Effects of temperature gradient on the granite’s mechanical properties

Abstract

Temperature gradient significantly affects the production of surrounding rock stress in mining engineering. The mechanics and deformation characteristics of the rock will change under the temperature gradient, thereby increasing the probability of accidents in the roadway. This paper conducts uniaxial compression tests on granite at different temperatures from room temperature to 250 ${{}^{\circ}}$ C, and analyzes in detail the changes in the stress-strain curve, peak stress, peak strain and tangent modulus of granite under high temperature and different temperature gradient conditions. The results of this study are as follows: (1) Under high temperature conditions, the granite’s peak stress and tangent elastic modulus increased with temperature from 17 to 100 ${}^{\circ}$ C, then decreased from 100 ${}^{\circ}$ C to 250 ${}^{\circ}$ C, whereas the granite’s peak strain increased steadily with increasing temperature; (2) under temperature gradient, the granite’s peak stress and tangent modulus first decreased and then increased with increasing temperature gradient, while the granite’s peak strain first decreased and then increased at 100 ${}^{\circ}$ C, but first increased and then decreased from 150 ${}^{\circ}$ C to 250 ${}^{\circ}$ C.

Keywords

Granite high temperature temperature gradient mechanical properties

1. Introduction

As the mining goes deeper and deeper, the influence of temperature on the properties of surrounding rock become increasingly obvious, and temperature gradient may be generated in a certain range. The appearance of temperature gradient can significantly affect the surrounding rock stress in deep roadway and change the rock’s mechanical and deformation characteristics, thereby increasing the probability of the occurrence of accidents in deep roadway.

In recent years, the international scholars have conducted a great deal of researches on the rock’s mechanical properties under temperature gradients and gained many valuable results. Yang et al. [1] focus on the thermal-mechanical fracturing behaviors of granite after thermal cycling treatment by fully coupled dynamic method based on general state. Yin et al. [2] Studied the pore characteristics, permeability, Critical Reynolds Number and flow nonlinearity of granite exposed at 100 $\sim$ 800 ${}^{\circ}$ C He et al. [3] experimentally analyze the effect of temperature levels on the permeability of granite samples in the laboratory. Jin et al. [4] introduced the changes of physical, mechanical and transport properties of the granite after two different thermal cycling treatment methods in detail. Edoardo Rossi et al. [5] studied the difference of rock strength after oven heating and flame treatment when heated to 650 ${{}^{\circ}}$ at a heating rate of 0.17–20 ${{}^{\circ}}$ /s respectively. Shao et al. [6] investigated the bulk density, P-wave velocity, uniaxial compression strength (UCS) and elastic modulus of granite after heating from 25 ${}^{\circ}$ C (room temperature) to 1000 ${}^{\circ}$ C. Shu et al. [7] test the properties of stone under different heating rates and temperatures, then the dynamic compressive properties of granite were studied by using split opkinson pressure bar (SHPB) in a variable speed heating furnace. Yin et al. [8] studied the transport characteristics and permeability evolution characteristics of rocks exposed to high temperature (25–800 ${{}^{\circ}}$ C). Zheng et al. [9] studied the effects of microwave treatment on heating rate, spatial temperature distribution, ultrasonic velocity, elastic modulus and bearing capacity of gabbro, monzogranite and granite; in addition, various simulation methods and digital image correlation (DIC) technique are utilized with the advancement of technology, and Scholars proposed the material model with temperature differences and the simplified constitutive equations. Fu et al. [10] studied the tensile failure process of brittle materials such as rock and concrete in high temperature environment by using the theory of tensile failure and heat conduction, and established a thermal cracking numerical model with thermal-mechanical coupling effect. Wang et al. [11] use the numerical simulations to investigate the microcracks of the rock. With the heating rate of 200 ${{}^{\circ}}$ C/min, 300 ${{}^{\circ}}$ C/min and ISO 834 standard fire curve, the target temperature reaches 400 ${{}^{\circ}}$ C and 800 ${{}^{\circ}}$ C respectively. Wu et al. [12] proposed a coupled FEM-DEM (finite element method and discrete element method) method to investigate the transient thermal conduction in fractured rock mass. Then the simulation and Monte Carlo method are used to experiment and verify. Yang et al. [13] carried out dynamic compression tests on siliceous sandstone at room temperature (25 ${{}^{\circ}}$ C) and different high temperatures (200, 400, 600 and 800 ${{}^{\circ}}$ C) using split Hopkinson pressure bar (SHPB). Zhu et al. [14] analyzed the cracking mechanism of granite impacted by high temperature and cold water, and established the thermal shock stress equation of high temperature water cooling. In FEA (finite element simulation), Wang et al. [15] analyzed the thermal stress and crack changes of rock under the action of short pulse microwave energy at different temperatures by using a two-dimensional circular plate containing two-phase minerals.

As stated above, a lot of achievements have been made worldwide regarding the granite’s mechanical property under high-temperature conditions; however, the granite’s mechanical properties under temperature gradient are poorly investigated. Therefore, in this study, we conducted uniaxial compression tests on the granite for systematically investigating the stress – strain characteristics under different temperature gradients within a temperature range from roomtemperature to 200 ${}^{\circ}$ C, and then investigated the effects of temperature gradient on the granite’s peak stress, peak strain, and tangent modulus. The acquired important test results will be of great significance in exploring the rock’s mechanical property variations and mining safety.

2. Tests

2.1 Sample preparation and instrument

The rock samples used in this study were the sesame white granite collected from Daye, Hubei, China. The granite shows a grainy texture in black and white, with an average density of 2.766 g/cm ${}^{3}$ and is mainly composed of quartz, feldspar, mica, hornblende and a small quantity of cementing materials. According to the testing regulations in National Standardin Geology and Mining of the People’s Republic of China, the cuboid samples with a size of 50 $\times$ 50 $\times$ 100 mm ${}^{3}$ were prepared. These sampleshad intact and dense surfaces, without macro fractures and holes.

The uniaxial compression tests were carried out by electro-hydraulic servo universal testing machine (WAW-1000). During the tests, the samples were heated in an electro-thermostatic forced air drying oven (DHG-9030A, Shanghai Feixue Experimental Instrument Co., Ltd., China) and the stainless steel heating plate.

2.2 Test method and process

The whole test process is described as follows. First, before the test, therock samples were numbered and the sizes were measured. Then, the samples were divided into four groups, and each group had four samples. After division, the samples were placed in a thermostatic drying oven for 12-hour heating, and then taken out and insulated after reaching the preset-temperature. The bottom of the sample was placed on a heating plate with the same temperature as the thermostatic drying oven, whereas the top was exposed to the air for natural cooling. Next, uniaxial compression tests were conducted on the rock samples at room temperature (17 ${}^{\circ}$ C) and different temperatures, during which the loading rate was set as 0.25 MPa/s. Finally, after the test finished, the test process and results were recorded, organized and analyzed. Table 1 lists the heating and cooling temperatures for all the samples in different groups.

Table 1
Working conditions in the tests

Group number	Heating temperature	Top cooling temperature	Number of repetition	Group number	Heating temperature	Top cooling temperature	Number of repetition
1	17 ${}^{\circ}$ C	0	4	10	200 ${}^{\circ}$ C	0	4
2	100 ${}^{\circ}$ C	0	4	11	200 ${}^{\circ}$ C	160 ${}^{\circ}$ C	4
3	100 ${}^{\circ}$ C	70 ${}^{\circ}$ C	4	12	200 ${}^{\circ}$ C	120 ${}^{\circ}$ C	4
4	100 ${}^{\circ}$ C	40 ${}^{\circ}$ C	4	13	200 ${}^{\circ}$ C	17 ${}^{\circ}$ C	4
5	100 ${}^{\circ}$ C	17 ${}^{\circ}$ C	4	14	250 ${}^{\circ}$ C	0 ${}^{\circ}$ C	4
6	150 ${}^{\circ}$ C	0 ${}^{\circ}$ C	4	15	250 ${}^{\circ}$ C	210 ${}^{\circ}$ C	4
7	150 ${}^{\circ}$ C	120 ${}^{\circ}$ C	4	16	250 ${}^{\circ}$ C	170 ${}^{\circ}$ C	4
8	150 ${}^{\circ}$ C	90 ${}^{\circ}$ C	4	17	250 ${}^{\circ}$ C	17 ${}^{\circ}$ C	4
9	150 ${}^{\circ}$ C	17 ${}^{\circ}$ C	4

3. Test results and analysis

3.1 Stress–strain curve

Figure 1 shows the granite’s stress – strain curve at different temperatures, indicating that the granite underwent four phases during the compression from 17 ${}^{\circ}$ C to 250 ${}^{\circ}$ C. These four phases are as follows.

(1)
Initial compaction phase: In this phase, the stress – strain curve was concave upward; with increasing stress, the deformation became violent because of the closure of some micro-fractures in the granite under compression.
(2)
Approximately elastic deformation phase: In this phase, the stress – strain curve was almost a line, and the slope can be approximated as the rock’s average tangent elastic modulus.
(3)
Micro-crack evolution phase: In this phase, with increasing axial compressive force, the broken line appeared in the rock’s stress – strain curve and the stress on the tip of the cracks increased steadily. Moreover, the stress even reached the tip stress intensity factor of the cracks, which would gradually destroy the micro-elements in the rock with low intensity and producing new cracks. Overall, the rock’s mechanical property decreased and the internal losses developed more rapidly, leading to the instantaneous release of some energy.
(4)
Failure phase: In this phase, the stress reached the maximum and the rock underwent obvious brittle failures.

As shown in Fig. 1, the increase in temperature from 17 ${}^{\circ}$ C to 250 ${}^{\circ}$ C did not impose any significant effects on the granite’s stress – strain curve, and all the granite samples underwent brittle failures; however, the micro-crack evolution phase became more conspicuous.

Figure 1.
Granite’s stress – strain curves at different temperatures.

Figure 2.
Granite’s stress – strain curves at different temperatures under different cooling conditions.

Figure 2 shows the granite’s stress – strain curves at different temperatures under different cooling conditions, indicating that (1) at 100 ${}^{\circ}$ C, the granite’s stress overall strain curves under different cooling conditions show almost same variation tendencies, while the stress – strain curves under different cooling conditions are different at the other temperatures; (2) at 150, 200 and 250 ${}^{\circ}$ C, the granite’s initial compaction phases were longer under smaller temperature gradients, and the phases without cooling were also longer than those from cooling to room temperature, mainly due to the fact that the thermal expansion at high temperature would result in the closure of micro-fractures in the rock in advance; (3) at 150, 200 and 250 ${}^{\circ}$ C, the approximately elastic deformation phases were shorter under smaller temperature gradients, and the phases without cooling condition were also shorter than those under cooling to room temperature, mainly because the thermal stress generated in the temperature gradient and pressure stress accelerated the development of micro-fractures in the rock.
3.2 Peak stress

3.2.1 Granite’s peak stress characteristics at different temperatures

Figure 3 shows the rock’s peak stresses under uniaxial compression test at different temperatures. Obviously, the granite’s peak stresses at each temperature are discrete; overall, the peak stress decreased with increasing temperature. The maximum peak stress at 100 ${}^{\circ}$ C is 143 MPa, i.e., granite is a rock with moderate intensity.

Figure 3.

Granite’s peak stresses at different temperatures.

The following conclusions were obtained. (1)The average peak stress increased as the temperature increased from 17 ${}^{\circ}$ C to 100 ${}^{\circ}$ C. Some micro-fractures in the rock closed under the action of temperature-induced thermal stress, improving the rock’s strength to a certain degree. (2) The average peak stress decreased as the temperature decreased from 100 ${}^{\circ}$ C to 250 ${}^{\circ}$ C. This is due to the fact that the high-temperature-induced thermal stress exceeded the maximum stress so that the rock’s micro-fractures could sustain, leading to the expansion and increase in the micro-fractures. Accordingly, the strength of rock decreased to a certain degree. (3) The minimum and maximum peak stresses occurred at 250 ${}^{\circ}$ C and 100 ${}^{\circ}$ C, respectively, and the average peak stresses at 100, 150, 200 and 250 ${}^{\circ}$ C all exceeded the average value at 17 ${}^{\circ}$ C, suggesting that increasing temperature would increase peak stress at $<$ 200 ${}^{\circ}$ C and improve the rock’s strength to a certain degree.

3.2.2 Granite’s peak stress characteristics under different temperature gradients

Figure 4 shows the variations between the rock’s peak stress and temperature under uniaxial compression test under different temperature gradients,indicating that the granite’s peak stresses at each temperature are discretely distributed; overall, the peak stress first decrease and then increase with increasing temperature gradient.

Figure 4.

Granite’s peak stress at different temperatures under different cooling conditions.

The following conclusions can be reached from Fig. 4.

(1)

The rock’s average peak under a smaller temperature gradient is smaller than that under high-temperature condition;

(2)

The rock’s average peak under a large temperature gradient is greater than that under a small temperature gradientand is also smaller than that under high-temperature condition;

Figure 5.

Granite’s peak strains at different temperatures.

Figure 6.

Granite’s peak strains at different temperatures under different cooling conditions.

(3)

As the rock was heated from cooling to room temperature, the average peak stress was larger than the average value under a large temperature gradientand was not slightly larger than the value after cooling;

(4)

As the temperature gradient increased, the rock’s average peak stress first dropped and then increased,preliminarily indicating that from high-temperature to small-temperature gradient, then large temperature gradient and finally room temperature, the micro-fractures in the rock grew gradually because of the heat-expansion and cool-contraction action induced by the variations in the temperature and temperature gradient, thereby decreasing the rock’s strength. However, when temperature/temperature gradient increased to a certain value, the rock strength can be improved.

3.3 Peak strain

3.3.1 Granite’s peak strain characteristics at different temperatures

Figure 3 shows the rock’s peak strains under the uniaxial compression test at different temperatures. The granite’s peak strains at different temperatures are all discrete; however, the overall peak strain increased with increasing temperature.

Figure 7.

Granite’s tangent modulus values at different temperatures.

3.3.2 Granite’s peak strain characteristics under different temperature gradients

Figure 6 displays the variations between the rock’s peak strain and temperature under the uniaxial compression test at different temperature gradients.

Overall, under uniaxial compression, the granite’s peak strain first increased and then decreased with increasing temperature gradient except at 100 ${}^{\circ}$ C. As shown in Fig. 6, at 100 ${}^{\circ}$ C, the granite’s peak strain decreased with increasing temperature gradient, probably because of the fact that the micro-fractures in the rock closed in advance at 100 ${}^{\circ}$ C due to the thermal stress caused by the temperature gradient; therefore, the rock strength improved to a certain extent. In contrast, at 150, 200, and 250 ${}^{\circ}$ C, the granite’s peak strain increased with increasing temperature gradient, because the temperature-gradient-induced thermal stress exceeded the maximum stress and the micro-fractures could sustain, thereby destroying the rock’s micro-fractures and resulting in the development of micro-fractures.

3.4 Tangent modulus

3.4.1 Granite’s peak tangent modulus characteristics at different temperatures

We then selected the straight line segment in stress – strain curve and calculated the slope of the tangent line of this segment. The slope can thus be regarded as the granite’s tangentelastic modulus.

Figure 7 shows the rock’s tangent modulus values under the uniaxial compression test at different temperatures. Similarly, the tangent modulus values discretely distributed at each temperature; however, the granite’s tangent modulus overall decreased with increasing temperature and reached the maximum of 16.545 GPa at 100 ${}^{\circ}$ C.

The observations under the uniaxial compression test are as follows.

The granite’s average tangent modulus increased as the temperature increased from 17 ${}^{\circ}$ C to 100 ${}^{\circ}$ C. The thermal stress induced by increasing temperature would lead to the closure of micro-fractures, improving the rock strength to a certain degree.

The granite’s average tangent modulus decreased as the temperature increased from 100 ${}^{\circ}$ C to 250 ${}^{\circ}$ C. Since the thermal stress at high temperature exceeded the maximum stress,the rock’s micro-fractures can bear, the micro-fractures developed and increased, thus reducing the rock strength.

3.4.2 Granite’s peak tangent modulus characteristics under different temperature gradients

Figure 8 shows the variations between the rock’s tangent modulus and temperature under the uniaxial compression test at different temperature gradients. Overall, under temperature gradient, the granite’s tangent elastic modulus first decreased and then increased with increasing temperature gradient.

Figure 8.

Granite’s tangent modulus values at different temperatures under different cooling conditions.

4. Conclusions

In this study, the granite was subjected to uniaxial compression test at different temperatures and temperature gradient conditions. The conclusions of this study are as follows.

During the uniaxial compression process, the granite’s failure can be divided into the following four phases – initial compaction phase, approximately elastic deformation phase, micro-fracture evolution phase, and failure phase.

At high temperature, the granite’s peak stress first increased and then decreased with increasing temperature and reached the maximum at100 ${}^{\circ}$ C. After cooling, the granite’s peak stress first decreased and then increased with increasing temperature gradient.

At high temperature, the granite’s peak strain increased with increasing temperature. After cooling, the granite’s peak strain at 100 ${}^{\circ}$ C first decreased and then increased with increasing temperature gradient. In contrast, at150, 200 and 250 ${}^{\circ}$ C, with the increase of

At high temperature, the tangent elastic modulus of granite first increases, then decreases with the increase of temperature, and reaches the maximum value of 100 ${{}^{\circ}}$ . After cooling, the granite’s tangent elastic modulus first decreased and then increased with the increase of temperature gradient.

Footnotes

Acknowledgments

This work was financially supported by the Natural Science Foundation of Hubei Province, China (Grant No: 2014CFB879).

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Effects of temperature gradient on the granite’s mechanical properties

Abstract

Keywords

1. Introduction

2. Tests

2.1 Sample preparation and instrument

2.2 Test method and process

Table 1 Working conditions in the tests

3.1 Stress–strain curve

3.2.1 Granite’s peak stress characteristics at different temperatures

3.3.1 Granite’s peak strain characteristics at different temperatures

3.4 Tangent modulus

3.4.1 Granite’s peak tangent modulus characteristics at different temperatures

3.4.2 Granite’s peak tangent modulus characteristics under different temperature gradients

Footnotes

Acknowledgments

References

Table 1
Working conditions in the tests