Properties of failure mode and thermal damage for limestone at high temperature

M INING SCIENCE AND TECHNOLOGY Mining Science and Technology 19 (2009) 0290–0294

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Properties of failure mode and thermal damage for limestone at high temperature MAO Xian-biao1,2, ZHANG Lian-ying3, LI Tian-zhen3, LIU Hai-shun1 1

2

School of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China State Key Laboratory of Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China 3 School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, China

Abstract: The mechanical properties of limestone such as the stress-strain curve, the variable characteristics of peak strength and the modulus of elasticity of limestone were studied under the action of temperatures ranging from room temperature to 80°C. Our results show that: 1) the temperature has not clear effect on the mechanical properties of limestone from room temperature to 600 °C. However, the mechanical properties of limestone deteriorate rapidly when the temperature is above 600 °C. In this case, the peak stress and modulus of elasticity decrease rapidly. When the temperature reaches 800 °C, the entire process, showing the stress-strain curve is displayed indicating an obvious state of plastic-deformation; 2) the failure mode of limestone shows the breakdown of tensile strength from room temperature to 600 °C, as well as the compress shearing damage over 600 °C; 3) combining our test results with the concept of thermal damage, a thermal damage equation was derived. Keywords: limestone; high temperature effect; mechanical properties; damage

1

Introduction

In rock mechanics dealing with rock engineering problems at high temperatures is a new challenge. Most rock masses such as found in nuclear waste burial sites, geothermic exploitation and underground development in big cities may undergo high temperatures and therefore rock strength and deformation characteristics under high temperature need to be studied in detail. Correspondingly, mechanical parameters are basic and fundamental values that should be known and understood when dealing with excavation of underground rock engineering, support design and stability analysis of the surrounding rock. Rock mechanical properties have been widely investigated at home as well as abroad and numerous research results of theoretical importance and practical value have been obtained, such as: 1) measurements of basic physical and mechanical parameters, including modulus of rock deformation, Poisson ratios, tensile strength, compressive strength, cohesion, internal friction angle, viscosity and thermal expansion coefficients[1–5]; 2) research in thermal cracking[6–7]; 3) research of deformation mechanisms[8–9]; 4) investi-

gation of failure criteria, constitutive equations and so on[10–11]. However, most of the previous studies focused on mechanical properties of rock materials after high-temperature due to the limitation of experimental conditions. In fact, thermal expansion of rock is irreversible, it is affected by its heating history, where many changes occur in micro-structures when rock material is heated to high temperatures and cooled to room temperature again in experiments. Therefore, these results do not always reflect the essential characteristics of rock masses at high temperature. China is rich in hot dry rock geothermal resources. It has been predicted that in Tengchong, Yunnan province and in Yangbajing, Tibet alone the amount of these resources is more than 1.56×1011 kW·a[12–13]. Their development and utilization is of great strategic importance if we want to improve our energy structure and guarantee energy security in China. In order to extract geothermal energy from the hot dry rocks at depth of up to 5000 m and temperatures above 300 °C, we need to drill holes into the hot dry rock for the construction of artificial reservoirs based on hydraulic fracturing techniques and as well keep monitoring the

Received 12 September 2008; accepted 20 December 2008 Projects 50490273 supported by the National Natural Science Foundation of China, 2007CB209400 by the National Basic Research Program of China, 08KJD130003 by the Basic Research Program of University in Jiangsu Province and XKY2007219 by Xuzhou Institute of Technology Corresponding author. Tel: +86-516-83884881; E-mail address: [email protected]

MAO Xian-biao et al

Properties of failure mode and thermal damage for limestone at high temperature

breakdown of reservoirs. These efforts need a thorough and meticulous research on the mechanical conduct of hot dry rocks[12,14]. The mechanical properties of limestone under high temperature were studied by using a MTS810 hydraulic servo system and a MTS 653.02 high temperature furnace. As well, the variation of mechanical properties and failure modes of limestone between room temperature and 800 °C were discussed and a thermal damage equation was derived. The results can provide valuable references for rock engineering study under high temperatures.

2 2.1

Fig. 1

Experimental Specimens and preparation

3

291

MTS810 hydraulic servo system and MTS 653.02 high temperature furnace

Mechanical properties of limestone under high temperature

Our specimens used were taken from a mine in the Xuzhou area. Generally, different dimensions and configurations exert obvious effects on the measurement of rock mechanical parameters. Considering the limited space of the high temperature furnace in our investigation, cylindrical rock specimens were chosen, about 45 mm in length and 20 mm in diameter, to meet the requirement of ‘‘test specification for the physical & mechanical properties for rock’’. The specimens were divided into eight groups, in which the temperature reached 20, 100, 200, 300, 400, 600, 700 and 800 °C with 5~6 specimens to each group.

The stress-strain curves of limestone under high temperatures were presented in Fig. 2 according to the axial load and displacement obtained from the uniaxial compression tests and subsequently the peak strength of samples were obtained. The modulus of elasticity was calculated from the approximately straight line section before the peak strength of the entire process stress-strain curve. The variation of peak strength and modulus of elasticity of limestone specimens under high temperature are listed in Table 1.

2.2 Equipment and processes

Table 1

The experiments were conducted with a MTS810 hydraulic servo system and a MTS 653.02 high temperature furnace, as shown in Fig. 1. The entire experimental process was completed according to the requirements established beforehand by the TeststarĊ system, which has optimum control of the test process. Using the menu of the main form, the system has functions for the distribution of sensors, definitions of the control model, setting boundaries, an automatic zero set of sensitive elements, selection output signals and setting some parameters as required. This system software includes GUI, a data interface, a software function generator, program designs and system tools. First, the specimens of each group were placed into the MTS 653.02 high temperature furnace, where the specimens were heated at a rate of 2 °C/s. The temperature was kept constant for 2.0 h so that the specimens could be heated to the assigned value from the outside to the inside. The specimens were loaded by an electro-hydraulic loading servo system with a displacement rate of 0.004 mm/s. The mechanical characteristics such as axial load, axial displacement, axial stress and strain were obtained in the process of rock deformation and destruction by using the Teststar II control program.

Serial number

Results of main mechanical peak strains of limestone T (°C)

1 2 3

25

4 5 6

141.457 129.876

Average

123.938

128.229 90.401 100

7 8 9 10

σ c (MPa) Test value 96.303

101.934

57.591 52.894

18.278 18.844

91.457

17.114

99.559

14.975 10.933

11

98.559

16.056

94.524 67.531

19.482 10.129

16 17

300

400

18 19 20

600

100.793

109.393 75.401

700

90.903

92.397

34.787 30.942

16.827 13.695

15.038

15.261

17.828 14.801

16.315

16.069 12.842 93.510

92.306 24.176 800

14.877 15.665

15.256

14.801

89.041 96.118

24 25 26 27

105.399 96.186

86.266

99.897

21 22 23

127.070 55.940

17.034

16.951 19.861

12 13 14 15

17.769

18.212 17.038

82.041 188.192 200

E (GPa) Test value Average 15.713

11.171

12.007

12.008 3.661 29.968

1.654 4.306

3.207

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3.1 Process stress-strain curves Fig. 2 shows that: 1) when T<600 °C, the features of the stress-strain curves of limestone are similar to those under room temperature, including the compression phase, elastic deformation and brittle deformation; 2) for limestone, when T•600 °C, an obvious plastic deformation appears besides the compression phase and the elastic stage; the plastic properties of limestone increase, while the brittle properties decrease with the increase in temperature. 

σ (MPa)

  

ć

ć

ć

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It can be seen from Fig. 4 that the modulus of elasticity of limestone decreases with temperature rising from room temperature to 200 °C and little change is shown from 20 to 600 °C. At temperatures over 600 °C, the modulus of elasticity decreases rapidly with rising temperatures. It decreased from 17.8 GPa at room temperature to 3.2 GPa at 800 °C, an 80% decrease, which indicates that the internal structure of limestone has changed over this 600 °C range. The result shows that a critical temperature, TC (about 600 °C) exists for limestone under uniaxial compression; when TTC, limestone shows to be sensitive to temperature, the modulus of elasticity decreases rapidly and the deformation resistance of limestone also decreases.

ć



No.3



 











( *3D

 



ε (mm)

Fig. 2

Axial stress-strain curves for limestone under high temperature

3.2 Variation in peak strength

σ c (MPa)

Fig. 3

Changing of peaks tress with temperature for limestone

3.3 Variation in modulus of elasticity Variations in the modulus of elasticity of limestone specimens as a function of temperature are presented in Fig. 4.

 









7 ć

σc

Variations in the curves of peak strength (uniaxial compressive strength) of limestone as a function of temperature are shown in Fig. 3. The peak strength for limestone shows clear variation at high temperatures, compared with that under room temperature (Fig. 3 and Table 1): 1) the peak strength of limestone decreases from 124 to 91 MPa and decreases by about 26% from room temperature to 100 °C; 2) the peak strength of limestone shows little changes from 100 to 700 °C; 3) the peak strength of limestone decreases sharply from 90 to 30 MPa, a 66.7% decrease at 800 °C. Whether the rapid decrease of the strength means that 700 °C is the critical temperature of its internal structure needs further study and investigation.



Fig. 4 Variation in modulus of elasticity, as a function of temperature for limestone

4

Effect of temperature on the failure mode of limestone

It can be seen from the process stress-strain curves of limestone (Fig. 2) that the destruction of limestone specimens is a fracture failure from room temperature to 400 °C. When T•600 °C, limestone indicates a clear state of plastic-deformation. Plastic properties of limestone can be increased while brittle features decrease with increases in temperature. Pictures of limestone fractures from room temperature to 800 °C are presented in Fig. 5. Fig. 5 shows that 1) within the range of 25~600 °C, the angle between the fracture surface of limestone specimens and the axial direction is relatively small. The crack propagating in the crystals leads to damage of limestone from pullingˈso the fractured surface was damaged simultaneously on different surfaces and the primary shear surface could not be formed; 2) when the temperature is higher than 600 °C, the angle between the fracture surface of limestone specimens and the axial direction is about 30. The fractured surface is shown as compression and shear failure. In fact, when T>600 °C, the peak strength σ c and the modulus of elasticity decrease sharply with rising temperatures, the ability to withstand deformation and the load capacity of rock specimens are greatly decreased and are the cause for the decrease in shear resistance. The failure mode is shown as compression and shear failure.

MAO Xian-biao et al

(a) 25 °C

(e) 400 °C

Properties of failure mode and thermal damage for limestone at high temperature

(b) 100 °C

293

(c) 200 °C

(f) 600 °C

(d) 300 °C

(g) 700 °C

(h) 800 °C

Fig. 5 Pictures of limestone fractures

5

Establishment of the thermal damage development equation

Under high temperatures, internal thermal stress is introduced in the rock, where inevitably a number of micro-cracks appear, which gradually expand with rising temperatures, leading to a considerable decrease in the modulus of elasticity. This implies that high temperatures cause damage to rocks. The modulus of elasticity is specified as a function of temperature (Fig. 4). The effect of temperature on the mechanical properties of rock is characterized by the modulus of elasticity as a damage parameter. A cubic polynomial has been fitted in order to show the relation between modulus of elasticity and temperature (Fig. 6), i.e.,

D(T). It is defined as follows: D (T ) = 1 − ET / E0

(1)

where ET is the modulus of elasticity at T °C and E0 at T=25 °C. The values of thermal damage, obtained from Eq.(1), are presented in Table 2. Table 2 Temperature T (°C)

20

Damage value at different temperatures 100

200

300

400

600

700

800

Thermal 0.000 0.041 0.141 0.154 0.141 0.082 0.324 0.820 damage D(T)

The regression curve and equation of damage values as a function of temperature are shown in Fig. 7.

' 7

E (T ) = a 0 + a1T + a 2T 2 + a3T 3 where a0 , a1 , a 2 and a3 are material constants, with the following values: a0 = 19.607 , a1 = 0.0546 , a2 = 0.0002 , a3 = −2 × 107 .

( *3D

Fig. 7

Fig. 6 Regression curve and equation of modulus of elasticity as a function of temperature for limestone

The concept of thermal damage was proposed, given that the modulus of elasticity is presented in Reference [10] as a parameter of thermal damage

Relationship between damage value and temperature

It is seen from Fig. 7 that the peak damage appears at T=200 °C. For heating temperatures between 200~400 °C, water in the samples seeks to penetrate fractures and escape through evaporation, while the fractures become longer and wider. The expansion of grain in rocks causes the fractures to heal, but this is not enough to offset the damage done by the escaping water. The damage decreases at T=600 °C. At this point, most of the water in the rock has escaped, the grain in the rock has expanded until the fracture is, refilled, so the rock can bear great pressure and the degree of damage is minimal. At 700 °C, grain ex-

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pansion causes structural stress from extrusion and tensile stress appears within the grains. These excessive internal interactions leads to weakening of the rocks beyond the 600 to 700°C range and sharply increases the damage. An equation describing the damage of limestone is shown as: D(T ) = −0.1036 + 0.0031T (2) − 1 × 10−5 T 2ˇ1 × 10−8 T 3

limestone specimens and the axial direction is about 30°, where the fractured surface shows mainly compression and shear failure. 4) Combining our test results with the concept of thermal damage, the thermal damage equation and the effect of heat on the mechanical properties of limestone can be predicted relatively accurately.

The development equation of thermal damage for limestone is obtained as the first derivative of D(T ) :

[1]

D′(T ) = 0.0031 − 2.0 × 10 −5 Tˇ3 × 10−8 T 2

[2]

(3)

References

From Eq.(1) we can obtain: ET = E0 [1ˉD(T )]

(4)

Eq.(3) is an development equation of thermal damage as a function of temperature and Eq.(4) is the development equation of the modulus of elasticity as a damage variable.

6

[3]

[4]

Conclusions

We have carried out experimental research on mechanical properties of limestone under high temperature and analyzed the characteristic features of deformation and damage for limestone we draw the following conclusions: 1) Features of stress-strain curves of limestone specimens are quite similar under room temperature up to 400°C and show only brittle deformation; when T•600 °C, obvious plastic deformation appears both during the compression phase and the elastic stage. 2) The mechanical properties of limestone specimens are clearly different from those under room temperature. The modulus of elasticity of limestone specimens shows a downward trend from room temperature to 200 °C and little change occurs from 200 to 600 °C, but it decreases rapidly when the temperature is over 600 °C, showing a decreases of 80% from 600 to 800 °C. The peak strength of limestone specimens shows a downward trend from room temperature to 100 °C, only small changes from 100 to 600 °C, but rapid decreases with temperature rising over 600 °C. At 800 °C, the decrease is 70%. 3) For limestone fractured surfaces under uniaxial compression and high temperature, the angle between the fractured surface of limestone specimens and the axial direction is relatively small. The limestone specimens show damage between 25 and 600 °C from pulling. When the temperature is higher than 600 °C, the angle between the fractured surface of

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