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Observation of time-dependent local deformation of crystalline rocks using a confocal laser scanning microscope
ARTICLE IN PRESS
International Journal of Rock Mechanics & Mining Sciences 45 (2008) 431–441 www.elsevier.com/locate/ijrmms
Technical Note
Observation of time-dependent local deformation of crystalline rocks using a confocal laser scanning microscope Jung Hae Choi, A.H.M. Faisal Anwar1, Yasuaki Ichikawa Department of Environmental Engineering and Architecture, Graduate School of Environmental Studies, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan Received 8 November 2006; received in revised form 13 June 2007; accepted 2 July 2007 Available online 17 August 2007
1. Introduction There is a strong demand for constructing deep underground space in many fields of rock engineering such as mining activities, petroleum production and disposal for high level radioactive wastes (HLW). Characteristics of time-dependent deformation and failure around the underground opening are a major concern for stability and safety. Creep under constant stress and relaxation under constant strain are two typical time-dependent phenomena of materials. In natural geological systems true creep or relaxation is, however, hard to be implemented, that is, a combination of creep and relaxation is commonly observed. In view of microscale behavior the time-dependent deformation and failure of rock materials are a result of complex processes. We must take into account both the lithological controls (such as mineralogy, composition of intra-/intergranular fluid, grain size, lattice-preferred orientation, porosity and permeability) and the external controls (such as temperature, lithostatic pressure, differential stress, fluid pressure and externally imposed strain rate) [1]. Rocks, by their nature, contain numerous discontinuous micro-structures including grain boundary, microcrack, microcavities and cleavages of minerals offering dominant deformation under compressive and/or shearing stress. Thus the behavior of deformation and failure affected by the discontinuities shows a strong nonlinearity [2]. Among others, grain boundaries play an important role for Corresponding author. Tel.: +81 52 789 3829; fax: +81 52 789 1176.
E-mail address: [email protected] (Y. Ichikawa). Current address: Department of Water Resources Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh. 1
1365-1609/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2007.07.004
polycrystalline rocks [3]. Although many studies have been performed on this topic, the knowledge in view of microstructures is limited. A number of experimental techniques have been developed for observing the surface deformation behavior at grain boundaries for polycrystalline materials including atomic force microscopy (AFM), digital speckle methods and electron backscatter diffraction (EBSD) [4–7]. Combining AFM and EBSD methods, Chandrasekaran and Nygards [3] experimentally evaluated the surface deformation of ultra-low carbon steel at the grain boundaries. In rock mechanics several researches have been contributed to the creep behavior [2,8], while a limited number of studies are found on the relaxation behavior. Studies on the relaxation were mainly carried out for metals rather than rocks [3–7]. Seo et al. [9] investigated the crack generation and propagation under a uniaxial relaxation condition for coarse-grain granite. Using a stereoscopic microscope equipped with a digital camera Seo [10] reported continuous states of crack propagation for coarse and fine-grain granite samples and discussed the damage process. However a grain-scale of strain distribution has not yet been reported for rocks under water saturated stress relaxation condition. The confocal laser scanning microscope (CLSM) is an optical imaging system applied to extensive fields of science and engineering recently. Freidrich [11] used it to observe three-dimensional (3D) images of porous media for investigating mass transport phenomena. Liu et al. [12] observed microcrack generation and propagation in granite using CLSM during uniaxial compression. In this study we developed a new testing equipment for stress relaxation which could continuously record stress– strain data and simultaneously take microphotographs
ARTICLE IN PRESS J.H. Choi et al. / International Journal of Rock Mechanics & Mining Sciences 45 (2008) 431–441
432
using CLSM. Digital data of CLSM were analyzed using a B-matrix formulation of finite elements. Local strain distributions were observed and various mechanisms of local straining are discussed for some samples of crystalline rocks.
R2
Bedding Plane
R1
2. Materials and methods R3
2.1. Materials Three types of rocks [13] were provided; an arkose sandstone (mined in the Hukui, Japan), a coarse-grain Inada granite and a fine-grain Inada granite (mined in Tsukuba, Japan). Model compositions of the sandstone and granites are given in Table 1. Mineral compositions of these rocks were determined by the point counting method. Microphotographs for this purpose were taken by an optical microscope (Nikon E600Pol, Japan). Sandstone specimens were prepared perpendicular and parallel to the bedding plane, which were named as R1, R2 and R3, respectively (Fig. 1). Specimen R1 and R3 were chosen for the stress-relaxation experiments. In granite we commonly find three mutually perpendicular cleavages called rift-, grain- and hardway-planes [16] (Fig. 2). The specimens were prepared parallel to the grain, hardway- and rift-planes and labeled as No. 1, 2 and 3, respectively. The specimen No. 1 of coarse-grain granite was noted as C1 while the specimen No. 1 of fine-grain granite was noted as F1, and similar notations were used for other samples. The specimens C2 and F2 were used for observing surface deformation under stress relaxation condition. Specimen size is ð40 mm 20 mm 5 mmÞ and the observation method using CLSM is similar to Liu et al. [12].
Fig. 1. Method of specimen preparation (sandstone).
C-2, F-2 Hardway Grain R
Hardway
R
Rift
G
Rift
H G
H
Grain
C-1, F-1
C-3, F-3
Fig. 2. Method of specimen preparation (Granite).
2.2. Experimental setup The experimental setup shown in Fig. 3 consists of three subsystems: (a) the loading system, (b) the data acquisition system for stress and strain and (c) the controlling and imaging system of CLSM. The loading system allows us to apply stress and to keep the strain constant. It consists of a vessel, a hydraulic pump and a load cell (Tokyo-Sokki, DM6820). The data acquisition system is composed of a digital strain recorder (NEC DC3100) and a personal
Table 1 Mineral compositions of selected sandstone and granite Component
Sandstone (%)
Coarse granite-C (%)
Fine granite-F (%)
Quartz (Q) Feldspar (F) Biotite (B) Others
70.3 7.5 22.2
27.8 63.1 9.0 0.1
25.5 66.8 7.1 0.6
Grain size
0.30–0.32 mm
3–8 mm
1–4 mm
computer (Sony, Vaio type F). These are connected with the load cell and strain gauges pasted on the sample. The observation system is the CLSM: (Olympus OLS1100, Japan). In this OLS1100 system an Ar laser of wavelength 488 nm is used, while Fredrich [11] used a krypton–argon mixed gas laser with wavelength 568 nm for his study of reconstructing 3D images of porous media. The scanning method of OLS1100 is a light polarization using two galvano meter scanner mirrors. Resonant galvano mirrors enable high-speed, high resolution imaging of a wide area. There is an option of choice of five single optical lenses from 5 to 100 depending on desired scale. The size of image data is usually chosen as 1024 1024 pixels. Using this pixel size, the observation area can be selected. For example, using 100 lens one can obtain an image of 0:128 mm 0:128 mm observation area and 1 pixel size gives 125 nm. More accurate image data can be obtained by using a digital zooming of 1–6 times. A separate lens can be
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Observing system (CLSM) Conforal pinhole
Incident laser
Photo multiplier
Object lens Specimen Stopper
Local Cell
Controlling image observation Stress-strain data recording System
Strain gauge
Loading system Axial loading pump
Computer Digital stressstain recorder (IBM ThinkPad 240) (NEC DC3100)
Fig. 3. Schematic diagram of experimental setup.
Table 2 Specifications of OLS100 Unit
Specifications
Ar laser
5 mV output, linear polarization Forced air-cooled Ar ion laser Wave length: 488 nm
Scanning method
Light polarization using two galvano meter scanner mirrors
Shutter
Shut off laser when scanning is not performed
Scanning range
Square area inscribing the circle with a field number of 18 4:3 rectangular area inscribing the circle with a field number of 16
Pinhole
Round pinhole
Light detector
Photomultiplier
Z revolving
Up/down movement of revolving nosepiece, motorized objective switching Resolution: 0:01 mm
Autofocusing
Laser reflection type
used to observe a sample submerged under water. Specifications of OLS110 is summarized in Table 2. 2.3. Experimental process The specimen was saturated by distilled water in a vacuum container for one week assuming that this process could saturate the sample completely. The saturated specimen and the load cell were placed on the bottom surface of the stainless steel vessel ensuring that their centerlines are coincided. This loading subsystem was placed on the observation platform of the CLSM. The specimen chamber was flooded by distilled water and the sample was under water. The specimen was compressed at the rate of 0.2 MPa/s using a manually controlled pump.
The optical lens of 100 was used to observe the surface deformation under water saturated condition. For the relaxation test the displacements at both edges of the sample should be kept constant. In this system one edge was stopped by a wall of the vessel through the load cell and another edge was fixed by two stoppers after a specific applied stress. Prior to the relaxation test four separate uniaxial strength tests were performed for each type of samples and their stress–strain relationships were obtained. Each relaxation experiments ran for one week and the observations were made everyday at a 24ð1Þ h interval. The digital data were taken as 1024 1024 pixels and the microphotographs of grain surface and contact boundaries were obtained.
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Brittle failure of rocks has been investigated by many researchers [8,14]. In general the stress–strain response can be divided into four separate stages prior to the macroscopic failure as marked in Figs. 4 and 5 [10,14]. Stage 1 is the initial region which represents a closure process of existing microcracks in the specimen. The process depends on the density of initial cracks and their geometry. Stage 2 is considered as a linear, homogeneous and elastic response zone. Stage 3 is responsible to develop and propagate a large number of microcracks mainly parallel to the direction of maximum principal stress. The maximum rate of microcrack propagation may occur in this zone. Stage 4
3. Results and discussion 3.1. Stress–strain behavior Stress–strain curves obtained from the uniaxial tests are shown in Figs. 4 and 5. The mean uniaxial strengths of four specimens for each type of rocks are calculated as 137:8 3:25 MPa for R1, 117:1 1:13 MPa for R3, 208:48 14:45 MPa for C2 and 205:34 8:75 MPa for F2. The sandstone gives less uniaxial strength than the granite. Axial and inter-granular strains in the fine-grain granite are higher than ones in the coarse-grain granite.
Axial Stress (MPa) p (peak)
140
Stage 4: Unstabel Cracking
=80%P 100
Stage 3: Stabel Crack Propagation 60
=40%P
Axial Stress Axial Strain Gauge
Crack Initiation Stage 2: Elastic Region
20 0
-0.2
Lateral Strain Gauge
Stage 1: Crack Closing 0
0.2
Lateral Strain (%)
0.4
0.6
0.8
Axial Strain (%) Fig. 4. Stress–strain behavior sandstone.
Axial Stress (MPa) P
200 V Stage 4: Unstable Cracking =80%P
Stage 3: Stable crack Propagation
Fine Grain Granite
Crack Propagation
Coarse Grain Granite
100 Crack Initiation
=40%P Axial Stress
Stage 2: Elastic Region
Axial Strain Gauge Stage 1: Crack Closing
Lateral Strain Gauge 0
-0.2
-0.1
Lateral Strain (%)
0
0.1 Axial Strain (%)
Fig. 5. Stress–strain behavior of granite.
0.2
0.3
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represents the onset of marked localization of the microcrack growth and attains the macroscopic failure. The level of applied stress for the relaxation test was set by considering the maximum stress of Stage 3.
435
Q
Q 1
3.2. Stress relaxation behavior The relaxation process under constant strain was plotted with its elapsed time (Fig. 6). According to the results of relaxation tests we understand the following: (1) The relaxed stress (see Fig. 6) of the fine-grain granite is greater than the coarse-grain granite. (2) The higher stress relaxation is provided by a higher deformation in grain surfaces. And (3) the surface deformation of the fine-grain granite is much deformed than the coarse one. Similar stress relaxation behavior was also observed in the case of sandstone.
1
2
3
3
5
21
19
4 5
2
4
6
6
20
22
7 8
7
23
9
9
11
8
10
24
14
15 17
26
12
12 13
13
25
10
11
27
29 28
15
30
14 16
18
16
3.3. Surface deformation characteristics 0
Time-series of microphotographs were taken by CLSM for the grain surfaces of Quartz (Q)–Quartz (Q) and their contact boundary for sandstone samples. Similarly for granite samples, time-series of microphotographs were taken for the grain surface of Biotite (B)–Quartz (Q) and for their contact boundary. These microphotographs are
30µm
Fig. 7. Microphotograph of sandstone surface (Q–Q surface and their boundary)-R1-1 specimen.
Fig. 8. Microphotograph of sandstone surface (Q–Q surface and their boundary)-R3-3 specimen.
Fig. 6. Stress relaxation with time for different specimen.
shown in Figs. 7 and 8 for sandstone samples, and Figs. 9 and 10 for granite samples. We marked points on the grains and contact boundaries, and set up triangular meshes connecting each point as shown in Figs. 7–10. On the grain surfaces thirty triangular elements were arranged.
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Fig. 9. Microphotograph of granite surface (B–Q surface and their boundary)-F2-1 specimen.
Fig. 10. Microphotograph of granite surface (B–Q surface and their boundary)-C2-1 specimen.
Among them, the first to the eighteenth (1–18) were arranged on the left side grain and the rest (19–30) were on the right side grain. In the contact boundary sixteen triangular elements were arranged. Time-series of displacements were read for the marked points and the strain e of each triangular element was
Fig. 11. Principal strains in sandstone samples: (a–b) At the grain surfaces; (c–d) At the contact boundary.
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calculated by the theory of B-matrix of a constant strain triangular (CST) finite element (FE) approximation. The principal strains were also calculated. Principal strains of each element generated at the end stage of relaxation test are shown in Figs. 11 and 12 for sandstone and granite, respectively. The principal strains revealed at the grain surfaces in sandstone (i.e., Q–Q surfaces) and in granite (i.e., B–Q surfaces) increase with an increase of applied initial stress but the strain at each element may vary according to, mainly, the geometry of individual grains. In case of the contact boundaries between the mineral grains, it is found that the strains at the grain boundary are higher than the surfaces of individual grains. A level of shearing strain is identified by the norm of deviatoric strain ke0 k [15]. In our case the plane strain condition (e33 ¼ e13 ¼ e23 ¼ 0) is assumed, so the mean strain e¯ is given by e¯ ¼ ðe11 þ e22 Þ=3. The deviatoric strain tensor e0 is now written as 01 1 e12 0 3ð2e11 e22 Þ B C 1 e21 0 (1) e0 ¼ @ A. 3ðe11 þ 2e22 Þ 1 0 0 ðe e Þ 11 22 3 Its norm is calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ke0 k ¼ 6ð¯eÞ2 2e11 e22 þ 2e212 .
(2)
Time-changes of local mean and deviatoric strains for the specimen R1-1 are shown in Fig. 13 together with the timechange of the global relaxed stress. It is understood that the higher level of deviatoric strain is appeared at the earlier stage while the higher mean strain is observed at the latter stage. This fact is consistent with our intuitive knowledge of polycrystalline materials that at the early stage of loading the shearing is dominant and then the shearing strain is transformed into the volumetric strain by relaxation and/or creep. Local distributions of mean and deviatoric strains at the end stage of loading are shown for the samples R1-1 (sandstone) and F2-1 (granite) in Figs. 14 and 15, respectively, calculated for each element given in the microphotographs (Figs. 7 and 9). Results reveal that the deformation is mostly compression in granite but elongation in sandstone. In case of the grain boundary deformation, the B–Q deformation in granite is found higher than the Q–Q deformation in sandstone. It is interesting to note that the Q–Q boundary shows expansion whereas B–Q shows compression. It should be recalled that in sandstone quartz crystals are considered more spherical in shape while biotite in granite has a layered structure of iron magnesium aluminum silicate sheets weakly bonded together by layers of potassium ions. These potassium ion layers produce the perfect cleavage. During the relaxation experiments, quartz crystal may have 3D effects which might produce grain rotation to each other. This refers to the tension in the Q–Q grain boundary and quartz
Fig. 12. Principal strains in granite samples: (a–b) At the grain surfaces; (c–d) At the contact boundary.
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0.010
80
0.008
75
0.006 70
Elelment 2
0.004
Elelment 3
65
Stress
0.002
Stress (MPa)
Mean Strain
Elelment 1
60
0.000
55
-0.002 -0.004 0
20
40
60
80
100
120
50 140
Elapsed time (hr) 80
0.200 0.180
75
0.160
70
0.120 Elelment 1 0.100
Elelment 2
0.080
Elelment 3
0.060
Stress
0.040
65
Stress (MPa)
Deviation Strain
0.140
60
55
0.020 0.000 0
20
40
60
80
100
120
50 140
Elapsed time (hr) Fig. 13. Time-change of (a) mean strain and (b) deviatoric strain for the sandstone sample R1-1.
grain surfaces. On the other hand, B–Q grain boundary is stiff and biotite is softer mineral than the quartz. It is difficult to produce tension in the B–Q grain boundary because 3D grain rotation may not occur here. Moreover, due to the sheet like structure of biotite and its perfect cleavage, it is easy to break some parts of the mineral. As a result, overall deformation in sandstone shows expansion whereas granite shows compression. At the same time, the B–Q boundary shows compression and the Q–Q boundary shows expansion. 4. Conclusion Using a confocal laser scanning microscope (CLSM), local deformations of rock minerals of sandstone and
granite were observed under stress relaxation condition. The samples were water-saturated. By this newly developed loading/observation system we could record the stress– strain data continuously and microphotographs could be obtained simultaneously. For the sandstone samples microphotographs were taken for two adjacent quartz (Q) grains and their boundary. For the granite samples similar images were taken for biotite (B) and quartz (Q) and their boundary. The local strain distributions in the individual grain surfaces and their boundaries were calculated by using the B-matrix of finite elements. Triangle meshes were drawn on the microphotographs. Results show that the grain boundary deformation is higher than the individual grain surface deformation and it increases with an increase
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Fig. 14. Contour maps (by using GID) for local strain distribution for the sandstone sample R1-1 (left: Q-grain, middle: Q–Q boundary, right: Q-grain).
of initially applied stress, however, the strain at each element strongly varies according to the geometry of individual grains. Mean and deviatoric strains were also calculated for each element. Results show that the higher level of deviatoric strain is appeared at the earlier stage of loading
of stress relaxation while the higher mean strain is observed at the latter stage. This suggests that a deformation caused by shearing/dilatancy is dominant at the early stage and then the major deformation is transferred into the mean (i.e. volumetric) strain due to stress relaxation and/or creep.
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Fig. 15. Contour maps (by using GID) for local strain distribution for the granite sample F2-1 (left: B-grain, middle: B–Q boundary, right: Q-grain).
Acknowledgements Authors gratefully acknowledge the financial and technical supports provided by the Japan Atomic Energy Agency (JAEA) for this study. Authors also acknowledge the research support provided by Japan Society for the Promotion of Science (JSPS).
References [1] Passchier CW, Trouw RAJ. Microtectonics. Heidelberg, Berlin: Springer; 1996. [2] Weng MC, Jeng FS, Huang TH, Lin ML. Characterizing the deformation behavior of tertiary sandstones. Int J Rock Mech Min Sci 2005;42(3):388–401.
ARTICLE IN PRESS J.H. Choi et al. / International Journal of Rock Mechanics & Mining Sciences 45 (2008) 431–441 [3] Chandrasekaran D, Nygard M. A study of the surface deformation behaviour at grain boundaries in an ultra-low-carbon steel. Acta Mater 2003;51:5375–84. [4] Brinck A, Engelke C, Kopmann W, Neuhauser H. Structure and development of slip lines during plastic deformation of the intermetallic phases Fe3 Al and CuZn. Mater Sci Eng 2001;A239–240:180–7. [5] Man J, Obrtlik K, Blochwitz C, Polak J. Atomic force microscopy of surface relief in individual grains of fatigued 316L austenitic stainless steel. Acta Materiali 2002;50(15):3767–80. [6] Vinogradov A, Hashimoto S, Patlan V, Kitagawa K. Atomic force microscopic study on surface morphology of ultra-fine grained materials after tensile testing. Mat Sci Eng 2001;A319–321:862–6. [7] Balke P, De Hosson JThM. Orientation imaging microscopic observations of in situ deformed ultra low carbon steel. Scripta Mater 2001;44:461–6. [8] Brace WF, Paulding BW, Scholz C. Dilatancy in the fracture of crystalline rocks. J Geophys Res 1966;71:3939–53. [9] Seo Y, Seiki T, Ichikawa Y. Crack generation and propagation during stress relaxation of crystalline rock under water-saturated uniaxial condition. J Soc Mater Sci Japan 1999;48(11):1255–62 [in Japanese].
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[10] Seo Y. Damage process in granite: experimental observation, molecular dynamics simulation and its homogenization analysis. PhD thesis, Department of Geotech and Environ Eng. Nagoya University, Japan; 1999. p. 147. [11] Fredrich JT. 3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes. Phys Chem Earth (A) 1999;24(7):551–61. [12] Liu S, Anwar AHMF, Kim BC, Ichikawa Y. Observation of microcracks in granite using a confocal laser scanning microscope. Int J Rock Mech Min Sci 2006;43:1293–305. [13] Takahashi Y. Geology of the granitic rocks in the Tsukuba area. J Geological Soc Japan 1982;88(3):177–84. [14] Martin CD, Chandler NA. The progressive fracture of Lau du Bonnet granite. Int J Rock Mech Min Sci Geomech Abst 1994;31: 643–59. [15] Ichikawa Y. Introductions of finite element method in geomechanics. Nikka-Giren Pub; 1990 [in Japanese]. [16] Liu S, Anwar AHMF, Seiki T, Ichikawa Y. Microcrack generation and propagation in granite during stress relaxation under watersaturated tri-axial condition. J Geotech Eng 2006;62(3):623–30.
International Journal of Rock Mechanics & Mining Sciences 45 (2008) 431–441 www.elsevier.com/locate/ijrmms
Technical Note
Observation of time-dependent local deformation of crystalline rocks using a confocal laser scanning microscope Jung Hae Choi, A.H.M. Faisal Anwar1, Yasuaki Ichikawa Department of Environmental Engineering and Architecture, Graduate School of Environmental Studies, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan Received 8 November 2006; received in revised form 13 June 2007; accepted 2 July 2007 Available online 17 August 2007
1. Introduction There is a strong demand for constructing deep underground space in many fields of rock engineering such as mining activities, petroleum production and disposal for high level radioactive wastes (HLW). Characteristics of time-dependent deformation and failure around the underground opening are a major concern for stability and safety. Creep under constant stress and relaxation under constant strain are two typical time-dependent phenomena of materials. In natural geological systems true creep or relaxation is, however, hard to be implemented, that is, a combination of creep and relaxation is commonly observed. In view of microscale behavior the time-dependent deformation and failure of rock materials are a result of complex processes. We must take into account both the lithological controls (such as mineralogy, composition of intra-/intergranular fluid, grain size, lattice-preferred orientation, porosity and permeability) and the external controls (such as temperature, lithostatic pressure, differential stress, fluid pressure and externally imposed strain rate) [1]. Rocks, by their nature, contain numerous discontinuous micro-structures including grain boundary, microcrack, microcavities and cleavages of minerals offering dominant deformation under compressive and/or shearing stress. Thus the behavior of deformation and failure affected by the discontinuities shows a strong nonlinearity [2]. Among others, grain boundaries play an important role for Corresponding author. Tel.: +81 52 789 3829; fax: +81 52 789 1176.
E-mail address: [email protected] (Y. Ichikawa). Current address: Department of Water Resources Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh. 1
1365-1609/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2007.07.004
polycrystalline rocks [3]. Although many studies have been performed on this topic, the knowledge in view of microstructures is limited. A number of experimental techniques have been developed for observing the surface deformation behavior at grain boundaries for polycrystalline materials including atomic force microscopy (AFM), digital speckle methods and electron backscatter diffraction (EBSD) [4–7]. Combining AFM and EBSD methods, Chandrasekaran and Nygards [3] experimentally evaluated the surface deformation of ultra-low carbon steel at the grain boundaries. In rock mechanics several researches have been contributed to the creep behavior [2,8], while a limited number of studies are found on the relaxation behavior. Studies on the relaxation were mainly carried out for metals rather than rocks [3–7]. Seo et al. [9] investigated the crack generation and propagation under a uniaxial relaxation condition for coarse-grain granite. Using a stereoscopic microscope equipped with a digital camera Seo [10] reported continuous states of crack propagation for coarse and fine-grain granite samples and discussed the damage process. However a grain-scale of strain distribution has not yet been reported for rocks under water saturated stress relaxation condition. The confocal laser scanning microscope (CLSM) is an optical imaging system applied to extensive fields of science and engineering recently. Freidrich [11] used it to observe three-dimensional (3D) images of porous media for investigating mass transport phenomena. Liu et al. [12] observed microcrack generation and propagation in granite using CLSM during uniaxial compression. In this study we developed a new testing equipment for stress relaxation which could continuously record stress– strain data and simultaneously take microphotographs
ARTICLE IN PRESS J.H. Choi et al. / International Journal of Rock Mechanics & Mining Sciences 45 (2008) 431–441
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using CLSM. Digital data of CLSM were analyzed using a B-matrix formulation of finite elements. Local strain distributions were observed and various mechanisms of local straining are discussed for some samples of crystalline rocks.
R2
Bedding Plane
R1
2. Materials and methods R3
2.1. Materials Three types of rocks [13] were provided; an arkose sandstone (mined in the Hukui, Japan), a coarse-grain Inada granite and a fine-grain Inada granite (mined in Tsukuba, Japan). Model compositions of the sandstone and granites are given in Table 1. Mineral compositions of these rocks were determined by the point counting method. Microphotographs for this purpose were taken by an optical microscope (Nikon E600Pol, Japan). Sandstone specimens were prepared perpendicular and parallel to the bedding plane, which were named as R1, R2 and R3, respectively (Fig. 1). Specimen R1 and R3 were chosen for the stress-relaxation experiments. In granite we commonly find three mutually perpendicular cleavages called rift-, grain- and hardway-planes [16] (Fig. 2). The specimens were prepared parallel to the grain, hardway- and rift-planes and labeled as No. 1, 2 and 3, respectively. The specimen No. 1 of coarse-grain granite was noted as C1 while the specimen No. 1 of fine-grain granite was noted as F1, and similar notations were used for other samples. The specimens C2 and F2 were used for observing surface deformation under stress relaxation condition. Specimen size is ð40 mm 20 mm 5 mmÞ and the observation method using CLSM is similar to Liu et al. [12].
Fig. 1. Method of specimen preparation (sandstone).
C-2, F-2 Hardway Grain R
Hardway
R
Rift
G
Rift
H G
H
Grain
C-1, F-1
C-3, F-3
Fig. 2. Method of specimen preparation (Granite).
2.2. Experimental setup The experimental setup shown in Fig. 3 consists of three subsystems: (a) the loading system, (b) the data acquisition system for stress and strain and (c) the controlling and imaging system of CLSM. The loading system allows us to apply stress and to keep the strain constant. It consists of a vessel, a hydraulic pump and a load cell (Tokyo-Sokki, DM6820). The data acquisition system is composed of a digital strain recorder (NEC DC3100) and a personal
Table 1 Mineral compositions of selected sandstone and granite Component
Sandstone (%)
Coarse granite-C (%)
Fine granite-F (%)
Quartz (Q) Feldspar (F) Biotite (B) Others
70.3 7.5 22.2
27.8 63.1 9.0 0.1
25.5 66.8 7.1 0.6
Grain size
0.30–0.32 mm
3–8 mm
1–4 mm
computer (Sony, Vaio type F). These are connected with the load cell and strain gauges pasted on the sample. The observation system is the CLSM: (Olympus OLS1100, Japan). In this OLS1100 system an Ar laser of wavelength 488 nm is used, while Fredrich [11] used a krypton–argon mixed gas laser with wavelength 568 nm for his study of reconstructing 3D images of porous media. The scanning method of OLS1100 is a light polarization using two galvano meter scanner mirrors. Resonant galvano mirrors enable high-speed, high resolution imaging of a wide area. There is an option of choice of five single optical lenses from 5 to 100 depending on desired scale. The size of image data is usually chosen as 1024 1024 pixels. Using this pixel size, the observation area can be selected. For example, using 100 lens one can obtain an image of 0:128 mm 0:128 mm observation area and 1 pixel size gives 125 nm. More accurate image data can be obtained by using a digital zooming of 1–6 times. A separate lens can be
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Observing system (CLSM) Conforal pinhole
Incident laser
Photo multiplier
Object lens Specimen Stopper
Local Cell
Controlling image observation Stress-strain data recording System
Strain gauge
Loading system Axial loading pump
Computer Digital stressstain recorder (IBM ThinkPad 240) (NEC DC3100)
Fig. 3. Schematic diagram of experimental setup.
Table 2 Specifications of OLS100 Unit
Specifications
Ar laser
5 mV output, linear polarization Forced air-cooled Ar ion laser Wave length: 488 nm
Scanning method
Light polarization using two galvano meter scanner mirrors
Shutter
Shut off laser when scanning is not performed
Scanning range
Square area inscribing the circle with a field number of 18 4:3 rectangular area inscribing the circle with a field number of 16
Pinhole
Round pinhole
Light detector
Photomultiplier
Z revolving
Up/down movement of revolving nosepiece, motorized objective switching Resolution: 0:01 mm
Autofocusing
Laser reflection type
used to observe a sample submerged under water. Specifications of OLS110 is summarized in Table 2. 2.3. Experimental process The specimen was saturated by distilled water in a vacuum container for one week assuming that this process could saturate the sample completely. The saturated specimen and the load cell were placed on the bottom surface of the stainless steel vessel ensuring that their centerlines are coincided. This loading subsystem was placed on the observation platform of the CLSM. The specimen chamber was flooded by distilled water and the sample was under water. The specimen was compressed at the rate of 0.2 MPa/s using a manually controlled pump.
The optical lens of 100 was used to observe the surface deformation under water saturated condition. For the relaxation test the displacements at both edges of the sample should be kept constant. In this system one edge was stopped by a wall of the vessel through the load cell and another edge was fixed by two stoppers after a specific applied stress. Prior to the relaxation test four separate uniaxial strength tests were performed for each type of samples and their stress–strain relationships were obtained. Each relaxation experiments ran for one week and the observations were made everyday at a 24ð1Þ h interval. The digital data were taken as 1024 1024 pixels and the microphotographs of grain surface and contact boundaries were obtained.
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Brittle failure of rocks has been investigated by many researchers [8,14]. In general the stress–strain response can be divided into four separate stages prior to the macroscopic failure as marked in Figs. 4 and 5 [10,14]. Stage 1 is the initial region which represents a closure process of existing microcracks in the specimen. The process depends on the density of initial cracks and their geometry. Stage 2 is considered as a linear, homogeneous and elastic response zone. Stage 3 is responsible to develop and propagate a large number of microcracks mainly parallel to the direction of maximum principal stress. The maximum rate of microcrack propagation may occur in this zone. Stage 4
3. Results and discussion 3.1. Stress–strain behavior Stress–strain curves obtained from the uniaxial tests are shown in Figs. 4 and 5. The mean uniaxial strengths of four specimens for each type of rocks are calculated as 137:8 3:25 MPa for R1, 117:1 1:13 MPa for R3, 208:48 14:45 MPa for C2 and 205:34 8:75 MPa for F2. The sandstone gives less uniaxial strength than the granite. Axial and inter-granular strains in the fine-grain granite are higher than ones in the coarse-grain granite.
Axial Stress (MPa) p (peak)
140
Stage 4: Unstabel Cracking
=80%P 100
Stage 3: Stabel Crack Propagation 60
=40%P
Axial Stress Axial Strain Gauge
Crack Initiation Stage 2: Elastic Region
20 0
-0.2
Lateral Strain Gauge
Stage 1: Crack Closing 0
0.2
Lateral Strain (%)
0.4
0.6
0.8
Axial Strain (%) Fig. 4. Stress–strain behavior sandstone.
Axial Stress (MPa) P
200 V Stage 4: Unstable Cracking =80%P
Stage 3: Stable crack Propagation
Fine Grain Granite
Crack Propagation
Coarse Grain Granite
100 Crack Initiation
=40%P Axial Stress
Stage 2: Elastic Region
Axial Strain Gauge Stage 1: Crack Closing
Lateral Strain Gauge 0
-0.2
-0.1
Lateral Strain (%)
0
0.1 Axial Strain (%)
Fig. 5. Stress–strain behavior of granite.
0.2
0.3
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represents the onset of marked localization of the microcrack growth and attains the macroscopic failure. The level of applied stress for the relaxation test was set by considering the maximum stress of Stage 3.
435
Q
Q 1
3.2. Stress relaxation behavior The relaxation process under constant strain was plotted with its elapsed time (Fig. 6). According to the results of relaxation tests we understand the following: (1) The relaxed stress (see Fig. 6) of the fine-grain granite is greater than the coarse-grain granite. (2) The higher stress relaxation is provided by a higher deformation in grain surfaces. And (3) the surface deformation of the fine-grain granite is much deformed than the coarse one. Similar stress relaxation behavior was also observed in the case of sandstone.
1
2
3
3
5
21
19
4 5
2
4
6
6
20
22
7 8
7
23
9
9
11
8
10
24
14
15 17
26
12
12 13
13
25
10
11
27
29 28
15
30
14 16
18
16
3.3. Surface deformation characteristics 0
Time-series of microphotographs were taken by CLSM for the grain surfaces of Quartz (Q)–Quartz (Q) and their contact boundary for sandstone samples. Similarly for granite samples, time-series of microphotographs were taken for the grain surface of Biotite (B)–Quartz (Q) and for their contact boundary. These microphotographs are
30µm
Fig. 7. Microphotograph of sandstone surface (Q–Q surface and their boundary)-R1-1 specimen.
Fig. 8. Microphotograph of sandstone surface (Q–Q surface and their boundary)-R3-3 specimen.
Fig. 6. Stress relaxation with time for different specimen.
shown in Figs. 7 and 8 for sandstone samples, and Figs. 9 and 10 for granite samples. We marked points on the grains and contact boundaries, and set up triangular meshes connecting each point as shown in Figs. 7–10. On the grain surfaces thirty triangular elements were arranged.
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Fig. 9. Microphotograph of granite surface (B–Q surface and their boundary)-F2-1 specimen.
Fig. 10. Microphotograph of granite surface (B–Q surface and their boundary)-C2-1 specimen.
Among them, the first to the eighteenth (1–18) were arranged on the left side grain and the rest (19–30) were on the right side grain. In the contact boundary sixteen triangular elements were arranged. Time-series of displacements were read for the marked points and the strain e of each triangular element was
Fig. 11. Principal strains in sandstone samples: (a–b) At the grain surfaces; (c–d) At the contact boundary.
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calculated by the theory of B-matrix of a constant strain triangular (CST) finite element (FE) approximation. The principal strains were also calculated. Principal strains of each element generated at the end stage of relaxation test are shown in Figs. 11 and 12 for sandstone and granite, respectively. The principal strains revealed at the grain surfaces in sandstone (i.e., Q–Q surfaces) and in granite (i.e., B–Q surfaces) increase with an increase of applied initial stress but the strain at each element may vary according to, mainly, the geometry of individual grains. In case of the contact boundaries between the mineral grains, it is found that the strains at the grain boundary are higher than the surfaces of individual grains. A level of shearing strain is identified by the norm of deviatoric strain ke0 k [15]. In our case the plane strain condition (e33 ¼ e13 ¼ e23 ¼ 0) is assumed, so the mean strain e¯ is given by e¯ ¼ ðe11 þ e22 Þ=3. The deviatoric strain tensor e0 is now written as 01 1 e12 0 3ð2e11 e22 Þ B C 1 e21 0 (1) e0 ¼ @ A. 3ðe11 þ 2e22 Þ 1 0 0 ðe e Þ 11 22 3 Its norm is calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ke0 k ¼ 6ð¯eÞ2 2e11 e22 þ 2e212 .
(2)
Time-changes of local mean and deviatoric strains for the specimen R1-1 are shown in Fig. 13 together with the timechange of the global relaxed stress. It is understood that the higher level of deviatoric strain is appeared at the earlier stage while the higher mean strain is observed at the latter stage. This fact is consistent with our intuitive knowledge of polycrystalline materials that at the early stage of loading the shearing is dominant and then the shearing strain is transformed into the volumetric strain by relaxation and/or creep. Local distributions of mean and deviatoric strains at the end stage of loading are shown for the samples R1-1 (sandstone) and F2-1 (granite) in Figs. 14 and 15, respectively, calculated for each element given in the microphotographs (Figs. 7 and 9). Results reveal that the deformation is mostly compression in granite but elongation in sandstone. In case of the grain boundary deformation, the B–Q deformation in granite is found higher than the Q–Q deformation in sandstone. It is interesting to note that the Q–Q boundary shows expansion whereas B–Q shows compression. It should be recalled that in sandstone quartz crystals are considered more spherical in shape while biotite in granite has a layered structure of iron magnesium aluminum silicate sheets weakly bonded together by layers of potassium ions. These potassium ion layers produce the perfect cleavage. During the relaxation experiments, quartz crystal may have 3D effects which might produce grain rotation to each other. This refers to the tension in the Q–Q grain boundary and quartz
Fig. 12. Principal strains in granite samples: (a–b) At the grain surfaces; (c–d) At the contact boundary.
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0.010
80
0.008
75
0.006 70
Elelment 2
0.004
Elelment 3
65
Stress
0.002
Stress (MPa)
Mean Strain
Elelment 1
60
0.000
55
-0.002 -0.004 0
20
40
60
80
100
120
50 140
Elapsed time (hr) 80
0.200 0.180
75
0.160
70
0.120 Elelment 1 0.100
Elelment 2
0.080
Elelment 3
0.060
Stress
0.040
65
Stress (MPa)
Deviation Strain
0.140
60
55
0.020 0.000 0
20
40
60
80
100
120
50 140
Elapsed time (hr) Fig. 13. Time-change of (a) mean strain and (b) deviatoric strain for the sandstone sample R1-1.
grain surfaces. On the other hand, B–Q grain boundary is stiff and biotite is softer mineral than the quartz. It is difficult to produce tension in the B–Q grain boundary because 3D grain rotation may not occur here. Moreover, due to the sheet like structure of biotite and its perfect cleavage, it is easy to break some parts of the mineral. As a result, overall deformation in sandstone shows expansion whereas granite shows compression. At the same time, the B–Q boundary shows compression and the Q–Q boundary shows expansion. 4. Conclusion Using a confocal laser scanning microscope (CLSM), local deformations of rock minerals of sandstone and
granite were observed under stress relaxation condition. The samples were water-saturated. By this newly developed loading/observation system we could record the stress– strain data continuously and microphotographs could be obtained simultaneously. For the sandstone samples microphotographs were taken for two adjacent quartz (Q) grains and their boundary. For the granite samples similar images were taken for biotite (B) and quartz (Q) and their boundary. The local strain distributions in the individual grain surfaces and their boundaries were calculated by using the B-matrix of finite elements. Triangle meshes were drawn on the microphotographs. Results show that the grain boundary deformation is higher than the individual grain surface deformation and it increases with an increase
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Fig. 14. Contour maps (by using GID) for local strain distribution for the sandstone sample R1-1 (left: Q-grain, middle: Q–Q boundary, right: Q-grain).
of initially applied stress, however, the strain at each element strongly varies according to the geometry of individual grains. Mean and deviatoric strains were also calculated for each element. Results show that the higher level of deviatoric strain is appeared at the earlier stage of loading
of stress relaxation while the higher mean strain is observed at the latter stage. This suggests that a deformation caused by shearing/dilatancy is dominant at the early stage and then the major deformation is transferred into the mean (i.e. volumetric) strain due to stress relaxation and/or creep.
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Fig. 15. Contour maps (by using GID) for local strain distribution for the granite sample F2-1 (left: B-grain, middle: B–Q boundary, right: Q-grain).
Acknowledgements Authors gratefully acknowledge the financial and technical supports provided by the Japan Atomic Energy Agency (JAEA) for this study. Authors also acknowledge the research support provided by Japan Society for the Promotion of Science (JSPS).
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