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Real-time computerized tomography (CT) experiments on sandstone damage evolution during triaxial compression with chemical corrosion
ARTICLE IN PRESS
International Journal of Rock Mechanics & Mining Sciences 41 (2004) 181–192
Real-time computerized tomography (CT) experiments on sandstone damage evolution during triaxial compression with chemical corrosion Xia-Ting Fenga,b,*, Sili Chenb,c, Hui Zhoua a
Key Laboratory of Rock and Soil Mechanics, Institute of Rock and Soil Mechanics, the Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China b College of Resources and Civil Engineering, Northeastern University, Shenyang 110006, People’s Republic of China c Department of Civil Engineering, Shenyang University of Technology, Shenyang 110023, People’s Republic of China Accepted 3 April 2003
Abstract The computerized tomography (CT) images and CT values for the process of compression, micro-cracking, and dilation up to the failure of sandstone specimens under different loading levels have been obtained using the real-time CT technique for triaxial loading of sandstone subjected to chemical corrosion. Clear CT images and CT value of the stages from compression of microcavities-emergence of micro-cracks-bifurcation-development-fracture-collapse-unloading can be observed. The CT value, equivalent to rock density at the CT scan layer, is the most important parameter describing the damage evolution process of rock. The paper also presents results of the corrosive influence of chemical solutions with different pH values and ionic concentrations on the sandstone strength. Stronger acidity (pHo7) or causticity (pH>7) has a stronger effect on the rock micro-fracturing evolution. The mechanism of damage evolution of sandstone is analyzed and a damage model based on the chemical corrosive influence and CT values is proposed. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction Research on rock strength and its failure characteristics while subjected to chemical corrosion is one of the fundamental factors in nuclear waste disposal, geothermal exploration, oil drilling, seismic aspects, toxic material disposal, long-term stability evaluation of rock engineering structures, etc. It is also one of the frontiers of rock mechanics research. The reason is because underground water exists almost everywhere. The chemical reaction of corrosive matter leads to rock strength decrease, failure acceleration and finally to instability [1–14]. Investigating the chemical influence on crack initial and propagation in geological processes may provide valuable fundamental data for long-term stability of rock cavern, seismic *Corresponding author. Key Laboratory of Rock and Soil Mechanics, Institute of Rock and Soil Mechanics, the Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China. Tel.: +86-27-8719-8913; fax: +86-27-8719-7386. E-mail address: [email protected] (X.-T. Feng). 1365-1609/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S1365-1609(03)00059-5
mechanisms and sub-critical crack propagation. For instance, if water contains a certain ionic concentration of NaCl, CaCl2, or Na2SO4, then the shear friction coefficient of sandstone will depend on the ionic concentration and pH value [12] and can decrease to 20–46% [13]. On the other hand, drilling efficiency may be increased by utilizing the chemical reaction. Research has shown that in wet conditions the fracture toughness will be lower than in dry conditions and the crack propagation velocity will be increased [1,2]. The x potential (the potential where distance from interface of solid and liquid is chemisorbed ions of thickness d [4]) is relevant to the crack propagation and drilling efficiency [3,4,7–10]. When the x potential is equal to zero, the rock material becomes more brittle and more sensitive to the environment, and has the lowest compressive strength; in addition, the sub-critical cracking velocity will increase by more than one order of magnitude [11]. Hence, if a chemical solution with zero x potential is put into the drilling solution, the drillability and breakability of rock will be enhanced.
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chemical corrosion for the first time by using the realtime CT testing technique. CT images and CT values for sandstone cross-sections under different loading levels were obtained. The mechanism of damage increase with chemical corrosion was analyzed and a chemical damage variable is proposed.
Research so far has been mainly concentrated on the influences of the chemical environment on the rock strength, crack velocity, fracture toughness, breakage work ratio, shear property, strain energy index, etc. [1–15]. There has been little research on the internal damage evolution process of rock under chemical corrosion. The corrosive fracture mechanism in a chemical environment has not been properly investigated. The constitutive relationship of coupled chemical and stress corrosion has not yet been properly established. Hence, effective modeling and behavior prediction are impossible. Mechanical experiments are an efficient means of exploring the evolution law of internal damage during rock breakage. The crack distribution on a rock surface in a certain stress state can be observed by optical or electronic microscope [15,19]. Furthermore, the crack distribution on an internal cross-section under a certain stress state can be established by using the computerized tomography (CT) technique [16,17]. Ref. [16] describes obtaining CT images by scanning the damaged rock specimen at a single given stage. That procedure cannot obtain real-time CT images at different stress stages during the full process of rock damage evolution. However, the method described in Ref. [17] can obtain real-time results, which are required to study the realtime process of rock damage evolution, but these were conducted without consideration of the chemical environment and water influences. This paper reports experimental research on the damage evolution properties of sandstone subjected to
2. Experiments 2.1. Rock source and experimental motivation The rock was lime-cemented sandstone taken from the dam foundation of Xianglangdi hydraulic project on the Yellow River, 40 km far from Luoyang City in Henan province, China. It is 130 km upstream Sanmenxia reservoir and 115 km downstream Huayuankou, Zhenzhou city (see Fig. 1). The main function of the project is to control flooding, with accessory functions to reduce silt, to irrigate, and to generate electricity. The project consists of a dam, flood discharge building, and generating electricity system. The dam, 1667 m length at the top and 154 m height, is a clay rockfill dam. There are ten water inlets, nine flood discharges and sand draining tunnels, a normal outflow tunnel, and three plunge pools arranged consecutively. The electricity generating system consists of six water-in tunnels, an underground power house, a main transformation house, a shiplock room, and three water-out tunnels. The total capacity of the three generator sets is 18 million kW. The project was completed on 31 December 2001.
Harbin
Xiaolangdi dam
Urumqi
Shenyang Hohhot
Yel
Rive r
Beijing
w lo
Yellow
Lanzhou
Ya ng zt e
Ri ve r
182
Xi'an
Nanjing
r ve Ri
Shanghai Wuhan
Chengdu
Lhasa Chengqing
Yan
g
te
er Riv z
Taiwan Kunming
Guangzhou Nanning
Haikou
Fig. 1. Location of Xiaolangdi Reservoir on the Yellow River in China.
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Table 1 shows quality statistics of the underground water in the dam area. It indicates that the water in this area is alkaline. The question raised is whether the project conditions are safe. In order to answer these questions, it is imperative to investigate the long-term impact of alkalinity on the rock strength and its fracture characteristics. Therefore, real-time full process CT scanning tests on sandstone subjected to water chemical corrosion have been conducted. The results are compared with tests without water chemical corrosion.
pH 2 is to attain a greater chemical corrosion effect separately from the time effect (a pH 7, water solution has a long-term corrosive effect on rock mass). In addition, the specimen is vacuumized and dried for 6 h at 105 C to induce a greater chemical corrosion effect by increasing the porosity of the specimen. The specimen thus processed was immersed for 200 days in different chemical solutions, distilled water or dam area water of Xiaolangdi, as listed in Table 2, until saturated. One specimen was tested for each set of conditions to establish the trends.
2.2. Rock composition and specimen preparation
2.3. Testing device and process
The sandstone consists of quartzitic sand particles with cement of calcspar. The sand particles have poor sphericity. The size of particles is about 0.1 mm. There is much cement between the particles, consisting mainly of calcspar and hydrous mica. The mineral components of sandstone are 75% quartz, 18% calcite, 2% hydrous mica, 1% plagioclase, less than 0.1% detritus (silica), 0.1% muscovite, 3% limonite, less than 0.1% tourmaline, etc. The texture image of the rock specimen is provided in Fig. 2. The rock specimen is a 54 108 mm2 cylinder. According to the chemical ion and acidity of the underground water in the dam area, as listed in Table 1, different chemical solutions were prepared with the main chemical ions (Table 2). The reason for the preparation of chemical solutions with pH 12 and
The tests have been conducted at the CT laboratory, Cold and Arid Region Environmental and Engineering Research Institute, Chinese Academy of Sciences. The X-ray CT scanner, SIEMENS SOMATOM plus and triaxial loading system designed specially for the CT scanner were used. The dimensions of the triaxial loading system are 240 mm 1000 mm, the maximum designed axial compression is 400 kN with a maximum confining pressure of 20 MPa and a maximum axial stroke of 40 mm. It can be used to measure axial stress and deformation. Collapse tests are possible for rock specimens processed in the internationally standard cylinder form. The specimen dimensions are (f) 50 mm and 100 mm (length). The space resolution of the CT machine is 0.35 mm 0.35 mm and the minimum recognizable volume is 0.1225 mm3 (with thickness 1 mm). Relative density resolution is 0.3% Hu. The sandstone specimen is taken out of the solution before the test and put into the triaxial pressure cell, which is in turn put on the CT bed horizontally (the CT bed can be moved vertically or horizontally). Initial positioning and CT scanning of the specimen is needed. There are altogether three to five layers. The confining pressure is gradually increased up to 5 MPa and then fixed. Then, the axial stress is applied with the given loading rate (the average loading rate is 1.3 MPa/min) until the specimen breaks. Real-time CT scanning for
Table 1 Underground water quality statistics in dam area (in mg/l) Place
PH
Ca2+
Na+
Cl
SO2 4
HCO 3
N. bank River bed S. bank
7.4 7.7
61.9 57.7 83.6
15.4 17.7 24.3
9.7 9.7
20.2 12.3 23.3
85.0 82.5 82.0
Table 2 Specimen Nos. soaked with different water solutions or air
Fig. 2. SEM photomicrograph of sandstone obtained under orthogonal light.
No.
Water solution
pH value
Ionic concentration (M)
1 2 3 4 5 6 7 8 9 10
Distilled water NaCl NaCl NaCl NaCl CaCl2 NaHCO3 Yellow river water Air NaCl
7.0 7 9 2 12 9 9 8.3
0.01 0.01 0.01 0.01 0.01 0.01
7
0.01
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selected cross-sections has been conducted for different loading states. The scanning thickness is 3 mm.
3. Test results and analysis 3.1. Definition of the CT value According to Professor Hounsfield, one of the inventors of the CT machine, the CT value Hrm is defined by Hrm ¼ 1000
m mm r mw ; mm w
ð1Þ
m where mm r and mw are mass absorbing coefficients for rock matrix material and pore water, respectively. The unit name of the CT value is Hu (Hounsfield Unit), and 1000 is the scaling factor of Hu. According to the definition, the CT value is 1000 Hu for air and 0 Hu for pure water. The CT value of a material essentially reflects its density, i.e. the higher the CT value of the material, the higher its density. One may define a relative percentage of the CT value, i.e. ðCTi CT0 =CT0 Þ 100% where CT0 is the initial CT value and CTi is the CT value for the ith loading level.
3.2. Analysis of damage development for sandstone
(1) Initial scanning (1st scanning, Fig. 4a) is made for each layer before loading. The CT values, their variations and internal images are different. This means that the initial internal damage for Xiaolangdi sandstone varies and manifests the non-homogeneity of the internal micro-crack distribution. (2) When the stress difference ðs1 s3 Þ reaches 14.04 MPa (2nd scanning, initial damage, Fig. 4b), the CT values of each layer are increasing. This means that the internal micro-cracks and cavities are closing and a curved segment appears on the stress–strain curve. The local darkness of each layer can be observed on the CT images. (3) When the stress difference ðs1 s3 Þ reaches 50.42 MPa (3rd scanning, rock material compressed, density increased, Fig. 4c), the CT values of each layer are increasing, except for the local part of the first scanned layer (Fig. 5), where the CT value has the maximum value and the images of each layer have little change. (4) When the stress difference reaches 87.28 MPa (4th scanning, Fig. 4d), the CT value of the 1st scan layer reaches its maximum value and a small amount of dilatancy appears. The 2nd and 3rd scan layers have a slight increase. The stress–strain curve approximates to a straight line. The rock specimen is in the elastic compressive stage. In the
1
30mm
24mm
The damage evolution law is analyzed for No. 10 specimen in Table 2 as an example. Fig. 3(a) and (b) are the plane CT sheets illustrating the specimen before and after breakage. The specimen was scanned at the upper,
middle, and lower three layers along the lateral direction for every loading level. The sandstone damage evolution is analyzed according to the CT values and root square variation of each layer listed in Table 3 as well as the CT images of the first scanned layer of specimen No. 10 in different stress states (altogether 9 scans) as shown in Fig. 4(a)–(i).
30mm
2
24mm
3
(a)
(b)
Fig. 3. CT images pre/post-failure of sandstone specimen: (a) pre-failure, and (b) post-failure.
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Table 3 Test results of scan layers of sandstone specimen No. 10 Scan no.
1 2 3 4 5 6 7 8 9
Scan layer 1
Scan layer 2
Scan layer 3
Local zone
CT value
RMS*
CT value
RMS*
CT value
RMS*
CT value
RMS*
2012.5 2013.4 2014.9 2015.1 2014.4 2014.2 2013.9 2012.2 1766.4
47.83 47.18 46.97 47.89 47.86 48.28 48.53 48.28 526.46
2031.6 2033.5 2035.4 2036.4 2037.4 2037.9 2036.0 2035.7 1959.4
48.26 46.92 48.67 47.69 49.18 48.23 49.53 49.01 554.91
2013.4 2016.0 2016.3 2016.5 2017.3 2016.4 2016.5 2015.4 1787.1
49.57 49.90 49.21 48.26 49.40 48.23 49.00 48.81 508.64
2003.1 2003.3 2008.1 2005.4 2001.3 1995.7 1992.1 1985.9 1334.9
48.52 49.65 47.04 43.54 44.55 47.76 45.97 48.59 794.1
*RMS: Root mean square.
(5)
(6)
(7)
(8)
(9)
local area of the 1st scan layer, however, the CT value begins to decrease. When the stress difference reaches 112.28 MPa (fifth scanning, Fig. 4e), the CT value of the first scan layer begins to decrease. Micro-cracks emerge on the edge of the local area image. The CT values of the 2nd and 3rd scan layers, however, are increasing. This means that different layers of the same specimen have different damage evolution characteristics, i.e. the damage evolution is inhomogeneous. When the stress difference reaches 124.67 MPa (6th scanning, Fig. 4f), the image clearly shows that the cracks in the 1st scan layer have begun to expand; meanwhile, the CT value of the 2nd scan layer continues to increase and the CT value of the 3rd scan layer begins to decrease. This further indicates that even at the same stress state, different layers of the rock specimen have different damage evolution characteristics, and that the internal damage evolution has its own complexity. When the stress difference reaches 130.60 MPa (7th scanning, Fig. 4g), the CT values of each scan layer are decreasing, and it can be seen from the 1st scan layer image that cracks are almost connected. This is the fastest stage of the internal damage evolution of the sandstone and serves as the precursor to rock specimen breakage. When the stress difference reaches 136.07 MPa (8th scanning, Fig. 4h), the main cracks are connected and the crack widths increase. When the stress difference reaches 138.35 MPa, i.e. at the peak load, the rock specimen abruptly collapses. The CT scanning at the peak is impossible due to the swift stress decrease. The 9th scanning (Fig. 4i) is conducted when the stress difference in unloading is 2.87 MPa. It can be seen from the image and plane sheet that the rock specimen has already collapsed and that the expansion direction of the main crack is almost in coincidence with the direction of s1 :
The above-mentioned results have indicated that clear images of sandstone material subjected to different loads from compression of micro-cavitiesemergence of micro-cracks-bifurcation-developmentfracture-collapse-unloading can be observed. In order to investigate the damage law of crack initiation, its bifurcation and development in the main crack region, the 1st scan layer of No. 10 rock specimen, which contains the main crack area, is taken for detailed analysis (elliptical area in Fig. 5). It can be seen from the analysis of the last crack emergence and development area (Table 3) that the initial CT value of the area is 2003.1, which is less by 16.07 than the average CT value of the specimen, 2019.17. This means that the density of the area before loading is lower than the average density of the specimen and leads to the emergence of the first main crack area. In the interval of s1 s3 from 50.42 to 136.07 MPa, the CT value of local zone decreases by 22.2; in the same interval, the average CT value of the sandstone specimen decreases by 1.1. The decrease of the CT value in this area is about 20 times lower than that of the whole specimen. This indicates that the final collapse of rock material is dependent on single or multiple main cracks. This region has more initial cavities (damage), i.e. non-homogeneous structures, and is apt to failure. This is the localized phenomenon of rock damage propagation as seen in CT images.
4. Determination of the damage variable The CT value provides an effective means of quantitative analysis of rock damage evolution. Since there is a proportional relationship between the CT value and rock material density, the distribution of the CT values reflects the distribution of rock damage density. Let H be the CT value. H is proportional to the X-ray absorbing coefficient of the rock material. Hence, H ¼ km
ð1Þ
ARTICLE IN PRESS X.-T. Feng et al. / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 181–192 160 140
120 100 80 60 40 20 0
120 100 80 60 40 20 0 0.0
σ1-σ3 (MPa)
160 140
0.0MPa
0.0
σ1-σ3 (MPa)
(a)
1.0 2.0 ε (× 10-2)
3.0
(b)
160 140
160 140
120 100 80 60 40 20 0 0.0
120 100 80 60 40 20 0 0.0
(c)
σ1-σ3 (MPa)
σ1-σ3 (MPa)
186
50.42MPa
1.0 2.0 ε (× 10-2)
3.0
(d)
1.0
2.0
σ1-σ3 (MPa) 3.0
120 100 80 60 40 20 0 0.0
(g)
120 100 80 60 40 20 0 0.0
87.28MPa
1.0 2.0 ε (× 10-2)
160 140 120 100 80 60 40 20 0
3.0
124.67MPa
1.0
2.0
3.0
ε (× 10-2)
(f)
130.6MPa
3.0
136.07MPa
σ1-σ3 (MPa)
σ1-σ3 (MPa)
160 140 σ1-σ3 (MPa)
112.28MPa
ε (× 10-2)
(e)
1.0 2.0 ε (× 10-2)
160 140
160 140 120 100 80 60 40 20 0 0.0
14.04MPa
1.0 2.0 ε (× 10-2)
3.0
(h)
0.0
1.0 2.0 ε (× 10-2)
3.0
σ1-σ3 (MPa)
160 140
(i)
120 100 80 60 40 20 0 0.0
2.87MPa
1.0 2.0 ε (× 10-2)
3.0
Fig. 4. (a–i) CT images during increased axial loading in triaxial compression of the first scanned layer of No. 10 sandstone specimen. Images are taken at convenient loading intervals.
where m is the absorbing coefficient of X-rays for rock material, and k is a constant. Assume that all the micro-cracks in the rock material are filled with water. Then
m m ¼ mm r ¼ ð1 nÞrr mm r þ nrw mw ;
ð2Þ
where rr and rw are matrix material density of rock and pore water density, respectively, and n is the porosity.
ARTICLE IN PRESS X.-T. Feng et al. / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 181–192
From Eq. (2) we have m rr mm r n¼ : rw mm r mm r w r
ð3Þ
The initial CT value H0 ¼ ð1 n0 ÞHr þ n0 Hw can be obtained from Eqs. (1) and (2). Hence Hr ¼
From Eqs. (1) and (3) we have Hr H ; n¼ Hr Hw
ð4Þ
where Hr and Hw are the CT values of rock matrix material and pore water, respectively. Because cracks are fully filled with water, the density in the distinguishable element can be expressed as r ¼ ð1 nÞrr þ nrw By substituting Eq. (4) in Eq. (5) we have H Hw Hr H r¼ r þ r : Hr Hw r Hr Hw w
187
H 0 n0 H w : 1 n0
ð8Þ
By substituting Eqs. (7) and (8) in Eq. (6) we have r¼
1 ½ðH Hw Þr0 ðH H0 Þrw : H0 Hw
ð9Þ
ð5Þ
By mathematical modeling of the CT value, the following expression for the damage variable is given in [18]:
ð6Þ
D¼
Let the initial density of rock be r0 and the initial porosity of rock n0 : Then, from Eq. (5) we have r n0 rw rr ¼ 0 : ð7Þ 1 n0
1 Dr ; m20 r0
ð10Þ
where D is rock damage variable, m0 is the space resolution of CT machine and Dr is the change in density during the damage evolution process of rock material, i.e. Dr ¼ r r0 : Thus, we have Dr ¼
1 ðH H0 Þðr0 rw Þ: H0 Hw
ð11Þ
By substituting Eq. (11) into Eq. (10), we have D¼
Fig. 5. Partial CT image of the 1st scan layer of sandstone specimen No. 10.
1 ðH H0 Þðr0 rw Þ: m20 ðH0 Hw Þr0
ð12Þ
Eq. (12) is a newly defined damage variable based on the chemical corrosive influence and CT value definition. It takes into account the pore water influence upon the rock damage evolution. In the meantime, the pore water density rw of different chemical solutions, the initial rock density r0 and the CT value Hw may cause different changes to the rock damage variable D: In order to facilitate the analysis, for sandstone soaked in NaCl solution of pH 7 and concentration of the following values can be approximations taken: 0.01 M, Hw ¼ 1000; sw ¼ 1 t=m3 ; m0 ¼ 0:35; r0 ¼ 2:7 t/m3. Then the values of the damage variable D are listed in Table 4.
Table 4 Stress, strain, average CT value and damage variable of sandstone specimen No. 10 Scan layer no.
s1 s3
e1 ( 102)
Average CT value
Load (%)
D
Note
1 2 3 4 5 6 7 8 9
0.0 14.04 50.42 87.28 112.28 124.67 130.60 136.07 2.87
0.0 0.41 1.10 1.73 2.12 2.34 2.44 2.55 4.70
2019.17 2020.97 2022.20 2022.67 2023.03 2022.83 2022.13 2021.10 1837.63
10 36 63 81 90 94 98
0.0 0.00306 0.00516 0.00596 0.00657 0.00623 0.00504 0.00329 0.3091
Initial Compression Compression Compression Compression Cracking Propagation Propagation Collapse
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5. Discussion Rock material is a complex solid medium. It has many initial internal micro-cracks especially between the mineral particles. Therefore, the rock material in engineering is unavoidably subject to corrosive action of permeated water in the initial micro-cracks, as well as chemical solution that may be present. It thus weakens the connection between mineral particles and corrodes the mineral particles, eventually leading to a change in the micro-structure and mechanical properties of rock. Consequently, the long-term stability characteristics will become more complex. Research on the damage mechanism under chemical corrosion can more correctly provide important fundamental technical parameters for appraisal and calculation of rock engineering stability related to dam foundations, slopes, tunnels, etc. Therefore, in-depth research on rock crack and fracture characteristics subjected to water chemical corrosion is a new issue facing rock mechanics research. 5.1. Damage induced by the water chemical corrosion process It can be seen from Table 3 for sandstone specimen No. 10 that the CT values reach then maximum when the loads are about 63%, 90%, 81%, 36%, 81% of peak load for the 1st scan layer, the 2nd scan layer, the 3rd scan layer, local region (dangerous area), and all three scan layer, respectively, and then begin to decrease. The CT values have large drops (by about 10–30%) and damage variable decreases by about 48 times when the failure of the sandstone specimen approaches. The damage variable gets a similar relationship with the average CT value for all three scan layers (Table 4). Accordingly, the phenomena of emergence, propagation, connection and failure of the micro-cracks can be
seen in the CT image within the resolution of the technique. The large decrease of the CT values and damage variable was a precursor of rock failure. All other specimens tested have similar law. For example, for sandstone specimen No. 5, the CT values reach then maximum when the loads are about 65%, 72%, 77%, 82% of peak load for the 1st scan layer, the 2nd scan layer, the 3rd scan layer, and local region (dangerous area), respectively, and then begin to decrease (Table 5 and Fig. 6). The average CT value for all three scan layers reaches its maximum when load is 65% of peak load, the damage variable gets its maximum at the same load level (Table 6). Then the CT values decreases by about 10–30% and damage variable decrease by about 39 times when the failure of the sandstone specimen occurs. In some cases, the CT values (i.e. density) fluctuate locally (Fig. 6 and Table 5). These indicate that characteristics of damage localization due to the inhomogeneous distribution of micro-cracks. There is again a close correspondence between the large decrease in the CT values and damage variable and the approach of the rock fracture. The results, indicated by CT values and damage variable are consistent with the conclusion based on the temporal fractals [20] and the spatial fractals [21,22]. Therefore, the CT value (equivalent to rock density at the scan layer) and damage variable are useful parameters in describing the damage evolution process of rock. It can be seen in Fig. 7 that in the triaxial loading condition, no matter what kind of water chemical corrosion the specimen is subjected to, the main failure forms are similar, i.e. the main failure surface is almost parallel to the main loading stress direction. Moreover, the so-formed main failure surface is not a plane but a curved surface and the material on the two sides of the main crack produces dilatancy due to sliding on the main failure surface.
Table 5 Test results of scan layers of sandstone specimen No. 5 Scan no.
1 2 3 4 5 6 7 8 9 10 11
Scan layer 1
Scan layer 2
Scan layer 3
Local zone
CT value
RMS*
CT value
RMS*
CT value
RMS*
CT value
RMS*
1916.1 1917.6 1920.0 1923.6 1920.3 1920.5 1920.4 1920.2 1916.9 1917.3 1604.6
45.11 44.98 44.18 43.41 44.65 45.14 45.56 45.27 43.04 42.34 446.08
1923.1 1921.8 1923.9 1924.5 1925.2 1924.2 1924.8 1925.2 1924.4 1923.1 1692.6
43.64 44.17 44.42 44.98 44.77 45.29 45.05 45.14 45.55 45.25 468.63
1945.64 1953.2 1954.5 1955.7 1956.0 1956.1 1955.6 1955.1 1955.3 1955.9 1830.1
44.25 44.00 45.02 47.49 46.52 45.68 44.79 45.18 44.65 43.49 313.64
1942.5 1945.4 1947.2 1951.0 1951.0 1951.1 1953.5 1951.2 1932.3 1924.3 1282.1
45.01 45.17 44.67 46.36 47.13 47.26 47.70 47.90 39.70 40.44 450.82
*RMS: Root mean square.
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5.2. Effect of water chemical corrosion on the triaxial compressive strength of sandstone
189
The pH value of the chemical solution thus has a great influence on the sandstone strength (Fig. 9). The stronger the acidity (pHo7) or causticity (pH>7), the stronger the corrosive effect on rock microfracturing evolution. When the chemical solution is of pH 7 (neutral) the rock strength has about 10% decrease in comparison with that in the natural state. For a NaCl chemical solution of 0.01 M, the peak stress of rock specimen in acid (pH 2) solution has about 30% decrease relatively in comparison with that in neutral (pH 7) solution, while in caustic (pH 12) solution, it has about 11% decrease in comparison with that in the neutral (pH 7) solution.
The peak stress s1 for sandstone in the natural state is about 160 MPa, while for those corroded in distilled water (pH 7) and Yellow River water (pH 8.3) the values are about 151 and 120 MPa, respectively. The decreases are about 5% and 26%, respectively. Under the influence of solutions NaCl, CaCl2 and NaHCO3 with 0.01 M and pH 9, the peak stresses are about 136, 112, and 153 MPa, respectively, the decreases are about 15%, 30%, and 4.4%, respectively, in comparison with those in the natural state (as shown in Fig. 8).
2100
2100
1700
CT value
CT value
1900
1500 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1300 1100 900 0.0
1.0
2.0 3.0 4.0 Strain ε (× 0.01)
(a)
2000 Scan layer 1 1900
Scan layer 3 Scan layer 5
5.0
1800 0.0
6.0
1.0
(b)
2.0 3.0 Strain ε (× 0.01)
4.0
5.0
2000
2100 2000
1950
1900 1800
CT value
CT value
2050
1900 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1850 1800 1750 0.0
1.0
2.0 3.0 Strain ε (× 0.01)
(c)
1700 1600 1500
Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1400 1300 4.0
5.0
0
1
(d)
2000
2200
1980
2000
2 3 Strain ε (× 0.01)
4
5
1940 1920
1800 1600
1900
Scan layer 1
1880
Scan layer 2
1400
1860
Scan layer 3 Local area with large CT value
1200
1840 1820 0.0
(e)
CT value
CT value
1960
Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1000
1.0
2.0
3.0 4.0 Strain ε (× 0.01)
5.0
6.0
0.0
(f)
1.0
2.0 3.0 Strain ε (× 0.01)
4.0
5.0
Fig. 6. Change of CT value during damage evolution of sandstone specimens saturated in different water solutions or air: (a) in air, (b) in distilled water, (c) in Yellow River water, (d) in NaCl, pH 7, 0.01 M, (e) in NaCl, pH 2, 0.01 M, (f) in NaCl, pH 9, 0.01 M, (g) in NaCl, pH 12, 0.01 M, (h) in CaCl2, pH 9, 0.01 M, and (i) in NaHCO3, pH 9, 0.01 M.
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190
2000
2200
1800
2000
1600
Scan layer 1 Scan layer 2 Scan layer 3 Local area withl arge CT value
1400 1200 1000 0.0
CT value
CT value
2200
1.0
(g)
2.0 3.0 4.0 Strain ε (× 0.01)
5.0
1800 1600
Scan layer 1
1400
Scan layer 2
1200
Scan layer 3 Local area with large CT value
1000 0.0
6.0
1.0
(h)
2.0 3.0 4.0 Strain ε (× 0.01)
5.0
6.0
2100
CT value
2000 1900 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1800 1700 1600 0.0
0.5
1.0
(i)
1.5 2.0 Strain ε (× 0.01)
2.5
3.0
Fig. 6 (continued). Table 6 Stress, strain, average CT value and damage variable of sandstone specimen No. 5 Scan layer no.
s1 s3
e1 ( 102)
Average CT value
RMS*
Load (%)
D
Note
1 2 3 4 5 6 7 8 9 10 11
0.0 17.32 64.07 82.45 91.82 97.48 103.90 113.51 120.45 123.35 6.13
0.0 0.48 1.27 1.71 1.88 1.99 2.08 2.26 2.39 2.46 5.08
1928.27 1930.87 1932.80 1934.60 1933.83 1933.60 1933.60 1933.50 1932.20 1932.10 1709.10
44.33 44.38 44.54 45.29 45.31 45.37 45.13 45.18 44.38 43.69 409.45
13.7 50.6 65.1 72.5 77.0 82.1 89.7 95.1 97.4
0.0 0.00456 0.00795 0.01036 0.00976 0.00936 0.00936 0.00918 0.00690 0.00672 0.3847
Initial Compression Compression Compression Cracking Cracking Cracking Cracking Propagation Propagation Collapse
*RMS: Root mean square.
This kind of influence law is in general coincident with that of the uniaxial case [19]. 6. Conclusions The CT technique is an effective method for studying the rock damage evolution process. From the CT experiments described here we develop the following conclusions: (1) The CT technique has been successfully used in loading experiments of triaxial damage evolution
process of sandstone under chemical corrosion for the first time. (2) The phenomena of the inhomogeneous distribution of the internal micro-cracks as well as the different damage evolution characteristics at different layers in the specimens can be observed at a given stress state. The results indicate the complexity of the damage evolution process in intact sandstone. (3) The corrosive influence of different chemical solutions with different pH values on the mechanical properties of Xiaolangdi sandstone is clear:
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
191
(i) Fig. 7. Final fracture image of triaxial compressive sandstone specimens saturated in different water solutions or air: (a) in pH 7, NaCl, (b) in pH 9, NaCl, (c) in pH 12, NaCl, (d) in air, (e) in Yellow River water, (f) in distilled water, (g) in pH 9, CaCl2, (h) in pH 2, NaCl, and (i) in pH 9, NaHCO3.
160 140 σ1-σ3 (MPa)
Peak stress (MPa)
180
180 160 140 120 100 80 60 40 20 0
120 100 Air Distilled water Yellow River water 0.01M NaCl 0.01M CaCl2 0.01M NaHCO3
80 60 40 20
Natural state
Distilled water
Yellow River water
NaCl
CaCl2
NaHCO3
Fig. 8. Influence of water solution with different constituents on triaxial compressive strength of sandstone specimens.
0 0
1
2
3
4
5
6
7 pH
8
9
10
11
12
13
14
Fig. 9. Influence of different pH values on triaxial compressive strength of sandstone specimens.
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chemical corrosion changes the mechanical properties of the rock. In the meantime, the other factors accelerating rock failure, such as rock genesis, structure, micro-cracks, water-absorbability, adhesive property, mineral constituents, as well as in the homogeneity variation of physical properties, are pending further research. (4) The quantitative analysis of the internal rock damage evolution process is also possible via the CT value and a damage variable has been proposed, Eq. (12).
Acknowledgements Financial support from the Special Funds for Major State Basic Research Project under Grant No. 2002CB412704 and the National Nature Science Foundation of China under Grant No. 10072073 are gratefully acknowledged. The authors would like to acknowledge to Professors J.A. Hudson and Yongjia Wang’s helpful suggestions to improve the manuscript, and Mr. Yibin Pu and Professor Wei Ma for their help in real-time CT experiment. References [1] Lajtai EZ, Schmidtke RH, Bielus LP. The effect of water on the time-dependent deformation and fracture of a granite. Int J Rock Mech Min Sci Geomech Abstr 1987;24(4):247–55. [2] Charles RJ, The strength of silicate glasses and some crystalline oxides. In: Fracture, Proceedings of International Conference on the Atomic Mechanisms of Fracture, MIT Press, Cambridge, MA, 1959. p. 225–49. [3] Westood ARC, Macmillan NH. Environmental-sensitive hardness of nonmetals. In: The science of hardness testing. Celveland, OH: ASTM, 1973. p. 377–417. [4] Seto M, Vutukuri VS, Nag DK, Katsuyama K. The effect of chemical additives on strength of rock. In: Proceedings of Civil Engineering 1998; Japan, No. 603/III-44: p. 157–66. [5] Swolfs HS, Chemical effects of pore fluids on rock properties. In: Cook TD, editor. Underground Waste Management and Environment Implications, 1972. p. 224–34. [6] Karfakis MG, Askram M. Effects of chemical solutions on rock fracturing. Int J Rock Mech Min Sci Geomech Abstr 1993;37(7):1253–9.
[7] Engelmann WH, Watson PJ, Tuzinski PA, Pahlman JE. Zeta potential control for simultaneous enhancement of penetration rates and bit life in rock drilling. US Bureau of Mines RI9103 1987. [8] Geilikman MB, Dusseault MB. Mechano-chemical corrosion of shales in borehole-mud contact. In: Rock Mechanics Tools and Techniques. vol. 1, Rotterdam: A.A. Balkema, 1996. p. 959–64. [9] Bottai A, Cigni U. Completion techniques in deep geothermal drilling. Geomechanica 1985;14(2–3):309–14. [10] Wilson G. How to reduce drillstring fatigue failure in a corrosive environment. World Oil 1998;219(10):40–2. [11] Ishido T, Mizutani H. Experimental and theoretical basis of electrokinetic phenomena in rock-water systems and its applications to geophysics. J Geophys Res 1984;86:1763–75. [12] Dunning J, Douglas B, Millar M, McDonald S. The role of the chemical environment in frictional deformation: stress corrosion cracking and comminution. Pageoph 1994;143(1/2/3): 151–78. [13] Feucht LJ, Logan JM. Effects of chemically active solutions on shearing behavior of a sandstone. Tectonophysics 1990;175: 159–76. [14] Rebinder PA, Schreiner LA, Zhigach KF. Hardness reducers in drilling: a physico-chemical method of facilitating mechanical destruction of rocks during drilling. Akad Naunk, USSR, Moscow, 1984 (Tansl. By CSIRO, Melboune, Australia). [15] Lin Jinaming. Study on damage mechanics of jointed rock masses and its time dependency, Ph.D. thesis. Tongji University, Shanghai, 1992. p. 55–9. [16] Kawakata H, Cho A, Kiyama T, Yanagidani T, Kusunose K, Shimada M. Three-dimensional observations of faulting process in Westerly granite under uniaxial and triaxial conditions by Xray CT scan. Tectonophysics 1999;313:293–305. [17] Ge Xiuren, Ren Jianxi, Pu Yibin, Ma Wei, Yuanlin Zhu. A realtime CT triaxial testing study of meso-damage evolution law of coal. Chin J Rock Mech Eng 1999;18(5):497–502. [18] Yang Gengshe, Xie Dingyi, Zhang Changqing. Quantitative analysis of CT distribution law of rock damage. Chin J Rock Mech Eng 1998;17(3):279–85. [19] Feng Xia-Ting, Chen Si-li, Li Shao-jun. Effects of water chemistry on micro-cracking and compressive strength of granite. Int J Rock Mech Min Sci 2001;38(4):557–68. [20] Feng X-T, Seto M. Fractal structure of the time distribution of microfracturing in rocks. Geophys J Int 1999;136:275–85. [21] Main IG. Damage mechanics with long-range interactioncorrelation between the seismic b-value and the fractal 2-point correlation dimension. Geophys J Int 1996;111:531–41. [22] Sammonds PR, Meredith PG, Main IG. Role of pore fluid in the generation of seismic precursors to shear fracture. Nature 1992;359:228–30.
International Journal of Rock Mechanics & Mining Sciences 41 (2004) 181–192
Real-time computerized tomography (CT) experiments on sandstone damage evolution during triaxial compression with chemical corrosion Xia-Ting Fenga,b,*, Sili Chenb,c, Hui Zhoua a
Key Laboratory of Rock and Soil Mechanics, Institute of Rock and Soil Mechanics, the Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China b College of Resources and Civil Engineering, Northeastern University, Shenyang 110006, People’s Republic of China c Department of Civil Engineering, Shenyang University of Technology, Shenyang 110023, People’s Republic of China Accepted 3 April 2003
Abstract The computerized tomography (CT) images and CT values for the process of compression, micro-cracking, and dilation up to the failure of sandstone specimens under different loading levels have been obtained using the real-time CT technique for triaxial loading of sandstone subjected to chemical corrosion. Clear CT images and CT value of the stages from compression of microcavities-emergence of micro-cracks-bifurcation-development-fracture-collapse-unloading can be observed. The CT value, equivalent to rock density at the CT scan layer, is the most important parameter describing the damage evolution process of rock. The paper also presents results of the corrosive influence of chemical solutions with different pH values and ionic concentrations on the sandstone strength. Stronger acidity (pHo7) or causticity (pH>7) has a stronger effect on the rock micro-fracturing evolution. The mechanism of damage evolution of sandstone is analyzed and a damage model based on the chemical corrosive influence and CT values is proposed. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction Research on rock strength and its failure characteristics while subjected to chemical corrosion is one of the fundamental factors in nuclear waste disposal, geothermal exploration, oil drilling, seismic aspects, toxic material disposal, long-term stability evaluation of rock engineering structures, etc. It is also one of the frontiers of rock mechanics research. The reason is because underground water exists almost everywhere. The chemical reaction of corrosive matter leads to rock strength decrease, failure acceleration and finally to instability [1–14]. Investigating the chemical influence on crack initial and propagation in geological processes may provide valuable fundamental data for long-term stability of rock cavern, seismic *Corresponding author. Key Laboratory of Rock and Soil Mechanics, Institute of Rock and Soil Mechanics, the Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China. Tel.: +86-27-8719-8913; fax: +86-27-8719-7386. E-mail address: [email protected] (X.-T. Feng). 1365-1609/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S1365-1609(03)00059-5
mechanisms and sub-critical crack propagation. For instance, if water contains a certain ionic concentration of NaCl, CaCl2, or Na2SO4, then the shear friction coefficient of sandstone will depend on the ionic concentration and pH value [12] and can decrease to 20–46% [13]. On the other hand, drilling efficiency may be increased by utilizing the chemical reaction. Research has shown that in wet conditions the fracture toughness will be lower than in dry conditions and the crack propagation velocity will be increased [1,2]. The x potential (the potential where distance from interface of solid and liquid is chemisorbed ions of thickness d [4]) is relevant to the crack propagation and drilling efficiency [3,4,7–10]. When the x potential is equal to zero, the rock material becomes more brittle and more sensitive to the environment, and has the lowest compressive strength; in addition, the sub-critical cracking velocity will increase by more than one order of magnitude [11]. Hence, if a chemical solution with zero x potential is put into the drilling solution, the drillability and breakability of rock will be enhanced.
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chemical corrosion for the first time by using the realtime CT testing technique. CT images and CT values for sandstone cross-sections under different loading levels were obtained. The mechanism of damage increase with chemical corrosion was analyzed and a chemical damage variable is proposed.
Research so far has been mainly concentrated on the influences of the chemical environment on the rock strength, crack velocity, fracture toughness, breakage work ratio, shear property, strain energy index, etc. [1–15]. There has been little research on the internal damage evolution process of rock under chemical corrosion. The corrosive fracture mechanism in a chemical environment has not been properly investigated. The constitutive relationship of coupled chemical and stress corrosion has not yet been properly established. Hence, effective modeling and behavior prediction are impossible. Mechanical experiments are an efficient means of exploring the evolution law of internal damage during rock breakage. The crack distribution on a rock surface in a certain stress state can be observed by optical or electronic microscope [15,19]. Furthermore, the crack distribution on an internal cross-section under a certain stress state can be established by using the computerized tomography (CT) technique [16,17]. Ref. [16] describes obtaining CT images by scanning the damaged rock specimen at a single given stage. That procedure cannot obtain real-time CT images at different stress stages during the full process of rock damage evolution. However, the method described in Ref. [17] can obtain real-time results, which are required to study the realtime process of rock damage evolution, but these were conducted without consideration of the chemical environment and water influences. This paper reports experimental research on the damage evolution properties of sandstone subjected to
2. Experiments 2.1. Rock source and experimental motivation The rock was lime-cemented sandstone taken from the dam foundation of Xianglangdi hydraulic project on the Yellow River, 40 km far from Luoyang City in Henan province, China. It is 130 km upstream Sanmenxia reservoir and 115 km downstream Huayuankou, Zhenzhou city (see Fig. 1). The main function of the project is to control flooding, with accessory functions to reduce silt, to irrigate, and to generate electricity. The project consists of a dam, flood discharge building, and generating electricity system. The dam, 1667 m length at the top and 154 m height, is a clay rockfill dam. There are ten water inlets, nine flood discharges and sand draining tunnels, a normal outflow tunnel, and three plunge pools arranged consecutively. The electricity generating system consists of six water-in tunnels, an underground power house, a main transformation house, a shiplock room, and three water-out tunnels. The total capacity of the three generator sets is 18 million kW. The project was completed on 31 December 2001.
Harbin
Xiaolangdi dam
Urumqi
Shenyang Hohhot
Yel
Rive r
Beijing
w lo
Yellow
Lanzhou
Ya ng zt e
Ri ve r
182
Xi'an
Nanjing
r ve Ri
Shanghai Wuhan
Chengdu
Lhasa Chengqing
Yan
g
te
er Riv z
Taiwan Kunming
Guangzhou Nanning
Haikou
Fig. 1. Location of Xiaolangdi Reservoir on the Yellow River in China.
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Table 1 shows quality statistics of the underground water in the dam area. It indicates that the water in this area is alkaline. The question raised is whether the project conditions are safe. In order to answer these questions, it is imperative to investigate the long-term impact of alkalinity on the rock strength and its fracture characteristics. Therefore, real-time full process CT scanning tests on sandstone subjected to water chemical corrosion have been conducted. The results are compared with tests without water chemical corrosion.
pH 2 is to attain a greater chemical corrosion effect separately from the time effect (a pH 7, water solution has a long-term corrosive effect on rock mass). In addition, the specimen is vacuumized and dried for 6 h at 105 C to induce a greater chemical corrosion effect by increasing the porosity of the specimen. The specimen thus processed was immersed for 200 days in different chemical solutions, distilled water or dam area water of Xiaolangdi, as listed in Table 2, until saturated. One specimen was tested for each set of conditions to establish the trends.
2.2. Rock composition and specimen preparation
2.3. Testing device and process
The sandstone consists of quartzitic sand particles with cement of calcspar. The sand particles have poor sphericity. The size of particles is about 0.1 mm. There is much cement between the particles, consisting mainly of calcspar and hydrous mica. The mineral components of sandstone are 75% quartz, 18% calcite, 2% hydrous mica, 1% plagioclase, less than 0.1% detritus (silica), 0.1% muscovite, 3% limonite, less than 0.1% tourmaline, etc. The texture image of the rock specimen is provided in Fig. 2. The rock specimen is a 54 108 mm2 cylinder. According to the chemical ion and acidity of the underground water in the dam area, as listed in Table 1, different chemical solutions were prepared with the main chemical ions (Table 2). The reason for the preparation of chemical solutions with pH 12 and
The tests have been conducted at the CT laboratory, Cold and Arid Region Environmental and Engineering Research Institute, Chinese Academy of Sciences. The X-ray CT scanner, SIEMENS SOMATOM plus and triaxial loading system designed specially for the CT scanner were used. The dimensions of the triaxial loading system are 240 mm 1000 mm, the maximum designed axial compression is 400 kN with a maximum confining pressure of 20 MPa and a maximum axial stroke of 40 mm. It can be used to measure axial stress and deformation. Collapse tests are possible for rock specimens processed in the internationally standard cylinder form. The specimen dimensions are (f) 50 mm and 100 mm (length). The space resolution of the CT machine is 0.35 mm 0.35 mm and the minimum recognizable volume is 0.1225 mm3 (with thickness 1 mm). Relative density resolution is 0.3% Hu. The sandstone specimen is taken out of the solution before the test and put into the triaxial pressure cell, which is in turn put on the CT bed horizontally (the CT bed can be moved vertically or horizontally). Initial positioning and CT scanning of the specimen is needed. There are altogether three to five layers. The confining pressure is gradually increased up to 5 MPa and then fixed. Then, the axial stress is applied with the given loading rate (the average loading rate is 1.3 MPa/min) until the specimen breaks. Real-time CT scanning for
Table 1 Underground water quality statistics in dam area (in mg/l) Place
PH
Ca2+
Na+
Cl
SO2 4
HCO 3
N. bank River bed S. bank
7.4 7.7
61.9 57.7 83.6
15.4 17.7 24.3
9.7 9.7
20.2 12.3 23.3
85.0 82.5 82.0
Table 2 Specimen Nos. soaked with different water solutions or air
Fig. 2. SEM photomicrograph of sandstone obtained under orthogonal light.
No.
Water solution
pH value
Ionic concentration (M)
1 2 3 4 5 6 7 8 9 10
Distilled water NaCl NaCl NaCl NaCl CaCl2 NaHCO3 Yellow river water Air NaCl
7.0 7 9 2 12 9 9 8.3
0.01 0.01 0.01 0.01 0.01 0.01
7
0.01
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selected cross-sections has been conducted for different loading states. The scanning thickness is 3 mm.
3. Test results and analysis 3.1. Definition of the CT value According to Professor Hounsfield, one of the inventors of the CT machine, the CT value Hrm is defined by Hrm ¼ 1000
m mm r mw ; mm w
ð1Þ
m where mm r and mw are mass absorbing coefficients for rock matrix material and pore water, respectively. The unit name of the CT value is Hu (Hounsfield Unit), and 1000 is the scaling factor of Hu. According to the definition, the CT value is 1000 Hu for air and 0 Hu for pure water. The CT value of a material essentially reflects its density, i.e. the higher the CT value of the material, the higher its density. One may define a relative percentage of the CT value, i.e. ðCTi CT0 =CT0 Þ 100% where CT0 is the initial CT value and CTi is the CT value for the ith loading level.
3.2. Analysis of damage development for sandstone
(1) Initial scanning (1st scanning, Fig. 4a) is made for each layer before loading. The CT values, their variations and internal images are different. This means that the initial internal damage for Xiaolangdi sandstone varies and manifests the non-homogeneity of the internal micro-crack distribution. (2) When the stress difference ðs1 s3 Þ reaches 14.04 MPa (2nd scanning, initial damage, Fig. 4b), the CT values of each layer are increasing. This means that the internal micro-cracks and cavities are closing and a curved segment appears on the stress–strain curve. The local darkness of each layer can be observed on the CT images. (3) When the stress difference ðs1 s3 Þ reaches 50.42 MPa (3rd scanning, rock material compressed, density increased, Fig. 4c), the CT values of each layer are increasing, except for the local part of the first scanned layer (Fig. 5), where the CT value has the maximum value and the images of each layer have little change. (4) When the stress difference reaches 87.28 MPa (4th scanning, Fig. 4d), the CT value of the 1st scan layer reaches its maximum value and a small amount of dilatancy appears. The 2nd and 3rd scan layers have a slight increase. The stress–strain curve approximates to a straight line. The rock specimen is in the elastic compressive stage. In the
1
30mm
24mm
The damage evolution law is analyzed for No. 10 specimen in Table 2 as an example. Fig. 3(a) and (b) are the plane CT sheets illustrating the specimen before and after breakage. The specimen was scanned at the upper,
middle, and lower three layers along the lateral direction for every loading level. The sandstone damage evolution is analyzed according to the CT values and root square variation of each layer listed in Table 3 as well as the CT images of the first scanned layer of specimen No. 10 in different stress states (altogether 9 scans) as shown in Fig. 4(a)–(i).
30mm
2
24mm
3
(a)
(b)
Fig. 3. CT images pre/post-failure of sandstone specimen: (a) pre-failure, and (b) post-failure.
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Table 3 Test results of scan layers of sandstone specimen No. 10 Scan no.
1 2 3 4 5 6 7 8 9
Scan layer 1
Scan layer 2
Scan layer 3
Local zone
CT value
RMS*
CT value
RMS*
CT value
RMS*
CT value
RMS*
2012.5 2013.4 2014.9 2015.1 2014.4 2014.2 2013.9 2012.2 1766.4
47.83 47.18 46.97 47.89 47.86 48.28 48.53 48.28 526.46
2031.6 2033.5 2035.4 2036.4 2037.4 2037.9 2036.0 2035.7 1959.4
48.26 46.92 48.67 47.69 49.18 48.23 49.53 49.01 554.91
2013.4 2016.0 2016.3 2016.5 2017.3 2016.4 2016.5 2015.4 1787.1
49.57 49.90 49.21 48.26 49.40 48.23 49.00 48.81 508.64
2003.1 2003.3 2008.1 2005.4 2001.3 1995.7 1992.1 1985.9 1334.9
48.52 49.65 47.04 43.54 44.55 47.76 45.97 48.59 794.1
*RMS: Root mean square.
(5)
(6)
(7)
(8)
(9)
local area of the 1st scan layer, however, the CT value begins to decrease. When the stress difference reaches 112.28 MPa (fifth scanning, Fig. 4e), the CT value of the first scan layer begins to decrease. Micro-cracks emerge on the edge of the local area image. The CT values of the 2nd and 3rd scan layers, however, are increasing. This means that different layers of the same specimen have different damage evolution characteristics, i.e. the damage evolution is inhomogeneous. When the stress difference reaches 124.67 MPa (6th scanning, Fig. 4f), the image clearly shows that the cracks in the 1st scan layer have begun to expand; meanwhile, the CT value of the 2nd scan layer continues to increase and the CT value of the 3rd scan layer begins to decrease. This further indicates that even at the same stress state, different layers of the rock specimen have different damage evolution characteristics, and that the internal damage evolution has its own complexity. When the stress difference reaches 130.60 MPa (7th scanning, Fig. 4g), the CT values of each scan layer are decreasing, and it can be seen from the 1st scan layer image that cracks are almost connected. This is the fastest stage of the internal damage evolution of the sandstone and serves as the precursor to rock specimen breakage. When the stress difference reaches 136.07 MPa (8th scanning, Fig. 4h), the main cracks are connected and the crack widths increase. When the stress difference reaches 138.35 MPa, i.e. at the peak load, the rock specimen abruptly collapses. The CT scanning at the peak is impossible due to the swift stress decrease. The 9th scanning (Fig. 4i) is conducted when the stress difference in unloading is 2.87 MPa. It can be seen from the image and plane sheet that the rock specimen has already collapsed and that the expansion direction of the main crack is almost in coincidence with the direction of s1 :
The above-mentioned results have indicated that clear images of sandstone material subjected to different loads from compression of micro-cavitiesemergence of micro-cracks-bifurcation-developmentfracture-collapse-unloading can be observed. In order to investigate the damage law of crack initiation, its bifurcation and development in the main crack region, the 1st scan layer of No. 10 rock specimen, which contains the main crack area, is taken for detailed analysis (elliptical area in Fig. 5). It can be seen from the analysis of the last crack emergence and development area (Table 3) that the initial CT value of the area is 2003.1, which is less by 16.07 than the average CT value of the specimen, 2019.17. This means that the density of the area before loading is lower than the average density of the specimen and leads to the emergence of the first main crack area. In the interval of s1 s3 from 50.42 to 136.07 MPa, the CT value of local zone decreases by 22.2; in the same interval, the average CT value of the sandstone specimen decreases by 1.1. The decrease of the CT value in this area is about 20 times lower than that of the whole specimen. This indicates that the final collapse of rock material is dependent on single or multiple main cracks. This region has more initial cavities (damage), i.e. non-homogeneous structures, and is apt to failure. This is the localized phenomenon of rock damage propagation as seen in CT images.
4. Determination of the damage variable The CT value provides an effective means of quantitative analysis of rock damage evolution. Since there is a proportional relationship between the CT value and rock material density, the distribution of the CT values reflects the distribution of rock damage density. Let H be the CT value. H is proportional to the X-ray absorbing coefficient of the rock material. Hence, H ¼ km
ð1Þ
ARTICLE IN PRESS X.-T. Feng et al. / International Journal of Rock Mechanics & Mining Sciences 41 (2004) 181–192 160 140
120 100 80 60 40 20 0
120 100 80 60 40 20 0 0.0
σ1-σ3 (MPa)
160 140
0.0MPa
0.0
σ1-σ3 (MPa)
(a)
1.0 2.0 ε (× 10-2)
3.0
(b)
160 140
160 140
120 100 80 60 40 20 0 0.0
120 100 80 60 40 20 0 0.0
(c)
σ1-σ3 (MPa)
σ1-σ3 (MPa)
186
50.42MPa
1.0 2.0 ε (× 10-2)
3.0
(d)
1.0
2.0
σ1-σ3 (MPa) 3.0
120 100 80 60 40 20 0 0.0
(g)
120 100 80 60 40 20 0 0.0
87.28MPa
1.0 2.0 ε (× 10-2)
160 140 120 100 80 60 40 20 0
3.0
124.67MPa
1.0
2.0
3.0
ε (× 10-2)
(f)
130.6MPa
3.0
136.07MPa
σ1-σ3 (MPa)
σ1-σ3 (MPa)
160 140 σ1-σ3 (MPa)
112.28MPa
ε (× 10-2)
(e)
1.0 2.0 ε (× 10-2)
160 140
160 140 120 100 80 60 40 20 0 0.0
14.04MPa
1.0 2.0 ε (× 10-2)
3.0
(h)
0.0
1.0 2.0 ε (× 10-2)
3.0
σ1-σ3 (MPa)
160 140
(i)
120 100 80 60 40 20 0 0.0
2.87MPa
1.0 2.0 ε (× 10-2)
3.0
Fig. 4. (a–i) CT images during increased axial loading in triaxial compression of the first scanned layer of No. 10 sandstone specimen. Images are taken at convenient loading intervals.
where m is the absorbing coefficient of X-rays for rock material, and k is a constant. Assume that all the micro-cracks in the rock material are filled with water. Then
m m ¼ mm r ¼ ð1 nÞrr mm r þ nrw mw ;
ð2Þ
where rr and rw are matrix material density of rock and pore water density, respectively, and n is the porosity.
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From Eq. (2) we have m rr mm r n¼ : rw mm r mm r w r
ð3Þ
The initial CT value H0 ¼ ð1 n0 ÞHr þ n0 Hw can be obtained from Eqs. (1) and (2). Hence Hr ¼
From Eqs. (1) and (3) we have Hr H ; n¼ Hr Hw
ð4Þ
where Hr and Hw are the CT values of rock matrix material and pore water, respectively. Because cracks are fully filled with water, the density in the distinguishable element can be expressed as r ¼ ð1 nÞrr þ nrw By substituting Eq. (4) in Eq. (5) we have H Hw Hr H r¼ r þ r : Hr Hw r Hr Hw w
187
H 0 n0 H w : 1 n0
ð8Þ
By substituting Eqs. (7) and (8) in Eq. (6) we have r¼
1 ½ðH Hw Þr0 ðH H0 Þrw : H0 Hw
ð9Þ
ð5Þ
By mathematical modeling of the CT value, the following expression for the damage variable is given in [18]:
ð6Þ
D¼
Let the initial density of rock be r0 and the initial porosity of rock n0 : Then, from Eq. (5) we have r n0 rw rr ¼ 0 : ð7Þ 1 n0
1 Dr ; m20 r0
ð10Þ
where D is rock damage variable, m0 is the space resolution of CT machine and Dr is the change in density during the damage evolution process of rock material, i.e. Dr ¼ r r0 : Thus, we have Dr ¼
1 ðH H0 Þðr0 rw Þ: H0 Hw
ð11Þ
By substituting Eq. (11) into Eq. (10), we have D¼
Fig. 5. Partial CT image of the 1st scan layer of sandstone specimen No. 10.
1 ðH H0 Þðr0 rw Þ: m20 ðH0 Hw Þr0
ð12Þ
Eq. (12) is a newly defined damage variable based on the chemical corrosive influence and CT value definition. It takes into account the pore water influence upon the rock damage evolution. In the meantime, the pore water density rw of different chemical solutions, the initial rock density r0 and the CT value Hw may cause different changes to the rock damage variable D: In order to facilitate the analysis, for sandstone soaked in NaCl solution of pH 7 and concentration of the following values can be approximations taken: 0.01 M, Hw ¼ 1000; sw ¼ 1 t=m3 ; m0 ¼ 0:35; r0 ¼ 2:7 t/m3. Then the values of the damage variable D are listed in Table 4.
Table 4 Stress, strain, average CT value and damage variable of sandstone specimen No. 10 Scan layer no.
s1 s3
e1 ( 102)
Average CT value
Load (%)
D
Note
1 2 3 4 5 6 7 8 9
0.0 14.04 50.42 87.28 112.28 124.67 130.60 136.07 2.87
0.0 0.41 1.10 1.73 2.12 2.34 2.44 2.55 4.70
2019.17 2020.97 2022.20 2022.67 2023.03 2022.83 2022.13 2021.10 1837.63
10 36 63 81 90 94 98
0.0 0.00306 0.00516 0.00596 0.00657 0.00623 0.00504 0.00329 0.3091
Initial Compression Compression Compression Compression Cracking Propagation Propagation Collapse
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5. Discussion Rock material is a complex solid medium. It has many initial internal micro-cracks especially between the mineral particles. Therefore, the rock material in engineering is unavoidably subject to corrosive action of permeated water in the initial micro-cracks, as well as chemical solution that may be present. It thus weakens the connection between mineral particles and corrodes the mineral particles, eventually leading to a change in the micro-structure and mechanical properties of rock. Consequently, the long-term stability characteristics will become more complex. Research on the damage mechanism under chemical corrosion can more correctly provide important fundamental technical parameters for appraisal and calculation of rock engineering stability related to dam foundations, slopes, tunnels, etc. Therefore, in-depth research on rock crack and fracture characteristics subjected to water chemical corrosion is a new issue facing rock mechanics research. 5.1. Damage induced by the water chemical corrosion process It can be seen from Table 3 for sandstone specimen No. 10 that the CT values reach then maximum when the loads are about 63%, 90%, 81%, 36%, 81% of peak load for the 1st scan layer, the 2nd scan layer, the 3rd scan layer, local region (dangerous area), and all three scan layer, respectively, and then begin to decrease. The CT values have large drops (by about 10–30%) and damage variable decreases by about 48 times when the failure of the sandstone specimen approaches. The damage variable gets a similar relationship with the average CT value for all three scan layers (Table 4). Accordingly, the phenomena of emergence, propagation, connection and failure of the micro-cracks can be
seen in the CT image within the resolution of the technique. The large decrease of the CT values and damage variable was a precursor of rock failure. All other specimens tested have similar law. For example, for sandstone specimen No. 5, the CT values reach then maximum when the loads are about 65%, 72%, 77%, 82% of peak load for the 1st scan layer, the 2nd scan layer, the 3rd scan layer, and local region (dangerous area), respectively, and then begin to decrease (Table 5 and Fig. 6). The average CT value for all three scan layers reaches its maximum when load is 65% of peak load, the damage variable gets its maximum at the same load level (Table 6). Then the CT values decreases by about 10–30% and damage variable decrease by about 39 times when the failure of the sandstone specimen occurs. In some cases, the CT values (i.e. density) fluctuate locally (Fig. 6 and Table 5). These indicate that characteristics of damage localization due to the inhomogeneous distribution of micro-cracks. There is again a close correspondence between the large decrease in the CT values and damage variable and the approach of the rock fracture. The results, indicated by CT values and damage variable are consistent with the conclusion based on the temporal fractals [20] and the spatial fractals [21,22]. Therefore, the CT value (equivalent to rock density at the scan layer) and damage variable are useful parameters in describing the damage evolution process of rock. It can be seen in Fig. 7 that in the triaxial loading condition, no matter what kind of water chemical corrosion the specimen is subjected to, the main failure forms are similar, i.e. the main failure surface is almost parallel to the main loading stress direction. Moreover, the so-formed main failure surface is not a plane but a curved surface and the material on the two sides of the main crack produces dilatancy due to sliding on the main failure surface.
Table 5 Test results of scan layers of sandstone specimen No. 5 Scan no.
1 2 3 4 5 6 7 8 9 10 11
Scan layer 1
Scan layer 2
Scan layer 3
Local zone
CT value
RMS*
CT value
RMS*
CT value
RMS*
CT value
RMS*
1916.1 1917.6 1920.0 1923.6 1920.3 1920.5 1920.4 1920.2 1916.9 1917.3 1604.6
45.11 44.98 44.18 43.41 44.65 45.14 45.56 45.27 43.04 42.34 446.08
1923.1 1921.8 1923.9 1924.5 1925.2 1924.2 1924.8 1925.2 1924.4 1923.1 1692.6
43.64 44.17 44.42 44.98 44.77 45.29 45.05 45.14 45.55 45.25 468.63
1945.64 1953.2 1954.5 1955.7 1956.0 1956.1 1955.6 1955.1 1955.3 1955.9 1830.1
44.25 44.00 45.02 47.49 46.52 45.68 44.79 45.18 44.65 43.49 313.64
1942.5 1945.4 1947.2 1951.0 1951.0 1951.1 1953.5 1951.2 1932.3 1924.3 1282.1
45.01 45.17 44.67 46.36 47.13 47.26 47.70 47.90 39.70 40.44 450.82
*RMS: Root mean square.
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5.2. Effect of water chemical corrosion on the triaxial compressive strength of sandstone
189
The pH value of the chemical solution thus has a great influence on the sandstone strength (Fig. 9). The stronger the acidity (pHo7) or causticity (pH>7), the stronger the corrosive effect on rock microfracturing evolution. When the chemical solution is of pH 7 (neutral) the rock strength has about 10% decrease in comparison with that in the natural state. For a NaCl chemical solution of 0.01 M, the peak stress of rock specimen in acid (pH 2) solution has about 30% decrease relatively in comparison with that in neutral (pH 7) solution, while in caustic (pH 12) solution, it has about 11% decrease in comparison with that in the neutral (pH 7) solution.
The peak stress s1 for sandstone in the natural state is about 160 MPa, while for those corroded in distilled water (pH 7) and Yellow River water (pH 8.3) the values are about 151 and 120 MPa, respectively. The decreases are about 5% and 26%, respectively. Under the influence of solutions NaCl, CaCl2 and NaHCO3 with 0.01 M and pH 9, the peak stresses are about 136, 112, and 153 MPa, respectively, the decreases are about 15%, 30%, and 4.4%, respectively, in comparison with those in the natural state (as shown in Fig. 8).
2100
2100
1700
CT value
CT value
1900
1500 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1300 1100 900 0.0
1.0
2.0 3.0 4.0 Strain ε (× 0.01)
(a)
2000 Scan layer 1 1900
Scan layer 3 Scan layer 5
5.0
1800 0.0
6.0
1.0
(b)
2.0 3.0 Strain ε (× 0.01)
4.0
5.0
2000
2100 2000
1950
1900 1800
CT value
CT value
2050
1900 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1850 1800 1750 0.0
1.0
2.0 3.0 Strain ε (× 0.01)
(c)
1700 1600 1500
Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1400 1300 4.0
5.0
0
1
(d)
2000
2200
1980
2000
2 3 Strain ε (× 0.01)
4
5
1940 1920
1800 1600
1900
Scan layer 1
1880
Scan layer 2
1400
1860
Scan layer 3 Local area with large CT value
1200
1840 1820 0.0
(e)
CT value
CT value
1960
Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1000
1.0
2.0
3.0 4.0 Strain ε (× 0.01)
5.0
6.0
0.0
(f)
1.0
2.0 3.0 Strain ε (× 0.01)
4.0
5.0
Fig. 6. Change of CT value during damage evolution of sandstone specimens saturated in different water solutions or air: (a) in air, (b) in distilled water, (c) in Yellow River water, (d) in NaCl, pH 7, 0.01 M, (e) in NaCl, pH 2, 0.01 M, (f) in NaCl, pH 9, 0.01 M, (g) in NaCl, pH 12, 0.01 M, (h) in CaCl2, pH 9, 0.01 M, and (i) in NaHCO3, pH 9, 0.01 M.
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190
2000
2200
1800
2000
1600
Scan layer 1 Scan layer 2 Scan layer 3 Local area withl arge CT value
1400 1200 1000 0.0
CT value
CT value
2200
1.0
(g)
2.0 3.0 4.0 Strain ε (× 0.01)
5.0
1800 1600
Scan layer 1
1400
Scan layer 2
1200
Scan layer 3 Local area with large CT value
1000 0.0
6.0
1.0
(h)
2.0 3.0 4.0 Strain ε (× 0.01)
5.0
6.0
2100
CT value
2000 1900 Scan layer 1 Scan layer 2 Scan layer 3 Local area with large CT value
1800 1700 1600 0.0
0.5
1.0
(i)
1.5 2.0 Strain ε (× 0.01)
2.5
3.0
Fig. 6 (continued). Table 6 Stress, strain, average CT value and damage variable of sandstone specimen No. 5 Scan layer no.
s1 s3
e1 ( 102)
Average CT value
RMS*
Load (%)
D
Note
1 2 3 4 5 6 7 8 9 10 11
0.0 17.32 64.07 82.45 91.82 97.48 103.90 113.51 120.45 123.35 6.13
0.0 0.48 1.27 1.71 1.88 1.99 2.08 2.26 2.39 2.46 5.08
1928.27 1930.87 1932.80 1934.60 1933.83 1933.60 1933.60 1933.50 1932.20 1932.10 1709.10
44.33 44.38 44.54 45.29 45.31 45.37 45.13 45.18 44.38 43.69 409.45
13.7 50.6 65.1 72.5 77.0 82.1 89.7 95.1 97.4
0.0 0.00456 0.00795 0.01036 0.00976 0.00936 0.00936 0.00918 0.00690 0.00672 0.3847
Initial Compression Compression Compression Cracking Cracking Cracking Cracking Propagation Propagation Collapse
*RMS: Root mean square.
This kind of influence law is in general coincident with that of the uniaxial case [19]. 6. Conclusions The CT technique is an effective method for studying the rock damage evolution process. From the CT experiments described here we develop the following conclusions: (1) The CT technique has been successfully used in loading experiments of triaxial damage evolution
process of sandstone under chemical corrosion for the first time. (2) The phenomena of the inhomogeneous distribution of the internal micro-cracks as well as the different damage evolution characteristics at different layers in the specimens can be observed at a given stress state. The results indicate the complexity of the damage evolution process in intact sandstone. (3) The corrosive influence of different chemical solutions with different pH values on the mechanical properties of Xiaolangdi sandstone is clear:
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
191
(i) Fig. 7. Final fracture image of triaxial compressive sandstone specimens saturated in different water solutions or air: (a) in pH 7, NaCl, (b) in pH 9, NaCl, (c) in pH 12, NaCl, (d) in air, (e) in Yellow River water, (f) in distilled water, (g) in pH 9, CaCl2, (h) in pH 2, NaCl, and (i) in pH 9, NaHCO3.
160 140 σ1-σ3 (MPa)
Peak stress (MPa)
180
180 160 140 120 100 80 60 40 20 0
120 100 Air Distilled water Yellow River water 0.01M NaCl 0.01M CaCl2 0.01M NaHCO3
80 60 40 20
Natural state
Distilled water
Yellow River water
NaCl
CaCl2
NaHCO3
Fig. 8. Influence of water solution with different constituents on triaxial compressive strength of sandstone specimens.
0 0
1
2
3
4
5
6
7 pH
8
9
10
11
12
13
14
Fig. 9. Influence of different pH values on triaxial compressive strength of sandstone specimens.
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chemical corrosion changes the mechanical properties of the rock. In the meantime, the other factors accelerating rock failure, such as rock genesis, structure, micro-cracks, water-absorbability, adhesive property, mineral constituents, as well as in the homogeneity variation of physical properties, are pending further research. (4) The quantitative analysis of the internal rock damage evolution process is also possible via the CT value and a damage variable has been proposed, Eq. (12).
Acknowledgements Financial support from the Special Funds for Major State Basic Research Project under Grant No. 2002CB412704 and the National Nature Science Foundation of China under Grant No. 10072073 are gratefully acknowledged. The authors would like to acknowledge to Professors J.A. Hudson and Yongjia Wang’s helpful suggestions to improve the manuscript, and Mr. Yibin Pu and Professor Wei Ma for their help in real-time CT experiment. References [1] Lajtai EZ, Schmidtke RH, Bielus LP. The effect of water on the time-dependent deformation and fracture of a granite. Int J Rock Mech Min Sci Geomech Abstr 1987;24(4):247–55. [2] Charles RJ, The strength of silicate glasses and some crystalline oxides. In: Fracture, Proceedings of International Conference on the Atomic Mechanisms of Fracture, MIT Press, Cambridge, MA, 1959. p. 225–49. [3] Westood ARC, Macmillan NH. Environmental-sensitive hardness of nonmetals. In: The science of hardness testing. Celveland, OH: ASTM, 1973. p. 377–417. [4] Seto M, Vutukuri VS, Nag DK, Katsuyama K. The effect of chemical additives on strength of rock. In: Proceedings of Civil Engineering 1998; Japan, No. 603/III-44: p. 157–66. [5] Swolfs HS, Chemical effects of pore fluids on rock properties. In: Cook TD, editor. Underground Waste Management and Environment Implications, 1972. p. 224–34. [6] Karfakis MG, Askram M. Effects of chemical solutions on rock fracturing. Int J Rock Mech Min Sci Geomech Abstr 1993;37(7):1253–9.
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