.5 1.0 Particle friction coefficient 1.2 1.2 Particle bond radius multiplier 1.0 1.0 Parallel bond normal/shear stiffness 1.2 2.7 Parallel bond modulus (GPa) 28.97 38.55

Table 4 - Comparison between laboratory test and PFC modeling Granite Limestone Experiment PFC Experiment PFC Tensile strength (Mpa) 9.5 8.63 ±0.9 8.2 8.9 ±0.6

Young’s modulus (GPa) 42.2 47.4 ±0.6 58.7 58.3 ±1.1

Poisson’s ratio 0.34 0.169 ±0.002 0.29 0.2 ±0.003

Specific heat and thermal conductivity were obtained from the experiments on the whole sample. However, the thermal expansion coefficient of each mineral was used from the data from Fei (1995) and Robertson (1988) (Table5). The heating source was located on the surface assuming the heat is transferred to the interior of the sample from the surface. The heating rate in numerical simulation is the same as laboratory experiments. Numerical modeling had the same experimental sequence; first heating up to 150 ℃ heating and cooling, second heating up to 150 ℃and cooling, final heating up to 250 ℃. In addition, simulations of higher temperature were performed which cannot be done experimentally due to limited experimental conditions; first heating up to 250 ℃ heating and cooling, second heating up to 250 ℃and cooling, final heating up to 400 ℃. From the series of numerical simulation, initial cracking occurrence temperature, critical cracking temperature, failure mode, failure pattern and cumulative crack numbers are evaluated.

Table 5 - Thermal properties used in PFC modeling (Robertson, 1988 and Fei, 1995) Thermal Expansion Specific heat Thermal conductivity Coefficient (/ ℃) Granite Quartz 16.6 E-06 Albite 7.47 E-06 Othoclase1 5.13 E-06 2185 kJ/m3-K 2.51 W/m-K Magnetite 11.7 E-06 Biotite 12.1 E-06 Limestone Calcite 1 6.7 E-06 Quartz 16.6 E-06 Muscovite 11.1 E-06 2430 kJ/m3-K 3.37 W/m-K Dolomite 3.2 E-06 Chlorite -

The numerical results showed that there is no difference in the initial thermal crack temperature and critical thermal crack temperature with the different final temperature such as 150℃, 250℃, 400 ℃. The initial thermal crack temperature of granite and limestone are 71.1 ± 11.3 ℃ and 83.0 ± 9.3 ℃, respectively. In the case of critical thermal crack temperature, it was determined at 113 ± 2.5 ℃ for granite and 151.1 ± 0.6 ℃ for limestone. Although determined temperatures in numerical simulation are slightly higher than experiments, The tendency is similar each other (Figure 3).

Figure 3 – Cumulative cracks by heating up to 250℃ (green solid line: granite, red dot line: limestone, black dot: 150℃ )

In the case of repeated heating, while cooling down, cracks were not generated as the experimental results. As shown in Figure 5, cracks rarely occurred until the highest temperatures previously experienced, but cracks were generated at the moment of passing through that temperature. From this simulation, the thermal Kaiser effect was confirmed. The cumulative number of tensile cracks and shear cracks for granite until 250 ℃ were 137 ± 27 and 1443 ± 114. In the case of limestone, 100 ± 37 of tensile cracks and 136 ± 38 of shear cracks were totally generated. At the finial temperate 400℃, 470 ± 56 of cumulative tensile cracks and 3728 ± 257 shear cracks for granite and 559 ± 132 of cumulative tensile cracks and 1365 ± 294 shear cracks for limestone were generated. This phenomenon, which the cumulative cracks of granite were more generated than limestone, is similar in the both of experiments and simulations. The patterns of generated cracks are similar with different final temperature of 250℃ and 400 ℃ (Figure 4).

Figure – 4 Thermal Kaiser effect during repeated heating (black dot line: heating pattern, green solid line: cumulative cracks of granite, red dot line: cumulative cracks of limestone

It was observed that the portion of occurred tensile and shear cracks of granite is around 11% and 89 % and in the case of limestone they are 29% and 71% respectively under the condition of heating up to 400 ℃. This indicates that the slip that occurs at the minerals boundary by the thermal expansion of each mineral. The ratio of the tensile cracks to shear cracks of granite was not greatly affected by the final heating temperature. However, the ratio of limestone was significantly changed from 0.74 at 250 ℃ to 0.39 at 400 ℃. The dominant shear failure in the thermal cracking simulation occurred more clearly in the granite than limestone. This is considered as there are more displacements between the boundaries of composing minerals in granite. Figure 8 - Crack mode (left: granite, right: Limestone). CONCLUSION

In this study, we performed the laboratory thermal experiments for Hwangdeun granite and Danyang limestone. We also performed numerical analysis using bonded-particle model in order to compare the results with the experiments and complement the limitation of the experiments, especially the limitation of maximum temperature. Laboratory results showed that the thermal induced cracks were generated due to different thermal expansion of composing minerals. The cracks were initially detected at 35 ± 7 ℃ for granite and 32 ± 4 ℃ for limestone using acoustic emission.

The critical thermal crack temperature was estimated as 69 ± 10 ℃ for granite and 49 ± 9 ℃ for limestone. The cumulative crack of granite in the experiments was approximately three times than those of limestone. We also confirmed the thermal Kaiser effect that there is no occurrence of cracks when heating temperature is lower or similar to the previous maximum temperature.

PFC2D numerical results showed that the initial thermal crack temperature of granite and limestone are 71.1 ± 11.3 ℃ and 83.0 ± 9.3 ℃, the critical thermal crack temperature are 113 ± 2.5 ℃ and 151.1 ± 0.6 ℃. The values between laboratory experiments and numerical analysis are different, but the pattern of cracks occurrence and crack modes are similar. The differences may result in measuring method for cracks; acoustic emission is used in experiments and counting the bonding failure of particles is used in numerical modelling. Shear cracks occurred dominantly by heating and showed more clearly in the granite than limestone.

Similarity exists between the results of thermal cracking and numerical simulation, but it also shows a difference such as the order of critical thermal cracking temperature. In order to reduce the differences, thermal and physical properties and micro-parameters used in numerical simulations will set to more realistic. We will take a more advanced method using AE and X-ray CT to observe the cracking phenomenon the after thermal cracking experiment.

REFERENCES

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