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The influence of cyclic wetting and drying on the fracture toughness of sandstone
International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
The influence of cyclic wetting and drying on the fracture toughness of sandstone Wen Hua, Shiming Dong n, Yifan Li, Jigang Xu, Qingyuan Wang College of Architecture and Environment, Sichuan University, Chengdu 610065, PR China
art ic l e i nf o Article history: Received 11 November 2014 Received in revised form 25 May 2015 Accepted 2 June 2015 Keywords: Sandstone Wetting and drying Central cracked Brazilian disc Fracture toughness Tensile strength
1. Introduction It is well known that there are some micro-cracks, pores or faults in a rock mass because of the complexity of rock structure, and the essence of the rock material failure process is micro-crack initiation, propagation, breakthrough and collection, in the end, resulting in rock failure. Rock fracture toughness characterizes the resistance to crack initiation and propagation, which is an important parameter in the mechanical properties of rock materials. It has an irreplaceable role in the rock mechanics theory research and practical applications.1 Rock deformation and failure usually involves water in practical engineering such as tunneling, mining and rock excavation. Water–rock interaction is an important factor affecting the safety and stability of geotechnical engineering.2 Rock masses are often in a state of cyclic drying and wetting due to the ground water level changing or for other reasons. It is closely related with water–rock interaction, such that a lot of geological disasters occurred in the past few decades such as landslides, debris flow, ground subsidence and collapse, etc. The safety and stability of geotechnical engineering under water–rock interaction is increasingly becoming the focus of attention. In the recent years, the influence of cyclic drying and wetting on the physical and mechanical properties of rock materials have been studied by many researchers.3–8 The physical properties of rock mainly include bulk density, specific gravity, apparent porosity, P-wave velocity, etc., whereas the mechanical properties of n
Corresponding author. E-mail address: [email protected] (S. Dong).
http://dx.doi.org/10.1016/j.ijrmms.2015.06.010 1365-1609/& 2015 Elsevier Ltd. All rights reserved.
rock materials mainly focus on uniaxial compressive strength, shear strength, cohesion resistance, elastic modulus, and so on. The results indicate that the physical and mechanics properties of rock materials have a different degree of deterioration after cyclic drying and wetting. The influence of water content on rock mechanical parameters was investigated by Taibi et al.9, Török et al.10 and Erguler et al.11 Gautam et al.12 pointed out rocks with higher clay contents slake more rapidly and extensively under natural climatic conditions than those with lower clay contents. Nara et al.13 investigated the effects of relative humidity and temperature on subcritical crack growth in igneous rock with double-torsion specimens. Although Tang et al.14 and Deng et al.15,16 conducted a series of experimental studies of the mechanical properties of rock fracture under water–rock interaction with three pointed bending specimens, they mainly focused on the pure mode I fracture toughness for rock materials after short or long term soaking with aqueous solution or chemical solution. However, so far, little has been reported on the study of the influence of cyclic wetting and drying on the mode I fracture toughness and tensile strength for rock materials. The aim of this paper is to undertake an experimental study on the influence of cyclic wetting and drying on the mode I fracture toughness and tensile strength of sandstone, and discuss the relationship between mode I fracture toughness and tensile strength of sandstone after cyclic wetting and drying. The crack propagation laws have also been studied in this paper in order to provide a theoretical basis for stability analysis in geotechnical engineering under complex conditions.
332
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
2. Experimental methods The central cracked Brazilian disc (CCBD) specimen has been extensively employed to investigate the fracture behavior of different brittle materials, because it can facilitate the realization of pure mode I, pure mode II and mixed mode loading by changing the loading angle, besides which the stress intensity factors have analytic solutions.17,18 We test pure mode I fracture toughness of sandstone after wetting–drying cycles with CCBD specimens. And the Brazilian splitting method is used to measure the tensile strength of sandstone after different number of wetting–drying cycles. The Brazilian disk nominal diameter D¼ 75 mm, nominal thickness B ¼25 mm, the nominal crack relative length α ¼ 0.6, and the groove width is about 1 mm for each specimen. A total 30 specimens are divided into 2 groups for testing the pure mode I fracture toughness and tensile strength of sandstone. Fig. 2. The results of X-ray diffraction analysis.
2.1. Stress intensity factors for the central cracked Brazilian disc A schematic diagram of the CCBD specimen diametrically loaded by a pair of concentrated forces is shown in Fig. 1. The thickness of the disc is B and the radius is R. The crack length is 2a, and the loading angle is β, which is the angle between the crack line and the loading direction. Dong et al.18 obtained analytic solutions of the stress intensity factors for the central cracked Brazilian disc under combined loading conditions by using the weight function method.
given by Dong et al.18 Generally speaking, in order to obtain more accurate results, the value of n which is related to the crack relative length α should be larger enough. However, we find that when the crack relative length α ≤ 0.9, the value of n ranging from 60 to 100, there is virtually no difference. That is to say, it is very accurate when n = 100. So, the value 100 of n was used in all the calculations.
n ⎡ ⎤ KI = σ πa ⎢ f11 + 2 ∑ A1i f1i α 2(i − 1)⎥ ⎢⎣ ⎥⎦ i=1
2.2. Specimens preparation and testing process
(1)
n
KII = 2σ πa
∑ A2i f2i α
2(i − 1)
i=1
(2)
The normalized stress intensity factors FI and FII can be written in the following forms: n
FI =
KI = f11 + 2 ∑ A1i f1i α 2(i − 1) σ πa i=1
FII =
KII = 2 ∑ A2i f2i α 2(i − 1) σ πa i=1
(3)
n
(4)
where α ¼a/R and s ¼F/(πBR), and α is defined as the crack relative length. The expressions for the coefficients f11, A1i, f1i, A2i and f2i are
Fig. 1. Diagrams of the CCBD specimen under compression.
The sandstone for this experiment was produced in Ziyang City, Sichuan Province, China. The mineralogical composition of this sandstone determined by X-ray diffraction (XRD) analysis (Fig. 2) indicates that this rock is mainly composed of quartz, albite, chlorite and serpentine. The CCBD specimens were used for pure mode I fracture toughness testing. Specimen processing included the following steps. Firstly, the sandstone cylinders were obtained from the rock mass by drilling cores, and then cutting them into pieces and grinding the two end faces with a grinding disk. Disk specimens of about 75 mm in diameter and 25 mm in thickness were obtained. After that, the disk specimens were fixed in a special fixture for processing a herringbone groove crack by coplanar milling with a cutter disc. On this basis, the herringbone part of both sides were sawn with a diamond saw blade, and extended to the root of the groove, and finally, the CCBD specimens were obtained. Wetting and drying cycles were performed by submerging the specimens in water for 48 h, then putting the samples into an oven with the temperature controlled at 105 °C to dry for 24 h, and then cooling to room temperature, which was regarded as a single wetting–drying cycle. The specimens were subjected to 1, 3, 5, and 7 wetting–drying cycles in the laboratory. After that, the sandstone specimens which went through setting times of the wetting– drying cycles were submerged in water for 48 h for testing. For the intact sandstone specimens which did not go through cyclic wetting and drying, they were regarded as going through 0 wetting– drying cycle. The experimentation was conducted in the Fundamental Mechanics Laboratory of Sichuan University. An electronic universal material testing machine was used for loading, and the loading mode was a displacement control. According to19,20, we choose a loading rate of 0.05 mm/min for all specimens. The specimens were loaded until the final fracture and the complete load–displacement data were recorded during each test.
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
3. Results and discussion 3.1. Load–displacement The load–displacement curves of the sandstone samples after cyclic wetting and drying for pure mode I loading conditions are shown in Fig. 3. The italic capital letter N in Fig. 3 represents the number of cyclic wetting and drying. We can see from the figure that the peak load of sandstone after cyclic wetting and drying is less than that for intact sandstone. In addition, the peak load decreases with increase of the number of wetting–drying cycles. The deformation and failure process of sandstone generally experiences three stages. The rock is compacted in the initial loading and the load–displacement curve is concave, which is due to the micro-cracks inside the rock closing under the external force. Then, the load–displacement presents a approximate linear relationship, and unloads rapidly after the force reaches a maximum value. With increase of the number of wetting–drying cycles, the compaction stage is more and more obvious, and the slope of the load–displacement curve in the elastic stage is reduced significantly. This is mainly because of the internal micro-cracks growth and expansion during wetting–drying cycles. The failure forms show obvious brittle fractures for intact sandstone samples and less wetting–drying cycles. However, when the number of wetting–drying cycles reached 7, the sandstone samples become more softened and ductile. That is to say the cyclic wetting and drying has an obvious influence on the failure characteristics of sandstone that changes from brittle failure to ductile failure. 3.2. The influence of wetting–drying cycles on the fracture toughness of sandstone A series of fracture toughness tests were conducted for sandstone after different wetting–drying cycles with CCBD specimens. The test results are shown in Table 1, and the degradation degree is given by the following formula:
Sj =
K0 − Kj K0
× 100% (j = 1, 3, 5, 7)
(5)
where Kj is the pure mode I fracture toughness or tensile strength of sandstone after j wetting–drying cycles. According to the test results in Table 1, the pure mode I fracture toughness decreases with increase of the number of wetting–drying cycles. When the number of wetting–drying cycles is respectively 1, 3, 5, 7, the pure mode I fracture toughness is reduced by 24.1%, 35.3%,
43.3%, 52.4%, respectively. At the beginning of testing, water–rock interaction is very fierce, and the pure mode I fracture toughness degenerate rapidly. With increase in the number of wetting–drying cycles, the water–rock interaction weakens gradually, and the rate of fracture toughness decrease tends to slow down. During wetting and drying processes, water–rock interaction including physical and chemical damage to sandstone happened, which may cause the degree of cementation between grains reduce, and make the internal micro-cracks growth and expansion. And secondary cracks can develop in the sandstone samples. With increase of the number of wetting–drying cycles, the porosity or water absorption ratio increase, this has a negative effect on its mechanical properties.3 The reasons for this change are that stress concentrations at the borders of voids reduce the strength of the sandstone; water in voids decreases the energy at the surfaces of particles; and cracks and failure planes spread according to the stress concentration at the borders of voids.7 3.3. The relationship between mode I fracture toughness and tensile strength of sandstone The Brazilian splitting method is used to measure the tensile strength of sandstone after different number of wetting and drying cycles. The tensile strength of sandstone is respectively 1.18, 0.97, 0.869, 0.782, 0.667 MPa, corresponding to the number of wetting– drying cycles 0, 1, 3, 5, 7. With increased number of wetting– drying cycles, the tensile strength of sandstone reduces gradually. After 7 wetting–drying cycles, the tensile strength is only 56.5% of intact sandstone. That is to say cyclic wetting and drying have a larger degradation effect on the tensile strength of sandstone. Fig. 4 shows the degradation degree of mode I fracture toughness and tensile strength of sandstone calculated by Eq. (5). As we can see from the graph, the degradation degree of mode I fracture toughness is always larger than that of tensile strength. For example, when the number of wetting and drying cycles reaches 7, the degradation degree of mode I fracture toughness and tensile strength are 52.4%, 43.5%, respectively. The relationship between the fracture toughness and tensile strength for rock materials has been studied by many researchers.21–23 And the results indicated that there is a good linear relationship between pure mode I fracture toughness and tensile strength. According to the test results in this paper, the relationship between the pure mode I fracture toughness KIC and tensile strength st of sandstone after different number of wetting– drying cycles is shown in Fig. 5. It can be seen from Fig. 5 that there is a good linear relationship between KIC and st of sandstone after cyclic wetting and drying. The fitting curve equation KIC = 0.1932σt − 0.0437 has been obtained through linear regression of the test data. There is a little difference to the results given by Zhang et al.22 This may be related to the types of sandstone and the different testing conditions and other factors. At the same time, it also can be seen from the figure that the pure mode I fracture toughness and tensile strength decrease with the increase of the number of wetting–drying cycles. For rock materials, the size of the fracture process zone in front of the crack tip, which is also named crack propagation radius rc, is usually taken as a material constant and can be calculated from the following equation24
rc =
Fig. 3. Load–displacement curves of sandstone specimens after cyclic wetting and drying for pure mode I loading condition.
333
2 1 ⎛ KIC ⎞ ⎜ ⎟ 2π ⎝ σt ⎠
(6)
where KIC and st are the pure mode I fracture toughness and the tensile strength, respectively. The crack propagation radius of sandstone after different wetting–drying cycles calculated by Eq. (6) is shown in Fig. 6. According to the graph, with the increase in
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W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
Table 1 The test results of fracture toughness of sandstone after cyclic wetting and drying. Wetting–drying cycles N/times
0
1
3
5
7
Diameter D/mm
74.56 74.54 74.58 74.79 74.65 74.66 74.74 74.65 74.56 74.60 74.57 74.68 74.05 74.61 74.50
Crack length 2a/mm
44.10 44.40 43.80 45.20 45.40 46.30 46.10 46.40 46.20 47.25 46.75 47.25 46.00 46.75 46.00
Thickness B/mm
25.06 24.81 24.84 24.89 24.81 25.00 25.03 24.91 24.91 25.21 24.93 25.11 24.50 25.05 25.00
Fig. 4. The degradation degree of mode I fracture toughness and tensile strength of sandstone.
Load F/N
1228 1308 1450 1104 944 862 849 800 769 764 666 658 630 663 472
KIC/ MPa m0.5
The degradation degree S/%
Test data
Average value
0.172 0.187 0.203 0.160 0.138 0.129 0.126 0.120 0.115 0.117 0.101 0.101 0.097 0.100 0.070
0.187
–
0.142
24.1
0.121
35.3
0.106
43.3
0.089
52.4
Fig. 6. The crack propagation radius of sandstone after different number of wetting–drying cycles.
of wetting and drying cycles reaches 5, the degradation degree of mode I fracture toughness and tensile strength are 43.3% and 33.7%, respectively. We can come to this conclusion that cyclic wetting and drying has somewhat degrading effect on the crack propagation radius of sandstone. Unfortunately, it is not clear that the mechanism of fracture process zone decreases with increasing number of wetting–drying cycles at present. And deeper mechanism is to be studied further.
4. Conclusions
Fig. 5. The relationship between pure mode I fracture toughness and tensile strength of sandstone.
the number of wetting–drying cycles, the crack propagation radius of sandstone decreases gradually. It also indirectly indicates that the degradation degree of mode I fracture toughness is always larger than that of tensile strength. For example, when the number
The influences of cyclic wetting and drying on the mode I fracture toughness and tensile strength of sandstone have been studied in this paper. Besides, we discuss the relationship between mode I fracture toughness and tensile strength of sandstone and investigate the influence of cyclic wetting and drying on crack propagation radius. A series of fracture toughness and tensile strength tests of sandstone after different number of wetting and drying cycles have been obtained. Both the pure mode I fracture toughness and tensile strength decrease with increase of the number of wetting and drying cycles. Besides, the degradation degree of mode I fracture toughness is always larger than that of tensile strength. Sandstone becomes more softened and ductile after cyclic
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
wetting and drying, and the failure characteristics of sandstone changes from brittle failure to ductile failure, especially, when the number of cyclic wetting and drying is large. There still exists a good linear relationship between the pure mode I fracture toughness and tensile strength of sandstone after cyclic wetting and drying; in addition, the fitting curve equation KIC = 0.1932σt − 0.0437 has been obtained. The cyclic wetting and drying has an influence on the crack propagation radius, the crack propagation radius of sandstone decreases gradually with increased number of wetting and drying cycles.
Acknowledgments The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Project no.11172186 &11327801).
References 1 Aliha MRM, Ashtar R, Aytollahi MR. Mode I and mode II fracture toughness testing for a coarse grain marble. Appl Mech Mater. 2006;5-6:181–188. 2 Yao HY, Zhang ZH, Zhu CH, Shi YC, Li Y. Experimental study of mechanical properties of sandstone under cyclic drying and wetting. Rock Soil Mech. 2010;31(12)3704–3708. 3 Hale PA, Shakoor A. A laboratory investigation of the effects of cyclic heating and cooling, wetting and drying, and freezing and thawing on the compressive strength of selected sandstones. Environ Eng Geosci. 2003;9(2)117–130. 4 Li N, Zhu YM, Su B, Gunter S. A chemical damage model of sandstone in acid solution. Int J Rock Mech Min Sci. 2003;40:243–249. 5 Lin ML, Jeng FS, Tsai LS, Huang TH. Wetting weakening of tertiary sandstonesmicroscopic mechanism. Environ Geol. 2005;48:265–275. 6 Sumner PD, Loubser MJ. Experimental sandstone weathering using different wetting and drying moisture amplitudes. Earth Surf Proc Land. 2008;33:985– 990. 7 Ozbek A. Investigation of the effects of wetting-drying and freezing-thawing cycles on some physical and mechanical properties of selected ignimbrites. Bull
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Eng Geol Environ. 2014;73:595–609. 8 Torres-Suareza MC, Alarcon-Guzman A, Moya RB-D. Effects of loading-unloading and wetting-drying cycles on geomechanical behaviors of mudrocks in the Colombian Andes. J Rock Mech Geotech Eng. 2014;6:257–268. 9 Taibi S, Duperret A, Fleureau J-M. The effect of suction on the hydro-mechanical behaviour of chalk rocks. Eng Geol. 2009;106:40–50. 10 Török Á, Vásárhelyi B. The influence of fabric and water content on selected rock mechanical parameters of travertine, examples from Hungary. Eng Geol. 2010;115:237–245. 11 Erguler ZA, Ulusay R. Water-induced variations in mechanical properties of claybearing rocks. Int J Rock Mech Min Sci. 2009;46:355–370. 12 Gautam TP, Shakoor A. Slaking behavior of clay-bearing rocks during a one-year exposure to natural climatic conditions. Eng Geol. 2013;166:17–25. 13 Nara Y, Hiroyoshi N, Yoneda T, Kaneko K. Effects of relative humidity and temperature on subcritical crack growth in igneous rock. Int J Rock Mech Min Sci. 2010;47:640–646. 14 Tang LS, Zhang PC, Wang SJ. Testing study on effects of chemical action of aqueous solution on crack propagation in rock. Chin J Rock Mech Eng. 2002;21(6) 822–827. 15 Deng HF, Yuan XF, Li JL, Luo Q, He M. Fracture mechanics characteristics and deterioration mechanism of sandstone under reservoir immersion interaction. Earth Sci: J Chin Univ Geosci. 2014;39(1)108–114. 16 Deng HF, Li JL, Sun XS, Zhu M, Yuan XF, Luo Q. Experimental research of fracture mechanical effect of sandstone under water corrosion. Chin J Rock Mech Eng. 2012;31(7)1342–1348. 17 Atkinson C, Smelser RE, Sanchez J. Combined mode fracture via the cracked Brazilian disk test. Int J Fract. 1982;18(4)279–291. 18 Dong SM, Wang Y, Xia YM. Stress intensity factors for central cracked circular disk subjected to compression. Eng Fract Mech. 2004;71:1135–1148. 19 Khan K, Al-Shayea NA. Effect of specimen geometry and testing method on mixed mode I–II fracture toughness of a limestone rock from Saudi Arabia. Rock Mech Rock Eng. 2000;33(3)179–206. 20 Aliha MRM, Ayatollahi MR. Mixed mode I/II brittle fracture evaluation of marble using SCB specimen. Procedia Eng. 2011;10:311–318. 21 Zhang ZX, Kou SQ, Lindqvist PA, Yu Y. The relationship between the fracture toughness and tensile strength of rock. In: Strength theories: applications, development & prospects for 21st century. Beijing, NewYork: Science Press; 1998. p. 215–219. 22 Zhang ZX. An empirical relation between mode I fracture toughness and the tensile strength of rock. Int J Rock Mech Min Sci. 2002;39(3)401–406. 23 Wang JJ, Zhu JG, Chiu CF, Zhang H. Experimental study on fracture toughness and tensile strength of a clay. Eng Geol. 2007;94:65–75. 24 Ayatollahi MR, Aliha MRM. On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials. Eng Fract Mech. 2008;75:4631–4641.
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
The influence of cyclic wetting and drying on the fracture toughness of sandstone Wen Hua, Shiming Dong n, Yifan Li, Jigang Xu, Qingyuan Wang College of Architecture and Environment, Sichuan University, Chengdu 610065, PR China
art ic l e i nf o Article history: Received 11 November 2014 Received in revised form 25 May 2015 Accepted 2 June 2015 Keywords: Sandstone Wetting and drying Central cracked Brazilian disc Fracture toughness Tensile strength
1. Introduction It is well known that there are some micro-cracks, pores or faults in a rock mass because of the complexity of rock structure, and the essence of the rock material failure process is micro-crack initiation, propagation, breakthrough and collection, in the end, resulting in rock failure. Rock fracture toughness characterizes the resistance to crack initiation and propagation, which is an important parameter in the mechanical properties of rock materials. It has an irreplaceable role in the rock mechanics theory research and practical applications.1 Rock deformation and failure usually involves water in practical engineering such as tunneling, mining and rock excavation. Water–rock interaction is an important factor affecting the safety and stability of geotechnical engineering.2 Rock masses are often in a state of cyclic drying and wetting due to the ground water level changing or for other reasons. It is closely related with water–rock interaction, such that a lot of geological disasters occurred in the past few decades such as landslides, debris flow, ground subsidence and collapse, etc. The safety and stability of geotechnical engineering under water–rock interaction is increasingly becoming the focus of attention. In the recent years, the influence of cyclic drying and wetting on the physical and mechanical properties of rock materials have been studied by many researchers.3–8 The physical properties of rock mainly include bulk density, specific gravity, apparent porosity, P-wave velocity, etc., whereas the mechanical properties of n
Corresponding author. E-mail address: [email protected] (S. Dong).
http://dx.doi.org/10.1016/j.ijrmms.2015.06.010 1365-1609/& 2015 Elsevier Ltd. All rights reserved.
rock materials mainly focus on uniaxial compressive strength, shear strength, cohesion resistance, elastic modulus, and so on. The results indicate that the physical and mechanics properties of rock materials have a different degree of deterioration after cyclic drying and wetting. The influence of water content on rock mechanical parameters was investigated by Taibi et al.9, Török et al.10 and Erguler et al.11 Gautam et al.12 pointed out rocks with higher clay contents slake more rapidly and extensively under natural climatic conditions than those with lower clay contents. Nara et al.13 investigated the effects of relative humidity and temperature on subcritical crack growth in igneous rock with double-torsion specimens. Although Tang et al.14 and Deng et al.15,16 conducted a series of experimental studies of the mechanical properties of rock fracture under water–rock interaction with three pointed bending specimens, they mainly focused on the pure mode I fracture toughness for rock materials after short or long term soaking with aqueous solution or chemical solution. However, so far, little has been reported on the study of the influence of cyclic wetting and drying on the mode I fracture toughness and tensile strength for rock materials. The aim of this paper is to undertake an experimental study on the influence of cyclic wetting and drying on the mode I fracture toughness and tensile strength of sandstone, and discuss the relationship between mode I fracture toughness and tensile strength of sandstone after cyclic wetting and drying. The crack propagation laws have also been studied in this paper in order to provide a theoretical basis for stability analysis in geotechnical engineering under complex conditions.
332
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
2. Experimental methods The central cracked Brazilian disc (CCBD) specimen has been extensively employed to investigate the fracture behavior of different brittle materials, because it can facilitate the realization of pure mode I, pure mode II and mixed mode loading by changing the loading angle, besides which the stress intensity factors have analytic solutions.17,18 We test pure mode I fracture toughness of sandstone after wetting–drying cycles with CCBD specimens. And the Brazilian splitting method is used to measure the tensile strength of sandstone after different number of wetting–drying cycles. The Brazilian disk nominal diameter D¼ 75 mm, nominal thickness B ¼25 mm, the nominal crack relative length α ¼ 0.6, and the groove width is about 1 mm for each specimen. A total 30 specimens are divided into 2 groups for testing the pure mode I fracture toughness and tensile strength of sandstone. Fig. 2. The results of X-ray diffraction analysis.
2.1. Stress intensity factors for the central cracked Brazilian disc A schematic diagram of the CCBD specimen diametrically loaded by a pair of concentrated forces is shown in Fig. 1. The thickness of the disc is B and the radius is R. The crack length is 2a, and the loading angle is β, which is the angle between the crack line and the loading direction. Dong et al.18 obtained analytic solutions of the stress intensity factors for the central cracked Brazilian disc under combined loading conditions by using the weight function method.
given by Dong et al.18 Generally speaking, in order to obtain more accurate results, the value of n which is related to the crack relative length α should be larger enough. However, we find that when the crack relative length α ≤ 0.9, the value of n ranging from 60 to 100, there is virtually no difference. That is to say, it is very accurate when n = 100. So, the value 100 of n was used in all the calculations.
n ⎡ ⎤ KI = σ πa ⎢ f11 + 2 ∑ A1i f1i α 2(i − 1)⎥ ⎢⎣ ⎥⎦ i=1
2.2. Specimens preparation and testing process
(1)
n
KII = 2σ πa
∑ A2i f2i α
2(i − 1)
i=1
(2)
The normalized stress intensity factors FI and FII can be written in the following forms: n
FI =
KI = f11 + 2 ∑ A1i f1i α 2(i − 1) σ πa i=1
FII =
KII = 2 ∑ A2i f2i α 2(i − 1) σ πa i=1
(3)
n
(4)
where α ¼a/R and s ¼F/(πBR), and α is defined as the crack relative length. The expressions for the coefficients f11, A1i, f1i, A2i and f2i are
Fig. 1. Diagrams of the CCBD specimen under compression.
The sandstone for this experiment was produced in Ziyang City, Sichuan Province, China. The mineralogical composition of this sandstone determined by X-ray diffraction (XRD) analysis (Fig. 2) indicates that this rock is mainly composed of quartz, albite, chlorite and serpentine. The CCBD specimens were used for pure mode I fracture toughness testing. Specimen processing included the following steps. Firstly, the sandstone cylinders were obtained from the rock mass by drilling cores, and then cutting them into pieces and grinding the two end faces with a grinding disk. Disk specimens of about 75 mm in diameter and 25 mm in thickness were obtained. After that, the disk specimens were fixed in a special fixture for processing a herringbone groove crack by coplanar milling with a cutter disc. On this basis, the herringbone part of both sides were sawn with a diamond saw blade, and extended to the root of the groove, and finally, the CCBD specimens were obtained. Wetting and drying cycles were performed by submerging the specimens in water for 48 h, then putting the samples into an oven with the temperature controlled at 105 °C to dry for 24 h, and then cooling to room temperature, which was regarded as a single wetting–drying cycle. The specimens were subjected to 1, 3, 5, and 7 wetting–drying cycles in the laboratory. After that, the sandstone specimens which went through setting times of the wetting– drying cycles were submerged in water for 48 h for testing. For the intact sandstone specimens which did not go through cyclic wetting and drying, they were regarded as going through 0 wetting– drying cycle. The experimentation was conducted in the Fundamental Mechanics Laboratory of Sichuan University. An electronic universal material testing machine was used for loading, and the loading mode was a displacement control. According to19,20, we choose a loading rate of 0.05 mm/min for all specimens. The specimens were loaded until the final fracture and the complete load–displacement data were recorded during each test.
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
3. Results and discussion 3.1. Load–displacement The load–displacement curves of the sandstone samples after cyclic wetting and drying for pure mode I loading conditions are shown in Fig. 3. The italic capital letter N in Fig. 3 represents the number of cyclic wetting and drying. We can see from the figure that the peak load of sandstone after cyclic wetting and drying is less than that for intact sandstone. In addition, the peak load decreases with increase of the number of wetting–drying cycles. The deformation and failure process of sandstone generally experiences three stages. The rock is compacted in the initial loading and the load–displacement curve is concave, which is due to the micro-cracks inside the rock closing under the external force. Then, the load–displacement presents a approximate linear relationship, and unloads rapidly after the force reaches a maximum value. With increase of the number of wetting–drying cycles, the compaction stage is more and more obvious, and the slope of the load–displacement curve in the elastic stage is reduced significantly. This is mainly because of the internal micro-cracks growth and expansion during wetting–drying cycles. The failure forms show obvious brittle fractures for intact sandstone samples and less wetting–drying cycles. However, when the number of wetting–drying cycles reached 7, the sandstone samples become more softened and ductile. That is to say the cyclic wetting and drying has an obvious influence on the failure characteristics of sandstone that changes from brittle failure to ductile failure. 3.2. The influence of wetting–drying cycles on the fracture toughness of sandstone A series of fracture toughness tests were conducted for sandstone after different wetting–drying cycles with CCBD specimens. The test results are shown in Table 1, and the degradation degree is given by the following formula:
Sj =
K0 − Kj K0
× 100% (j = 1, 3, 5, 7)
(5)
where Kj is the pure mode I fracture toughness or tensile strength of sandstone after j wetting–drying cycles. According to the test results in Table 1, the pure mode I fracture toughness decreases with increase of the number of wetting–drying cycles. When the number of wetting–drying cycles is respectively 1, 3, 5, 7, the pure mode I fracture toughness is reduced by 24.1%, 35.3%,
43.3%, 52.4%, respectively. At the beginning of testing, water–rock interaction is very fierce, and the pure mode I fracture toughness degenerate rapidly. With increase in the number of wetting–drying cycles, the water–rock interaction weakens gradually, and the rate of fracture toughness decrease tends to slow down. During wetting and drying processes, water–rock interaction including physical and chemical damage to sandstone happened, which may cause the degree of cementation between grains reduce, and make the internal micro-cracks growth and expansion. And secondary cracks can develop in the sandstone samples. With increase of the number of wetting–drying cycles, the porosity or water absorption ratio increase, this has a negative effect on its mechanical properties.3 The reasons for this change are that stress concentrations at the borders of voids reduce the strength of the sandstone; water in voids decreases the energy at the surfaces of particles; and cracks and failure planes spread according to the stress concentration at the borders of voids.7 3.3. The relationship between mode I fracture toughness and tensile strength of sandstone The Brazilian splitting method is used to measure the tensile strength of sandstone after different number of wetting and drying cycles. The tensile strength of sandstone is respectively 1.18, 0.97, 0.869, 0.782, 0.667 MPa, corresponding to the number of wetting– drying cycles 0, 1, 3, 5, 7. With increased number of wetting– drying cycles, the tensile strength of sandstone reduces gradually. After 7 wetting–drying cycles, the tensile strength is only 56.5% of intact sandstone. That is to say cyclic wetting and drying have a larger degradation effect on the tensile strength of sandstone. Fig. 4 shows the degradation degree of mode I fracture toughness and tensile strength of sandstone calculated by Eq. (5). As we can see from the graph, the degradation degree of mode I fracture toughness is always larger than that of tensile strength. For example, when the number of wetting and drying cycles reaches 7, the degradation degree of mode I fracture toughness and tensile strength are 52.4%, 43.5%, respectively. The relationship between the fracture toughness and tensile strength for rock materials has been studied by many researchers.21–23 And the results indicated that there is a good linear relationship between pure mode I fracture toughness and tensile strength. According to the test results in this paper, the relationship between the pure mode I fracture toughness KIC and tensile strength st of sandstone after different number of wetting– drying cycles is shown in Fig. 5. It can be seen from Fig. 5 that there is a good linear relationship between KIC and st of sandstone after cyclic wetting and drying. The fitting curve equation KIC = 0.1932σt − 0.0437 has been obtained through linear regression of the test data. There is a little difference to the results given by Zhang et al.22 This may be related to the types of sandstone and the different testing conditions and other factors. At the same time, it also can be seen from the figure that the pure mode I fracture toughness and tensile strength decrease with the increase of the number of wetting–drying cycles. For rock materials, the size of the fracture process zone in front of the crack tip, which is also named crack propagation radius rc, is usually taken as a material constant and can be calculated from the following equation24
rc =
Fig. 3. Load–displacement curves of sandstone specimens after cyclic wetting and drying for pure mode I loading condition.
333
2 1 ⎛ KIC ⎞ ⎜ ⎟ 2π ⎝ σt ⎠
(6)
where KIC and st are the pure mode I fracture toughness and the tensile strength, respectively. The crack propagation radius of sandstone after different wetting–drying cycles calculated by Eq. (6) is shown in Fig. 6. According to the graph, with the increase in
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W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
Table 1 The test results of fracture toughness of sandstone after cyclic wetting and drying. Wetting–drying cycles N/times
0
1
3
5
7
Diameter D/mm
74.56 74.54 74.58 74.79 74.65 74.66 74.74 74.65 74.56 74.60 74.57 74.68 74.05 74.61 74.50
Crack length 2a/mm
44.10 44.40 43.80 45.20 45.40 46.30 46.10 46.40 46.20 47.25 46.75 47.25 46.00 46.75 46.00
Thickness B/mm
25.06 24.81 24.84 24.89 24.81 25.00 25.03 24.91 24.91 25.21 24.93 25.11 24.50 25.05 25.00
Fig. 4. The degradation degree of mode I fracture toughness and tensile strength of sandstone.
Load F/N
1228 1308 1450 1104 944 862 849 800 769 764 666 658 630 663 472
KIC/ MPa m0.5
The degradation degree S/%
Test data
Average value
0.172 0.187 0.203 0.160 0.138 0.129 0.126 0.120 0.115 0.117 0.101 0.101 0.097 0.100 0.070
0.187
–
0.142
24.1
0.121
35.3
0.106
43.3
0.089
52.4
Fig. 6. The crack propagation radius of sandstone after different number of wetting–drying cycles.
of wetting and drying cycles reaches 5, the degradation degree of mode I fracture toughness and tensile strength are 43.3% and 33.7%, respectively. We can come to this conclusion that cyclic wetting and drying has somewhat degrading effect on the crack propagation radius of sandstone. Unfortunately, it is not clear that the mechanism of fracture process zone decreases with increasing number of wetting–drying cycles at present. And deeper mechanism is to be studied further.
4. Conclusions
Fig. 5. The relationship between pure mode I fracture toughness and tensile strength of sandstone.
the number of wetting–drying cycles, the crack propagation radius of sandstone decreases gradually. It also indirectly indicates that the degradation degree of mode I fracture toughness is always larger than that of tensile strength. For example, when the number
The influences of cyclic wetting and drying on the mode I fracture toughness and tensile strength of sandstone have been studied in this paper. Besides, we discuss the relationship between mode I fracture toughness and tensile strength of sandstone and investigate the influence of cyclic wetting and drying on crack propagation radius. A series of fracture toughness and tensile strength tests of sandstone after different number of wetting and drying cycles have been obtained. Both the pure mode I fracture toughness and tensile strength decrease with increase of the number of wetting and drying cycles. Besides, the degradation degree of mode I fracture toughness is always larger than that of tensile strength. Sandstone becomes more softened and ductile after cyclic
W. Hua et al. / International Journal of Rock Mechanics & Mining Sciences 78 (2015) 331–335
wetting and drying, and the failure characteristics of sandstone changes from brittle failure to ductile failure, especially, when the number of cyclic wetting and drying is large. There still exists a good linear relationship between the pure mode I fracture toughness and tensile strength of sandstone after cyclic wetting and drying; in addition, the fitting curve equation KIC = 0.1932σt − 0.0437 has been obtained. The cyclic wetting and drying has an influence on the crack propagation radius, the crack propagation radius of sandstone decreases gradually with increased number of wetting and drying cycles.
Acknowledgments The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Project no.11172186 &11327801).
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