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Microscopic characteristics of problematic Tertiary sandstone as
revealed by grain-wide local deformation
M.C. Weng1,*; S.H. Tung1; M.H. Shih2
1 Dept. of Civil and Environmental Engineering, National University of Kaohsiung, Kaohsiung, Taiwan. 2
Department of Construction Engineering, National Kaohsiung First University of Science and Technology, Taiwan
* Corresponding author: [email protected]; Tel: +886 7 5919543, Fax:+886 7 5919378
1. Introduction
In Taiwan, Tertiary sandstones have a diagenetic age of no more than 36 million years, and such relatively short rock forming period is insufficient to enable them as hard rocks. Therefore, these Tertiary sandstones were often characterized as medium to weak rocks, which uniaxial strength ranges from 10 to 80 MPa [1, 2]. In the past, several squeezing and collapse cases have been reported while tunnels were constructed within these rock strata [3]. In order to identify the deformation behavior of such sandstones, Jeng et al. [1] studied a total of 13 kinds of sandstones obtained from 8 geological formations of Taiwan. From the comparison on the petrographic features with the mechanical properties of these Tertiary sandstones, including the uniaxial compressive strength (UCS) and the reduction of strength due to wetting (R = UCSwet / UCSdry), it
was found that these Tertiary sandstones can be classified into two groups: Type A and Type B (with R > 0.5 and R ≤ 0.5 respectively). The deformation characteristics of each group of sandstones are proposed:
(a) Type A – This group of sandstones has R > 0.5 and hence has relatively less tendency of wetting softening both in strength and stiffness; and
(b) Type B – This group of sandstones (R ≤ 0.5) is characterized by greater deformation and, what is worse, with more significant wetting softening.
Therefore, the mechanical properties of Type A are close to those of hard rocks except that
Type A sandstone has more significant shear dilation. Nevertheless, Type B sandstone, compared
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1. lower value of bulk modulus and shear modulus;
2. significant volumetric dilation and distortion induced by shearing;
3. substantial plastic deformation occurring prior to the failure state during shearing; 4. significant reduction in both the strength and the stiffness due to wetting.
These characteristics highlight that Type B can be the rock type liable to tunnel squeezing. Moreover, Lin et al. [4] investigated the fracture patterns of Type A and Type B sandstones based on observations of fracture surface under microscope. It was found that inter-granular fracture, instead of intra-granular fracture in dry condition, occurs primarily in Type B sandstone when the sandstone is wet. Moreover, the classification of a sandstone being Type A or Type B seems to depend on the nature of matrix.
Based on the previous research, it was concluded that the nature of the matrix plays an important role on the mechanical properties of Tertiary sandstones from the microscopic point of view. In addition, the weakening of the matrix may be the key point of the wetting deterioration [4, 5]. Therefore, it is important to quantitatively study the effect of the matrix on the deformation of the sandstone under external loading. This paper explores the microscopic deformation characteristics of the sandstones, especially Type B sandstones that account for the lower stiffness and significant reduction of strength and stiffness.
Gaining more insight into the deformation behavior of sandstones may require effective measurement of the strain field from micro-vision. The digital image correlation (DIC) method provides a solution to such problems. The DIC method is a well-developed optical measuring technique offering effective and high precision strain distribution for a field. Based on Chu et al.’s research [6], this measuring technique was developed by combining deformation theory and digital images. The DIC method is a technique for measuring surface deformation based on digital images, and it was used to analyze the so-called “random structural speckle” on the surface, which results in gray scale distribution on image surface. According to the distribution feature of gray scale, the characteristics of un-deformed and deformed images taken at different time instances are
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compared, and relative position of images inferred accordingly. Thus, displacement vectors of various image points are calculated, and other physical values, such as strain can also be inferred.
Afterward, owing to the modifications of the DIC method [7-11], including the quality of acquired images, the algorithms and the image correlation processing, good reliability and accuracy of the strain mapping results now can be achieved. According to Sutton et al. [12], the accuracy of the DIC method could be less than 0.01 pixels. Recently, the DIC method has been increasingly used for whole-field surface strain mapping applications in various materials, including rock [13], granular material [14], metal [15], concrete [16], and so on [17-19]. Based upon the aforementioned advantages, the DIC method is adopted in this paper to measure the grain-wide local deformation and to observe the fracture propagation of Tertiary sandstones through microscope. Afterward, the microscopic mechanism that accounts for the aforementioned characteristics is further explored.
2. Theoretical basis of strain analysis by DIC method
2.1 Theory of DIC
The theoretical basis of digital image correlation is briefly described as follows:
Let us denote the un-deformed image by image A and the deformed image by image B, as shown in Fig. 1. The coordinates (x, y) and (x*, y*) are related by the displacement function between the two images. If the motion of the object relative to the camera is parallel to the image plane, then the relationship of two points could be expressed as [20]:
) , ( * y x u x x = + (1) ) , ( * y x v y y = + (2)
where u( yx, ) and v( yx, ) are the displacement functions.
The un-deformed image can be firstly divided into discrete elements using the concept of finite element method, exemplified by the rectangular element a in the un-deformed image A in Fig. 1. The element in the i-th row and the j-th column at local coordinate will be referred as the (i, j)
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element. After deformation (i.e., image B), element a becomes element b, and the latter may become non-rectangular due to the deformation. Let P and P* be the central points of elements a and b, respectively.
Although the deformed element b is illustrated in Fig. 1, its exact location is unknown until the DIC analysis is done; in fact, the goal of the DIC analysis is to identify the locations of the deformed element in image B associated with each un-deformed element in image A. In order to identify the location of a deformed element, the grayscale values of pixels in the associated elements before and after the deformation are calculated. Theoretically, the gray values of pixels should be the same. However, in practice, the two digitized images are compared and a local correlation function of these two images is determined according to the method of the least-squares-matching. The following image correlation function [6, 20] can be used to determine the degree of similarity between these two images:
* * 2 2 * * ij i j ij i j g g COF g g = ⋅
∑
∑ ∑
(3) 92 93 94 95 96 97 98 99 100 101 102 103 104where COF is the image correlation function, and and are gray scale values of un-deformed element at and deformed sub-image at , respectively.
ij
g gi j* *
) ,
( ji ( *, *)i j
When COF = 1, the deformed sub-image exactly corresponds to the un-deformed sub-image after deformation, and then, the coordinate of deformed sub-image could be determined. If optimum function parameter for every sub-image is recognized by an optimization procedure, the nodal displacements at four corners of every sub-image could be obtained. Then, the displacement field in the sub-image could be interpolated by a bilinear function. Finally, by overlapping sub-images, the full-field displacement information is obtained.
2.2 Calculation of strain field
After the displacement field has been established, the strain field could be further computed based on the continuum mechanics, and the Green-Lagrange’s strain tensor E is adopted and defined as:
1 2
ij ki kj ij
E = ⎡⎣F F −δ ⎤⎦
105 (4)
Where, F is gradient tensor of displacement field, and δij is the Kronecker delta tensor. Tensor E is rewritten into the function of displacement field as follows:
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(
, ,)
, 1 1 2 2 ij ui j uj i u uk i k j ε = + + , 108 x (5) where i j k, , ∈( , )x y , and ui j, = ∂ui/∂ j , and the out-of-plane strains εz , εxz and εyz areassumed to zero. Moreover, the deviatoric strain 109
γ and volumetric strain εv is obtained as: 110 ' 2 2 J 2eij ij γ = = e 111 k (6) v k
ε
=ε
(7) 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127where ' is the second deviatoric strain invariant; e
2
J ij = second deviatoric strain tensor.
3. Setup of experimental study
3.1 Specimen preparation
Two kinds of sandstones were selected, two specimens for each kind, to study the deformation behavior and the effect of wetting softening. The first kind is the Mushan (MS) sandstone (R= 0.49, classified as Type B) sampled from northern Taiwan. Squeezing has been reported for some tunnels constructed within this stratum. The deformation characteristics of MS sandstone are of primary interest in this study. The MS sandstone was deposited under littoral facies sedimentary environments in Miocene. Its porosity is about 14.1 %, dry density is about 2.28 g/cm3, and saturated water content is about 5.92 %. As revealed by the petrographic analyses, the percentages of grains, matrix, and voids are 59.9 %, 26.0 % and 14.1%, respectively. The average grain diameter is about 0.24 mm. Mineralogically, the MS sandstone consists of 90.7% of quartz, 9.0% of rock fragments, and is classified as lithic greywacke according to Pettijohn et al [21]. Moreover, the specimens used in this research exhibit substantial weathering and wetting deterioration more than those studied by Jeng et al. [1] and Weng et al. [2].
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To serve as a contrast to the aforementioned MS sandstone, another kind of sandstone is selected for study: the Taliao (TL) sandstone (R= 0.69, classified as Type A), deposited under marine facies. The Taliao Formation directly overlies the Mushan Formation. The sampled TL specimens have the following mean physical properties: a porosity of 13.1 %, dry density of 2.36 g/cm3, and saturated water content of 2.61 %. Based on the petrographic analyses, the percentages of grains, matrix, and voids are 36.4 %, 57.0 % and 6.6 %, respectively. The average grain diameter is about 0.095 mm. Mineralogically, the TL sandstone consists of 86.5 % of quartz, 10.0% of rock fragments, and is classified as lithic greywacke.
In the present study, the sandstone specimens were obtained from drillings perpendicular to the bedding plane and have a size of 40 mm x 20 mm x 10 mm. The original image of MS sandstone is shown as Fig. 2a. In order to clearly distinguish matrix from grains, the sandstone surface (40 mm x 20 mm) was dyed with the red ink into the matrix, yet the color of grains remaining unchanged, to enhance the contrast between grains and matrix. The sample is then polished by emery powder to produce a smoother surface. Furthermore, to differentiate the texture of the images for the later DIC analysis, the surface was then sprayed with black tiny speckles, as shown in Fig. 2b. In order to understand the correlations between the local strain and the locations of grains and matrix, the grains in the analysis area are visually identified and further marked in Fig. 3.
Afterward, one of the two specimens in each kind was stored in dry condition and the rest was in wet condition. For the dry specimen, it was oven-dried (105 oC) for at least 24 hours to remove the humidity inside. For the wet specimen, it was saturated for at least 24 hours under the high vacuum condition. When the water content stops increasing, the specimen is considered as fully saturated. However, it should be noticed that the specimens should not be submerged into water for too long to avoid dissolving or leaching of the minerals.
3.2 Testing procedures
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uniaxial compression tests. The apparatus, as shown in Fig. 4, consists of two parts: (a) loading system and (b) the image acquisition system for DIC. The axial load was provided by a loading frame with a maximum capacity of 100 kN. The loading system is able to provide a loading rate ranging from 0.0005 mm/min to 1000 mm/min with a precision of 0.0005 mm/min. The image acquisition system consists of a microscope with a light source, a charge coupled device (CCD) and a data-recording computer. The microscope is mounted onto the clamping device of the specimen, so that the microscope is always aligned with the specimen. In addition, the CCD allows observing of the surface in real time for different load levels.
The specimen was then compressed at a rate of 0.05 mm/sec. Meanwhile, two cycles of unloading/reloading were conducted at the applied stress of 1 kN and 2 kN respectively to obtain elastic deformation. The plastic deformation can then be acquired by subtracting the elastic deformation from the total deformation.
The digital image has a size of 2048 × 1534 pixels, corresponding to an observation area of 2.59 mm × 1.94 mm for MS sandstone, and 1.93 mm × 1.45 mm for TL sandstone, respectively. Therefore, the resolution is 1.26 and 0.94 μm/ pixel respectively for the two kinds of sandstones.
Before the strain analysis, the image should be divided into smaller grids, aforementioned as elements. It is necessary to determine the adequate size of these elements since the size may influence the resolution for the strain analysis. According to Lecompte et al. [22], a larger element provides a higher accuracy of deformation field, but it can hardly reflect local or minor variations. In this research, to tradeoff between the size and the precision, the element size is selected to be 128 pixels, which is commensurate with the average size of sandstone grains. The analysis area is divided into 54 elements (6 columns and 9 rows), shown in Fig. 2b, in this test process. After the size of the elements is determined, a software developed by Tung et al. [23] is used to analyze the acquired images with the procedure presented in Section 2.1.
4. Results and discussion
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UCSdry = 15.5 MPa and UCSdry = 7.6 MPa for the MS sandstone; (2) UCSdry = 48.7 MPa and
UCSdry = 33.6 MPa for the TL sandstone. The MS sandstone has less uniaxial strength and
higher wetting weakening than the TL sandstone. To understand the deformation mechanism of MS (Type B) sandstone, the grain-wide deformation is further explored in the following section. In particular, the Type B sandstone specimen prepared in wet condition is studied in details in Section 4.1-4.3, while all four specimens will be jointly studied and compared in Section 4.4. To ease the presentation, the four specimens will be mentioned as follows: Wet B denoted the Type B (MS) sandstone specimen prepared in wet condition, and similar for the others.
4.1 Variations of strain field of Wet B specimen
The analyzed full-field strain patterns of the MS sandstone under wet condition (Wet B specimen) at different loading stages, including axial strain εy, lateral strain εx, deviatoric strain
190
γ and volumetric strain εv, are shown in Figs. 5 – 8. The observed characteristics of strain field
are described as follows: 191
192
Firstly, Fig. 5 illustrates the axial strain field εy at axial stress of 3.50 MPa, 7.61 MPa (peak
value) and post-peak condition. Owing to the complicated constituents of sandstones, non-uniform strain field is clearly observed under loading. At the earlier loading stage (as shown in Fig. 5a), compressive strain initially concentrates in the lower middle area. The accumulated compressive strain increases with increasing loading (as shown in Figs. 5b and 5c). Compared with Fig. 3b, the accumulated strain area corresponds to the lower left matrix portion (Region I in Fig. 3b), and the grain portion reveals little compression. For the lateral strains, Fig. 6 shows the 193 194 195 196 197 198 199 x
ε field at the three loading stages. Before the peak stress, the magnitude of lateral strain is minor to the axial strain (
200
x
ε < 0.012). However, during the post-peak state, a Y-shape band of larger tensile lateral strain
201
x
ε develops (max. εx = 0.11, as shown in Fig. 6c). This tendency of deformation can be also found in the variations of deviatoric strain
202
γ under different loading stages, as shown in Fig. 7. Moreover, this high density of shear band in Fig. 7c may represent the 203
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occurrence of fracture. According to Tung et al. [23], while fracture occurs, the strain pattern reveals the following characteristics: (1) large magnitude of deviatoric strain and (2) high gradient of the deviatoric strain field. Based on the DIC analysis result, the Y-shape band herein shows the both features. In fact, during a post-test visual inspection, a fracture surface was indeed clearly identified within the Y-shape area, shown as the dotted line in Fig. 8.
Figure 8 illustrates the variations of volumetric strain induced by uniaxial loading. The volumetric strain is initially contractive, and then transits to be dilative with increasing stress. It is found that the dilation mainly accumulates at the shear band. Therefore, it is concluded that the shear band generates not only significant deviatoric strain but also large volumetric dilation. The maximum and minimum values of axial strain εy, lateral strain εx, deviatoric strain γ and
volumetric strain 214
v
ε under different loading stages are summarized in Table 1. 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230
In addition, the fracture behavior can be further examined in Fig. 9. Figure 9 depicts that the Y-shape fracture surface is mainly formed by coalescence of inter-granular (or trans-matrix) cracks. This phenomenon concurs with the finding made by Lin et al. [4]. When the sandstone is wet, it exhibits a greater wetting softening behavior at the matrix portion so that stress concentration will not be induced within the grains, fracture surfaces only track through the matrix without passing through the grains and eventually induces no grain breakages.
4.2 Wetting deterioration behavior of Wet B specimen
In addition to the aforementioned full-field strain distributions, the stress-strain curves at micro-scale are presented in Fig. 10, where the micro-strains are obtained by averaging the strain field over two elements near the shear band in the Wet B specimen: one element is within the grains, while the other is within the matrix, with coordinates being (0.35, 0.75) and (0.35, 0.15), respectively. For comparison, two elements near the shear band in the Dry B specimen, one in grains and the other in matrix, are also chosen to demonstrate the stress-strain curves at micro-scale.
By comparing the two Dry B curves with the two Wet B curves in Fig. 10a, it is clear that the stiffness and strength of the latter two curves are significantly smaller than those of the former two
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curves, indicating that the soaking of the specimen may induce significant deterioration in both stiffness and strength. Also, by observing that the two matrix curves lie at the right hand side of the two grain curves, it is clear that under either dry or wet condition, the matrix portion exhibits more ductile in compressive behavior, especially in the early stage. The same tendency is also observed for the deviatoric strain shown in Fig. 10b. Moreover, the volumetric strains are shown in Figs. 10c: the volumetric strain is initially contractive, and then gradually transits to be dilative with the increasing axial stress. However, the tendencies of all volumetric strain curves are similar, but the magnitudes for the Wet B specimen are significantly larger than those for the Dry B specimen, indicating more ductility in both the grain and matrix portion.
Furthermore, deduced from the experimental results, the variations of secant modulus of each element under various axial stress ratios (σa UCS) are plotted in Fig. 11. It reveals that all the
moduli exhibit lower value during early stage and increase as axial stress arises. In addition, the secant moduli of grain are higher than that of matrix. At a stress ratio of 0.5, the secant modulus at the grain portion of the Dry B specimen is about 1.30 GPa, decreasing to 0.50 GPa for the Wet B specimen – a 61.5% decrease of stiffness. Similarly, for the matrix portion, a 59 % decrease of modulus occurs due to wetting. As a consequence, it is concluded that wetting deterioration phenomena exists in both the grain and matrix portion.
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4.3 Plastic deformation characteristics of Wet B specimen
Figure 12 illustrates the plastic strain field of the Wet B specimen from the unloading procedure. The plastic axial strain
y
p
ε , plastic deviatoric strain γp and plastic volumetric strain
250
p v
ε obtained during the unloading from 7.0 MPa are shown in Figs. 12a, 12b and 12c, respectively. The matrix portion around the upper left corner (Region II in Fig. 3b) and the lower middle area (Region I in Fig. 3b) exhibits more plastic strain. Therefore, the matrix is relatively weaker than the grain, and the deformation of matrix is mostly unrecoverable.
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and the plastic component at loading stage could be decomposed from the total strain, as shown in Fig. 13. Figure 13a illustrates the variations of the stress-strain curves of grain portion, and the strain curves of matrix portion are depicted in Fig. 13b. It is seen that at either grain or matrix portion, the plastic strain governs the majority of the total deformation.
4.4 Comparison between all four specimens
The above-mentioned experimental results only reveal the deformation characteristics of Type
B sandstone. To serve as contrast to the Type B sandstone, the stress vs. micro-strain curves at
elements near the shear band in the Wet A and Dry A specimens (recall A denotes “Type A”) are shown in Fig. 14. Since the grain size of the Type A sandstone is much smaller than the element size, the micro-strain obtained at the element-scale should be closer to the average strains at the matrix portion. Therefore, the following comparison between Types A and B specimens will be only made for the matrix portion. Shown together in Fig. 14 are the stress vs. micro-strain curves at the matrix portion near the shear band in the Wet B and Dry B specimens. Compared to Type B,
Type A (TL) sandstone is characterized by higher stiffness and brittle deformation, as shown in Fig.
14. This behavior is similar to hard rocks. Under wet condition, Type A sandstone also exhibits wetting deterioration, but the reduction in strength and stiffness is less significant. In addition, it behaves more linear deformation and less shear dilation.
It may seem that the above observations lead to a contradiction: in terms of the constituents, TL sandstone contains more matrix and seems to have the tendency toward more wetting softening. However, the observed trend is on the contrary: the Type A (TL) specimens exhibit much less wetting softening than the Type B specimens. One possible reason may be that the TL sandstone has very low porosity (6.6 %), hence less water content. Therefore, the wetting softening is limited by insufficient supply of water. This conclusion was previously made by Jeng et al. [1].
In summary, wetting softening will be pronounced only if the following two factors are present simultaneously: (1) high porosity and (2) sufficient matrix content. This explains why the MS sandstone is prone to wetting softening due to its high porosity and sufficient matrix content; it
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also explains why the TL sandstone is not prone to wetting softening: although its high matrix content, but its porosity is quite low. Hence, TL sandstone exhibits less wetting deterioration.
5. Conclusion
The microscopic deformation characteristics of problematic (Type B) Tertiary sandstone under uniaxial loading are explored through digital image correlation (DIC) method. According to the analysis results, the microscopic deformation is precisely measured and quantified, and the deformation of Type B sandstone possesses the following characteristics:
(1) the sandstone exhibits non-uniform strain pattern under loading, and in wet condition the accumulated strain concentrates in the matrix portion;
(2) when the stress approaches the ultimate strength, a shear band can be clearly identified, and the shear band mainly propagates through the matrix and generates not only significant deviatoric strain but also large volumetric dilation;
(3) according to the stress-strain curves, wetting deterioration phenomena exists in both the grain and matrix portion, and significant wetting-induced deformation mostly occurs in the matrix portion;
(4) deduced from stress-strain curves, the modulus of each portion can be obtained, and it reveals that all the secant moduli exhibit lower value during early stage and increase as axial stress arises; (5) the deformation is mainly plastic, and the plastic deformation accumulates in the matrix portion; and
(6) compared with Type A and Type B sandstone, wetting softening will be pronounced only if both high porosity and sufficient matrix content are present simultaneously.
The results not only provide the information to understand the micro-deformation mechanism of problematic sandstone but also produce database for further micro-mechanic analysis.
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The research is supported by the National Science Council of Taiwan, Grant no. NSC-96-2221-E-390-021. The authors are grateful to Prof. F. S. Jeng, Prof. J. Y. Ching, and two reviewers who kindly provided professional suggestions of this work, and Mr. Y. T. Huang, who helped to analyze the experimental data.
7. Reference
[1] Jeng FS, Weng MC, Lin ML, Huang TH. Influence of petrographic parameters on geotechnical properties of Tertiary sandstones from Taiwan. Eng Geol 2004; 73:71–91.
[2] Weng MC, Jeng FS, Huang TH, Lin ML. Characterizing the deformation behavior of Tertiary sandstones. Int J Rock Mech Min Sci 2005; 42:388-401.
[3] Weng MC, Jeng FS, Hsieh YM, Huang TH. A simple model for stress-induced anisotropic softening of weak sandstones. Int J Rock Mech Min Sci 2008; 45: 155-166.
[4] Lin ML, Jeng FS, Tsai LS, Huang TH. Wetting weakening of Tertiary sandstones – microscopic mechanism. Env Geol 2005; 48: 265-275.
[5] Hsieh YM, Li HH, Huang TH, Jeng FS. Interpretations on how the macroscopic mechanical behavior of sandstone affected by microscopic properties—Revealed by bonded-particle model. Env Geol 2008; 99: 1-10.
[6] Chu TC, Ranson WF, Sutton MA, Peters WH. Application of digital-image-correlation techniques to experimental mechanics. Experimental Mechanics 1985; 25: 232-244.
[7] Brillaud J, Lagattu F. Digital correlation of grainy shadow images for surface profile measurement. Optik 2006; 117: 411-417.
[8] Bruck HA, McNeill SR, Sutton MA, Peters WH. Digital image correlation using Newton-Raphson method of partial differntial correlations. Experimental Mechanics, 1989; 29: 261-267.
[9] Chen DJ, Chiang FP, Tan YS, Don HS. Digital speckle displacement using a complex spectrum method. Applied Optics, 1993; 32: 1839-1849.
332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 Mechanics, 1990; 30: 60-67.
[11] Vendroux G, Knauss WG. Submicro deformation field measurements,Part 2. improved digital image correlation. Experimental Mechanics, 1998; 38: 86-91.
[12] Sutton MA, Turner JL, Bruck HA, Chae TA. Full-field representation of discretely sampled surface deformation for displacement and drain analysis. Experimental Mechanics 1991; 31: 168-177.
[13] Louis L, Wong TF, Baud P. Imaging strain localization by X-ray radiography and digital image correlation: Deformation bands in Rothbach sandstone. Journal of Structural Geology, 2007; 29: 129-140.
[14] Rechenmacher AL, Finno RJ. Digital image correlation to evaluate shear banding in dilative sands. Geotechnical Testing Journal 2004; 27(l):13-22.
[15] Melrose P, Lopez-Anido R, Muszyñski L. Elastic properties of sandwich composite panels using 3-D digital image correlation with the hydromat test system. In: SEM XI International Congress and Exposition on Experimental and Applied Mechanics Costa Mesa, CA, 2004, No. 490.
[16] Choi S, Shah SP. Measurement of deformations on concrete subjected to compression using image correlation. Experimental Mechanics 1997; 37: 307-313.
[17] Li M, Zhang J, Xiong CY, Fang J. Fracture analysis of plastic bonded explosive by digital correlation technique. In: Third International Conference on Experimental Mechanics, 2002, 4537: 107-110.
[18] Mott L, Shaler SM, Groom LH. A novel technique to measure strain distributions in single wood fibers. Wood and Fiber Science 1996; 28: 429-437.
[19] Muszyñski L, Wang F, Shaler SM. Short term creep tests on phenol resorcinol formaldehyde (prf) resin undergoing moisture content changes. Wood and Fiber Science 2002; 34: 612-624. [20] Russell SS, Sutton MA. Strain field analysis acquired through correlation of x-ray radiography
of a fiber reinforced composite laminate. Experimental Mechanics 1989; 29: 237-240. [21] Pettijohn FJ, Potter PE, Siever R. Sand and sandstone. Berlin, Springer-Verlag; 1987.
359 360 361 362 363 364 365 366 367 368
[22] Lecompte D, Smits A, Bossuyt S, Sol H, Vantomme J, Van Hemelrijck D, Habraken AM. Quality assessment of speckle patterns for digital image correlation. Optics and Lasers in Engineering 2006; 44: 1132–1145.
[23] Tung SH, Shih MH, Sung WP. Development of digital image correlation method for analyzing crack of brick wall. Experimental Techniques 2008. Sadhana - Academy Proceedings in Engineering Science 2008; 33: Part 6, 767-779.
List of Tables
Table 1. Summary of the maximum and minimum amount of strains under different loading stages
Axial stress（MPa） 3.50 7.61 Post-peak Max. 2.44×10-2 3.14×10-2 4.48×10-2 Axial strain y ε Min. 1.26×10-3 0.52×10-3 -8.78×10-3 Max. 3.67×10-3 7.36×10-3 1.10×10-3 Lateral strain x ε Min. -1.18×10-2 -2.34×10-2 -11.05×10-2 Max. 1.80×10-2 2.16×10-2 8.78×10-2 Deviatoric strain γ Min. 1.27×10-3 2.24×10-2 3.82×10-2 Max. 2.28×10-2 3.16×10-2 3.44×10-2 Volumatric strain v ε Min. -0.66×10-2 -1.63×10-2 -7.83×10-2 369 370 371
Remarks: The sign “+” of axial strain and lateral strain is defined as “compression”, and the sign “－” is defined as “tension”.
372
Figure captions
Figure 1 Schematic diagram of deformed and un-deformed images in DIC analysis. Figure 2 The reference image of MS sandstone for DIC analysis.
Figure 3 The grain distribution in the analysis area. Figure 4 Schematic diagram of experimental setup.
Figure 5 Full-field axial strain patterns of Wet B specimen under different loading stages. The area of strain patterns are corresponding to Fig. 3b.
Figure 6 Full-field lateral strain patterns of Wet B specimen under different loading stages. Figure 7 Full-field deviatoric strain patterns of Wet B specimen under different loading stages. Figure 8 Full-field volumetric strain patterns of Wet B specimen under different loading stages. Figure 9 Fracture surface obtained from post-peak stage. Blue dotted lines mark the major
fracture surface. Inter-granular fracture occurred for Wet B specimen can be seen. Figure 10 Comparisons of the strains in grain and matrix portion of Dry B and Wet B specimens.
In figure, Dry B denoted the Type B (MS) sandstone specimen prepared in dry
condition, and similar for the others.
Figure 11 The variations of modulus corresponding to axial stress ratio. Figure 12 Full-field plastic strain patterns of Wet B specimen.
Figure 13 Deduced elastic and plastic components from total strain induced by uniaxial stress. Figure 14 Comparisons of the strains of all specimens.
