Study of Strain Localization and Microstructural Changes in Partially Saturated Sand During Triaxial Tests Using Microfocus X-Ray CT

SOILS AND FOUNDATIONS Japanese Geotechnical Society

Vol. 51, No. 1, 95–111, Feb. 2011

STUDY OF STRAIN LOCALIZATION AND MICROSTRUCTURAL CHANGES IN PARTIALLY SATURATED SAND DURING TRIAXIAL TESTS USING MICROFOCUS X-RAY CT YOSUKE HIGOi), FUSAO OKAii), SAYURI KIMOTOiii), TAISUKE SANAGAWAiv) and YOSHIKI MATSUSHIMAv) ABSTRACT It is well known that strain localization and microstructural changes are important issues in the onset of failure problems. In particular, unsaturated soil exhibits more brittle failure due to the collapse of the water meniscus, caused by shearing or the inˆltration of water, than saturated soil. The aim of this paper is to observe the strain localization behavior and the microstructural changes in partially saturated soil during the deformation process using microfocus Xray CT. The microfocus X-ray CT system employed in this study has a very high spatial resolution of 5 mm, which is enough to visualize the sand particles and the other particles individually. In addition, X-ray CT scans can be performed under triaxial conditions. The strain localization of fully saturated, partially saturated, and air-dried sand specimens during triaxial compression tests is observed and discussed. The microstructure of unsaturated soil, consisting of soil particles, pore water, and pore air, is successfully observed in partial CT scans. Through a comparison of the microstructures in the shear bands and in the initial state, the microstructural changes are discussed. Key words: microfocus X-ray CT, microstructural changes, partially saturated sand, strain localization, triaxial tests (IGC: D3/D6)

fore, to study the behavior of partially saturated soil under low conˆning pressure. The strain localization of geomaterials has been studied by many researchers through theoretical, experimental, and numerical methods, since the strain localization phenomenon is an important issue in the onset of failure problems. In particular, investigations of strain localization using X-ray computed tomography (CT) have produced various results (e.g., Desrues et al., 1996; Otani et al., 2000; Alshibli et al., 2000; Kodaka et al., 2006a, b), by which the strain localization behavior inside geomaterials has been observed in a nondestructive manner. For the strain localization of sand, Desrues et al. (1996) have successfully viewed shear bands under triaxial conditions using medical X-ray CT and have estimated the three-dimensional strain localization mode. Alshibli et al. (2000) and Otani et al. (2002, 2006) have also observed the strain localization in sand specimens under various conditions using industrial X-ray CT, which has very high X-ray energy. In these research works, strain localization has been identiˆed by the distribution of density in the specimens through the obtained CT values, since the

INTRODUCTION It is well known that having knowledge of the microstructure of soil, such as the arrangement of the soil particles and the void distribution, is the key to understanding the strain localization and the failure of geomaterials. The deformation characteristics of fully saturated soil are aŠected by the motion of the pore water. For partially saturated soil, the pore water exists as a meniscus with a suction force that behaves as a capillary force between the soil particles. The water meniscus strengthens the soil through this capillary force, while the collapse of the water meniscus causes a drastic loss in strength by shearing or by the inˆltration of water. Corresponding to the loss in strength, partially saturated soil exhibits a more brittle mode of failure, with a clear failure surface, than fully saturated soil, especially in cases of lower conˆning pressure (e.g., Cunningham et al., 2003). The typical failure problems of partially saturated soil include the surface failure of slopes and the collapse of river embankments, in which the partially saturated soil located near the ground surface is problematic. It is important, therei)

ii) iii) iv) v)

Assistant Professor, Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan (higo.yohsuke.5z＠kyotou.ac.jp). Professor, ditto. Associate Professor, ditto. Former Student, ditto (presently in Railway Technical Research Institute, Tokyo, Japan). Master Course Student, Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan. The manuscript for this paper was received for review on October 27, 2009; approved on October 1, 2010. Written discussions on this paper should be submitted before September 1, 2011 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month. 95

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spatial resolution of medical and industrial CT is not su‹cient for distinguishing individual sand particles or voids. Recently, microfocus X-ray CT (hereinafter referred to as ``mX-ray CT'') and X-ray micro CT using synchrotron radiation were able to accomplish a very high spatial resolution of less than 10 micrometers, which makes it possible to study microstructural changes in the ˆne-grained sand of shear bands (e.g., Oda et al., 2004; Matsushima et al., 2006; Hall et al., 2009; Viggiani et al., 2010). As for the study of microstructures by micro CT, the objects scanned are limited to small specimens, within 10 mm in diameter, because the X-ray energy of the microfocus X-ray tube or synchrotron radiation is rather low (Matsushima et al., 2006; Hall et al., 2009). mX-ray CT systems with high X-ray energy now exist; they can achieve CT scanning with a micron's level of high resolution using relatively larger specimens (Fujii and Uyama, 2003; Oda et al., 2004; Kikuchi, 2006). To the author's knowledge, however, the published studies are mainly for dry sand, although most natural geomaterials are fully saturated or unsaturated porous media. The aim of this study is to investigate strain localization and the microstructural changes in partially saturated sand using mX-ray CT. The mX-ray CT system employed in this study includes a microfocus X-ray tube with a very small focus size and high energy, i.e., a high tube voltage and a high tube current. With this system, therefore, it is possible to visualize microstructures with a high spatial resolution, even in relatively larger specimens (specimens for triaxial tests are normally 35 or 50 mm in diameter). In addition, since the triaxial cell can be mounted on a rotation table, X-ray CT scans can be conducted under triaxial conditions (Higo et al., 2010). In the present paper, using the mX-ray CT, strain localization and the microstructural changes during triaxial compression tests for air-dried, partially saturated, and fully saturated Toyoura sand specimens are presented. The specimens are 35 mm in diameter and 70 mm in height, and all the tests are performed under drained conditions for air and water. The progressive development of strain localization is observed by the X-ray CT scanning of the entire specimen during the triaxial compression tests. A series of experiments provides the three-dimensional CT images, the stress-strain relations, and the measured volume changes using the CT images. Through the obtained results, the strain localization behavior in partially saturated Toyoura sand is discussed by comparing the results with those for fully saturated sand and airdried sand specimens. In addition, the triaxial test results for the partially saturated sand specimens, with various initial void ratios, provide the basis for a discussion on the eŠect of the initial void ratio on strain localization. Furthermore, the microstructure of partially saturated sand under conˆning pressure is viewed in a partial CT scan, namely, a part of the specimen of interest is scanned with high magniˆcation. The spatial resolution of the partial CT scan is less than 10 micrometers, which is enough to distinguish the soil particles, the pore water existing as a water meniscus, and the pore air, individually.

In particular, focus is placed on the shear bands, and the microstructural changes in the shear bands are discussed. MATERIALS AND METHODS

Test Sample The test sample used in this study is Toyoura sand. An SEM image of Toyoura sand is shown in Photo 1, the grain distribution curve is demonstrated in Fig. 1, and the physical properties are listed in Table 1. Toyoura sand is semi-angular in shape with an average diameter D50 of 0.185 mm.

Photo 1.

Fig. 1.

SEM image of Toyoura sand

Grain size distribution curve for Toyoura sand

Table 1.

Physical properties of Toyoura sand

Particle density

2.64 (g/cm3)

Maximum void ratio

0.975

Minimum void ratio

0.614

Average diameter

0.185 (mm)

Uniformity coe‹cient

1.6

Fine content

0.1z

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Photo 2.

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Microfocus X-ray CT used in this study (KYOTO-GEOmXCT (TOSCANER–32250mHDK))

Microfocus X-ray Computed Tomography The X-ray computed tomography technique was originally developed for medical imaging by Hounsˆeld (1972). Since then, it has been widely recognized as a powerful tool for viewing the inside of materials nondestructively and in three dimensions, not only in the medical ˆeld, but also for industrial use. As for its industrial use, two types of X-ray CT have been developed, namely, industrial X-ray CT aimed at a high penetrating ability and microfocus X-ray CT aimed at a high spatial resolution (Fujii and Uyama, 2003). In the present study, the mX-ray CT system, KYOTOGEOmXCT (TOSCANER-32250mHDK), which was assembled by TOSHIBA IT and Control Systems Corporation and installed in the Department of Civil and Earth Resources Engineering of Kyoto University (Photo 2), has been used. The speciˆcations of the system are listed in Table 2. The focus size of the microfocus X-ray tube is very small, 4 mm, which provides the very high spatial resolution of 5 mm. The system also has a high penetrating ability due to the maximum voltage of 225 kV and the maximum current of 1 mA. The voltage and the current can be controlled independently, and the maximum electric power consumption is 200 W. Figure 2 presents a schematic ˆgure of the mX-ray CT system. The microfocus X-ray tube, seen in Photo 2, generates a cone-shaped white X-ray beam. A slice collimator installed just in front of the X-ray tube cuts oŠ the scattered X-rays. A two-dimensional X-ray image intensiˆer, also seen in Photo 2, takes the X-ray attenuation records at diŠerent angles, equally spaced for 3609, by rotating the object on a computer-controlled rotation table (rotate-only method). The X-ray image intensiˆer is a circular device and we can choose the size from 4.5, 6, and 9 inches (114.3 mm, 152.4 mm and 228.6 mm). The maximum projection views and accumulations are 4800 and 50, re-

Table 2. Speciˆcation of the microfocus X-ray CT (KYOTOGEOmXCT)

X-ray source

Work table

Maximum voltage

225 kV

Maximum current

1 mA

Maximum electric power consumption

200 W

Minimum focus size

4 mm

Maximum projection views

4800 (0.0759)

Maximum accumulation per 1 view

50

Maximum size of specimen

q700 mm, h700 mm

Maximum scanning area

q200 mm

Maximum weight of specimen

441 N (45 kgf)

Size of detector Image Intensiˆer Image matrix

9/6/4.5 inch (114.3/152.4/228.6 mm) 5122/10242/20482

Spatial resolution performance 5 mm CT image

Scanning method

Single scan (2D CT image)/Cone-beam scan (3D CT image)

spectively. The X-ray image intensiˆer converts an X-ray photon to visible light, and then the light is transformed to digital data by a CCD camera with selectable pixels of 512×512, 1024×1024, and 2048×2048. Using the data, the computed tomography technique provides a spatial distribution of CT values, i.e., CT images. Each CT value is deˆned as a linear function of linear attenuation coe‹cient m, namely,

CTvalue＝am＋b

(1)

where a and b are constants which arbitrarily chosen by

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Fig. 2.

Schematic ˆgure of the microfocus X-ray CT system

the users. The linear attenuation coe‹cient can be obtained using incident X-ray intensity I0, attenuated X-ray intensity I, and the path length through object x as

I＝I0 exp ( mx )

(2)

Since X-rays generated by a bremsstrahlung source have a broad spectrum, the intensity of each X-ray is given by the integration over the spectrum. The linear attenuation coe‹cient is written as

m＝rmm

(3)

in which r is the density and mm is the mass attenuation coe‹cient. mm depends on the X-ray energy and the atomic number of the object (e.g., Curry et al., 1990). For this reason, in principle, Eqs. (1) and (3) indicate that the relation between the densities and the CT values of several objects is exactly linear only when the CT values are measured under the conditions that the atomic numbers of the objects with diŠerent densities are ideally the same and the X-ray energy levels passing through the objects are constant. This suggests that it is quite di‹cult to precisely quantify the densities of soil specimens by the CT values because soil specimens are inherently heterogeneous even when the X-ray energy levels are constant. However, as can be seen in the literature (e.g., Desrues et al., 1996; Otani et al., 2000), it is empirically known that the CT values of geomaterials have almost a linear relation with the density. Figure 3 shows the relation between the average density of the specimen and the CT values obtained by the mX-ray CT system used in this study with the same scanning conditions ( see Fig. 3, e.g., the voltage is 150 kV and the current is 140 mA). The maximum values, the minimum values and the mode values of the histograms of the CT values for each specimen are plotted. These soil specimens are independent of the specimens used in the triaxial tests described hereinafter. In this ˆgure, we have converted the raw CT values into the Hounsˆeld unit values, in which the CT values of water and air are set to be 0 and －1000, respectively. It can be seen that the relation between the densi-

Fig. 3.

Relation between density and the CT values

ties and the CT values is almost linear. Using this approximate relation, it can be assumed in subsequent CT images that the higher density regions are denoted by the higher CT values in white or light gray, while the lower density regions are indicated by the lower CT values in black or dark gray. The total number of colors is 256. The cone beam technique gives several horizontal CT images in the vertical direction in one scanning; hence, we can ˆnally obtain a complete three-dimensional CT image by visualization software. Since the FCD (distance between the X-ray source and the rotation table) and the FID (distance between the X-ray source and the image intensiˆer) can be chosen independently ( see Fig. 2), the magniˆcation can be determined arbitrarily. The magniˆcation also depends on the user-selectable size of the image intensiˆer. In addition, since the triaxial cell can be mounted on a rotation table, specimens can be scanned during the triaxial tests. The users of mX-ray CT can choose the scanning condi-

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

tions arbitrarily, e.g., voltage and current of X-ray tube, the FID and the FCD, and CT values obtained with diŠerent scanning conditions are diŠerent for an exactly same object. In this sense, the absolute CT values are not always objective. It is, therefore, necessary to calibrate the relation between CT values and density for each scanning condition for mX-ray CT. In the present study, the relative changes and the distributions of CT values obtained under the same scanning conditions are discussed, through which strain localization and microstructural changes are studied.

Triaxial Test Apparatus for Microfocus X-ray CT In order to perform X-ray CT scanning during triaxial tests, the triaxial cell can be mounted on the rotation table of the mX-ray CT system shown in Photo 2. The cell does not have steel pillars to support the axial load because the attenuation of the X-ray, due to the steel, is very large and greatly aŠects the attenuation records detected by the image intensiˆer. Therefore, we have used a thin lucid acrylic cell, 15 mm in thickness, in order to make the cell as transparent as possible. The mechanism of the cell, used to avoid the X-ray attenuation due to the support pillars, is the same as that used in the published research (e.g., Otani et al., 2002; Kikuchi, 2006). Specimens that are 35 mm in diameter and 70 mm in height or 50 mm in diameter and 100 mm in height can be used. In the present study, we used the specimens with the former size. Axial displacement is applied by a screw jack and a DC servo motor. Even when the cell is on the rotation table, conˆning pressure and axial displacement can be applied and all the measurements can continue to be taken without disconnecting the cables. Hence, X-ray scanning can be performed during triaxial tests. Testing Procedure We used the conventional triaxial test procedure in which the moist-tamping method is applied to prepare the partially saturated specimens. Dry Toyoura sand was mixed with distilled water prior to the compaction to be the prescribed water content and then each sample was compacted in a steel split mould in several layers. Initial void ratio and initial saturation of the specimens were controlled by the amount of the wetted sample put into the mould. Air-dried specimens were also prepared by compacting method, but the sand was not mixed with water. After the compaction of each layer, the top surface of the layer was disturbed in order to make the connectivity between the layers homogeneous. For the fully saturated specimen, the water pluviation method was used. The compacting method was not employed for the fully saturated specimen, but the mould was tapped with a wooden hammer in order to achieve the prescribed void ratio. The sample saturation was probably ensured since the results obtained by the present study are consistent with the previous results with high enough B-values done by the authors' research group (e.g., Oka et al., 2002). The height of every specimen is 70 mm and the diameter is 35 mm. A negative pressure of 20 kPa was applied to

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each specimen, and then the split mould was removed and an acrylic cell was installed. After applying the conˆning pressure of 20 kPa, the negative pressure inside the specimen was released. Note that air pressure was used to apply the conˆning pressure to avoid the attenuation of the X-ray when using cell water. The prescribed conˆning pressure for each test was isotropically applied by air pressure under undrained conditions for air and water with the valves for the top and the bottom of the specimen closed. For the dry and the partially saturated sand specimens, the valves were opened to make the pressure inside the specimens equal to the atmospheric pressure, while for the fully saturated sand specimen, the valves were opened and consolidation was started without the use of any back pressure. The triaxial cell was mounted on the rotation table of the CT system and the CT scan was performed for the initial state of the specimen under the conˆning pressure. Then, the triaxial cell was kept on the rotation table and axial compression is initiated. The axial load is applied through a displacement control system with a constant axial strain rate of 0.5z/min under drained conditions for air and water. During the triaxial shearing, threedimensional CT images of the specimen were taken by the cone beam technique every axial strain of 2z. It takes time to scan an entire specimen. For instance, it takes about 20 minutes to scan with 1200 projection views and 10 accumulations. Hence, the axial loading was stopped during the scanning to avoid the movement of the specimen due to the loading. After the scanning, the axial loading was started again with the same axial strain rate.

Partial CT Scan In order to study microstructures, it is necessary to obtain CT images with a high enough spatial resolution to distinguish each soil particle from the others. For this purpose, a partial CT scan has been carried out as well as a full CT scan for the entire specimen. A partial CT scan means that the volume of interest of the specimen is partially scanned. Figure 4 illustrates the schematic ˆgure of a partial CT scan for comparison with a full CT scan. In the case of full CT scanning, a CT image of the entire specimen is obtained, while partial CT scanning nondestructively provides a CT image of a part of the specimen with a much higher magniˆcation. Since the specimen was as close as possible to the X-ray source, in order to

Fig. 4.

Schematic ˆgure of a partial CT scan

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Photo 3.

Partial CT scan of a sand specimen

accomplish higher magniˆcation, it was required that the acrylic cell be removed with a negative pressure of 20 kPa in the specimen as the conˆning pressure, as shown in Photo 3.

Measurement of Volume Changes in the Unsaturated Specimen by CT Images The volume changes in fully saturated specimens under drained triaxial conditions can be measured by the quantity of the water expelled or absorbed, since the compressibility of water and soil particles is very small. On the contrary, it is di‹cult to measure the volume changes in partially saturated specimens owing to the compressibility and the capillary eŠects in the air bubbles. To overcome these di‹culties, methods for measuring these volume changes in unsaturated soil have been studied by several researchers. The methods include the doublewalled triaxial cell method (e.g., Bishop and Henkel, 1957), direct measurements of the axial deformation and the radial deformation of the specimen using an internal LVDT (e.g., Goto et al., 1991; Kolymbas and Wu, 1989), and the digital image processing technique (e.g., Gachet et al., 2007). In the present study, we have measured the volume changes in unsaturated Toyoura sand specimens using CT images. CT values are converted to gray values of fourteen bits by the visualization software VGStudio MAX 2.0 (Volume Graphics GmbH), and a histogram of the gray value is obtained, as shown in Fig. 5. The threshold value, which divides the specimen and the surroundings, is uniquely chosen as a local minimal value between the mode value of the specimen and that of the surroundings. The CT image is transformed into a twovalued image in which the black area denotes the specimen and the white area is the atmosphere. Consequently, the volume of the specimen can be calculated with precision by the integration of the black voxels. The voxel size can be precisely calibrated by the CT scanning of the specimen with known size, by which the accuracy of the proposed method is ensured. Accuracy of this measurement is discussed in the APPENDIX.

Fig. 5. Histogram of the gray value and the schematic ˆgure for calculating the volume by CT images

TEST RESULTS

Testing Program The triaxial compression tests performed in this study are listed in Table 3. The void ratios shown in this table were calculated just before the axial loading, i.e., after applying conˆning pressure, in which the volume of the whole specimen was measured with X-ray CT images as expressed in the foregoing section. It is known that void ratio of loose sand specimen prepared by the moist-tamping method could be larger than the maximum void ratio (e.g., Ishihara, 1993). This is the reason why the relative density for the case of U-1 is negative. Voxel is a three-dimensional unit of CT image indicating spatial resolution and thickness of one CT image. The size of X-ray image intensiˆer was 6 inches (152.4 mm). Each CT image has 1024×1024 voxels. We placed a copper ˆlter, 1 mm in thickness, just in front of the X-ray source prior to transmitting the specimens. This cut the weak X-rays which can induce beam hardening. Comparison between Stress-strain Relations during the Triaxial Tests with and without CT Scanning Figure 6 shows the stress-strain relations for triaxial tests with X-ray CT scanning and without X-ray CT scanning (Case U-0). It is seen that stress relaxation occurs at each step of the scanning process because the axial strain is ˆxed during the scanning. One scanning takes about 40 minutes including the preparation for the scanning. The deviator stress decreases about 10–15z just after the axial loading has been stopped, then the stress level is maintained until the axial loading is started again. After the scanning, the constant axial strain rate of 0.5z/min is applied again and the deviator stress recovers the value at

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

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Table 3. Test cases (a) Specimen conditions Case no. Initial void ratio Conˆning pressure (kPa) Relative density (z) Water content (z) Initial degree of saturation (z) Wet density (g/cm3)

U–0 0.698 50 77 8.14 30.67 1.675

U–1 1.047 200 －20 15.00 37.70 1.478

U–2

U–3

0.858 50 32 15.00 45.98 1.628

0.782 50 53 15.00 50.45 1.697

U–4 0.719 50 71 15.00 54.87 1.759

U–5 0.673 50 84 15.00 58.62 1.852

S–1 0.659 50 88 25.06 100 1.983

D–1 0.652 50 89 0.16 0.66 1.598

(b) Scanning conditions Case no. Voltage (kV) Current (mA) Projection views Accumulation Voxel size† (mm) †

U–0

U–1

U–2

U–3

U–4

U–5

S–1

D–1

150 140 1200 10 532×80

150 140 1200 10 532×81

150 140 1200 10 532×81

150 140 1200 10 532×81

150 140 1200 10 532×90

150 140 1200 10 532×90

150 160 1200 20 512×80

150 140 1200 10 532×90

Voxel size: (spatial resolution)2×(thickness) of one CT image.

Fig. 6. Stress-strain relations for triaxial compression tests with and without X-ray CT scanning (Case U-0)

which the axial loading was stopped. The stress-strain curve obtained by the triaxial tests with X-ray CT scanning is similar to the curve obtained by the usual triaxial tests, namely, without scanning. This means that the stress relaxation time of about 40 min during the X-ray scanning does not signiˆcantly aŠect the behavior of the Toyoura sand specimens under triaxial conditions.

Stress-strain Relations and Strain Localization in Airdried, Partially Saturated, and Fully Saturated Sand Specimens The stress-strain relations for the triaxial compression tests on partially saturated, fully saturated, and air-dried sand specimens are shown in Figs. 7(a)–(c), respectively. The initial void ratios for the three tests are almost the same. It can be seen that the peak stress level of the partially saturated specimen is higher than that of the fully saturated specimen, and that the peak deviator stress of the air-dried specimen is lower than that of the fully saturated specimen. For the axial strain at the peak deviator

stress level, the strain at the peak stress of the partially saturated specimen is the smallest, i.e., 3.0z, and that of the air-dried specimen is the largest. These results suggest that partially saturated sand is more brittle than the other types of sand. Since the pore water of the partially saturated specimen exists as meniscus water, which produces the above-mentioned capillary force among the soil particles, the partially saturated specimen exhibits higher peak stress than the other specimens. However, the degradation of this capillary force during the shearing results in softening behavior. The possible reason why the peak stress for the fully saturated specimen is higher than that for the air-dried specimen is the diŠerence of the sample preparation method; namely, the air-dried specimen was prepared by the air pluviation, while the fully saturated specimen was prepared by the water pluviation. This is consistent with the experimental results that the shear strength of the specimens prepared by water pluviation (or sedimentation) is higher than that by air pluviation (e.g., Mulilis et al., 1977; Tatsuoka et al., 1986; Zlatovi ác and Ishihara, 1997). In addition, it is worth noting that the residual stress levels at an axial strain of 20z are almost the same for all three cases. This means that the steady states of the sand specimens are not in‰uenced by the degree of saturation. The relation between the volumetric strain and the axial strain is also shown in Fig. 7. The volume of the specimens has been measured by the above method, namely, the integration of the voxels in the CT image, even in the case of the fully saturated specimen. A low level of volume compression can be observed in the early stages of loading, e.g., at an axial strain of 2z, for the partially saturated specimen. Finally, all the specimens exhibit volume expansion. The volumetric strain levels at an axial strain of 20z are almost the same for all three cases. It seems that the drained condition for the fully saturated case was almost satisˆed since volumetric strain for the fully saturated specimen is almost the same as that of airdried one.

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Fig. 8.

Fig. 7. Deviator stress-axial strain relations and volumetric strain-axial strain relations for triaxial compression tests on partially saturated sand, fully saturated sand, and air-dried sand (Solid lines: deviator stress; Open marks with lines: volumetric strain; Compression is positive)

Locations of the cross sections

The locations of the cross sections are illustrated in Fig. 8. CT images for the partially saturated, the fully saturated, and the air-dried sand specimens are shown in Figs. 9–11, respectively. In each test, X-ray CT scanning has been performed at an axial strain of every 2z. In each ˆgure, the color tones of CT images at diŠerent axial strains are set to be the same. In the case of the partially saturated specimen, the lower density region, shown in black, can be seen at the center of the specimen at an axial strain of 4z. Then, several lower density regions are clearly seen to develop from an axial strain of 10z. Let us consider the lower density regions. Compared with the CT image at the initial state, volume expansion probably occurs in the lower density regions. The volume expansion is partly attributed to positive dilatancy, caused by shearing, because the results in Fig. 7(a) show that the whole specimen exhibits volume expansion with deviator stress, namely, shear stress, which suggests that the local volume expansion may be associated with the local shear deformation. Meanwhile, shear band can be deˆned as a thin layer that is bounded by two parallel material discontinuity surfaces of the incremental displacement gradient (Vardoulakis and Sulem, 1995). It can be seen in Figs. 9–11 that the boundaries between the lower density regions and the others are clear and the regions between the boundaries form band-like shapes. Thus, we can assume the lower density regions as shear bands. It is worth noting that shear deformation and volumetric strain can be quantiˆed by some image analysis techniques using CT images (e.g., Lenoir et al., 2007) if it is deˆnitely concluded that the lower density regions correspond to shear bands. It is clearly seen in Fig. 9 that several shear bands develop from an axial strain of 10z. The localization mode can be observed in the partially saturated specimen. The cone type of shear bands develop from the top and the bottom of the specimen, while radial shear bands appear in the middle of the specimen. The localization mode is similar to that in the results, e.g., Desrues et al. (1996) and Alshibli et al. (2000), in which the shear bands developed in the dense sand specimens are indicated by the lower density regions in the CT images. As seen in Fig.

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

Fig. 9.

103

CT images for partially saturated triaxial sand specimen (Case U-5)

Fig. 10.

CT images for fully saturated triaxial sand specimen (Case S-1)

10, the development of shear bands in the case of the fully saturated specimen is rather late compared to that of the partially saturated specimen. In other words, clear shear bands can be observed in the fully saturated sand specimen at an axial strain of 12z. Note that the black horizontal straight line seen in the CT images in Fig. 10 is an accidental artifact due to the slice collimator; it does not aŠect the CT values of the other parts. In the case of the air-dried sand specimen, seen in Fig. 11, the development of shear bands is seen at an axial strain of 14z,

which is later than both the fully and the partially saturated specimens. When shear bands start to develop, the axial strain for each case is almost the same as that at the peak stress level. As for the strain localization mode, the shear bands that developed in the partially saturated specimen are the clearest among these three cases. In the fully saturated case, it is seen that the shear bands developed from the top of the specimen; however, the number of shear bands is fewer than that in the partially saturated case. The

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Fig. 11.

CT images for air-dried triaxial sand specimen (Case D-1)

strain localization for the air-dried case is not so clear. It is also seen that the extent of the volume expansion region at the center of the specimen, shown in black for both the fully saturated and the air-dried specimens, is wider than that of the partially saturated specimen. This suggests that the strain localization behavior of the partially saturated sand specimen is signiˆcant because of the strain softening brought about by the degradation of the capillary force. In the case of the fully saturated specimen, the stressstrain behavior is more ductile than that of the partially saturated specimen and is stronger than that of the airdried specimen. In addition, the development of clear shear bands in the partially saturated specimen is consistent with strain softening, i.e., a large decrease in deviator stress in the stress-strain relation.

EŠect of the Initial Void Ratio on the Strain Localization of Partially Saturated Sand Stress-strain relations and volume changes measured with X-ray CT images for triaxial tests with diŠerent initial void ratios are shown in Fig. 12. It is seen in the cases of U-2, U-3, U-4, and U-5, with the same conˆning pressure of 50 kPa, that the specimens with smaller initial void ratios show higher peak stress and lower axial strain at the peak stress. From this ˆgure, it is seen that the specimens with larger initial void ratios exhibit compression behavior, while the specimens with smaller initial void ratios show volume expansion. The volume expansion probably due to positive dilatancy with smaller initial void ratio is larger. Initial degrees of saturation are also diŠerent among the test cases as a result of the diŠerent void ratios with the same water content. As for the eŠect of the initial degree of saturation, the specimens

with smaller initial degrees of saturation show lower deviator stress and the larger volumetric strain although strength of partially saturated soils with smaller degree of saturation is generally higher than that with larger degree of saturation. This means that the eŠect of the initial void ratio is more signiˆcant than that of the initial saturation on the stress-strain relation and the dilatancy behavior seen in the present study. The CT images at the initial state and after the tests are shown in Fig. 13. In the case of U-1 and U-2, a few white regions can be seen in the CT images before the test, which seem to be aggregates created by several soil particles being bonded together by the water meniscus. This is probably because the moist-tamping method is used to prepare the specimens. It can be seen in the cases with larger initial void ratios, U-1, U-2, and U-3, that the specimens deform to barrel-like shapes and shear bands cannot be seen clearly, i.e., these specimens show the diŠuse failure mode. On the other hand, for the specimens in Cases U-4 and U-5, it is clear that cone-shaped shear bands and radial shear bands develop. Figure 14 shows changes in void ratio and degree of saturation of the entire specimens calculated by the volumetric strain. Void ratios and degrees of saturation in the cases with the same conˆning pressure (U-2, U-3, U-4, and U-5) become closer to each other at the residual state. In particular, void ratios and degree of saturation at an axial strain of 20z in the cases of U-4 and U-5 are almost the same, in which the relatively clearer shear bands can be seen. On the other hand, in the cases of U-2 and U-3 with the diŠuse failure mode, void ratios are rather higher and degrees of saturation are rather lower than those in the cases of U-4 and U-5. It is necessary to discuss further by local void ratio in shear bands as reported

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

Fig. 12.

105

Stress-strain relations and volumetric strain-axial strain relations for partially saturated sand specimens with diŠerent initial void ratios

Fig. 13.

CT images for partially saturated sand specimens with diŠerent initial void ratios

for air-dried sand specimens in Desrues et al. (1996) as well as local degree of saturation. It is seen in the stress-strain relations that the residual stress levels for the cases with the same conˆning pressure of U-2, U-3, U-4, and U-5 are almost the same. In addition, it is worth mentioning that the residual stress levels for the partially saturated sand, the fully saturated sand, and the air-dried specimen, shown in Figs. 7(a)–(c), respectively, are almost the same. In other words, sand specimens with diŠerent initial void ratios and diŠerent degrees of saturation under the same conˆning pressure

reach almost the same steady state.

Visualization of Microstructures in Partially Saturated Sand Partial CT scans have been carried out at the initial state and at an axial strain of 20z for the case U-4. Figure 15 shows three-dimensional partial CT images and the location of the partial CT scan. As shown in this ˆgure, a partial CT scan has been performed at the center of the specimen, where the volume expansion, shown in black, occurs probably due to dilatancy. The scanned

106

Fig. 14.

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Changes in void ratio and degree of saturation of the entire specimens for partially saturated sand calculated by the volumetric strain

Fig. 15. Three-dimensional partial CT images and the location of the partial CT scan (Case U-4)

area is a cylinder with a diameter of 5.42 mm and a height of 3.06 mm. The voxel size of the partial CT image is 5.292×9.00 ( mm). The partial CT images of the axial cross section and the frontal cross section for the partially saturated sand are shown in Figs. 16 and 17, respectively. It is seen in the axial cross section and the frontal cross section at an axial strain of 20z that the white regions denote soil particles and the black or gray regions are the voids. The black area is the air void and the gray area is the pore water existing as the water meniscus or the bulk water, because the gray area can be seen among the soil particles existing close to each other. The partial CT image for the air-dried sand (Case D-1), scanned under the same conditions as the partially saturated case, is shown in Fig. 18. In the case of air-dried sand, the CT image is

characterized by white and black, namely, air-dried sand is composed of soil particles and air voids. This is because the water content is very small, 0.66z, as shown in Table 3. Now we will discuss the black, grey, and white regions in the CT images for the partially saturated sand and the air-dried sand. Figure 19 shows the relation between the material density and the CT values in the partial CT images for soil particles, the water, and the air. The scanning conditions for Figs. 16 and 18 are exactly the same. Since it is empirically known that the relation between the material density and the CT values is linear, the black, grey, and white regions indicate air, water, and soil particles, respectively. It can be seen in Figs. 16 and 17 that the aggregates consist of soil particles and void water. Aggregates are also seen in the CT image (A-2) shown in Fig. 15 denoted by the white area. These aggregates form when the specimen is prepared by the moist-tamping method and remain until an axial strain of 20z. The frontal cross section of the partial CT image at the initial state is shown in Fig. 20. Note that the locations of the partial CT images at both the initial state and at an axial strain of 20z are at the center of the specimen, but their positions are not exactly the same. It is very di‹cult to conduct partial CT scans at exactly the same positions for these two states because the position of the scanned area at the initial state changes after the axial compression. It is also seen that pore water and pore air exist in the voids at the initial state. Since volume expansion is observed at the center of the specimen, partly brought about by the dilatancy seen in the full CT images in Fig. 15, large voids can be found due to the rotation of soil particles and/or the aggregates which consist of soil particles and a water meniscus in the partial CT images. These large voids are also seen in the results for the airdried Toyoura sand specimen observed by Oda et al. (2004) using the mX-ray CT. In addition, the water meniscus cannot be seen in the large voids, probably because

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

107

Fig. 16. Partial CT image for partially saturated sand (Case U-4, axial strain: 20%, axial cross section)

Fig. 18. Partial CT image for air-dried sand (Case D-1, initial state, axial cross section)

Fig. 17. Partial CT image for partially saturated sand (Case U-4, axial strain: 20%, frontal cross section)

Fig. 20. Partial CT image for partially saturated sand (Case U-4, initial state, frontal cross section)

Fig. 19. Relation between density and the CT values in the partial CT images for the partially saturated and the air-dried sand specimens

the water meniscus is broken by the rotation of the soil particles.

Microstructures in the Shear Bands of Partially Saturated Sand For case U-5, partial CT scans have been performed. The scanned area is a cylinder with a diameter of 7.02 mm and a height of 3.74 mm. The voxel size of the partial CT image is 6.862×11.0 ( mm). The location and the area of the partial CT scan are shown in Fig. 21. The partial CT images near the shear bands are shown in Figs. 22 and 23. The region of shear band indicated between the two dashed lines in Fig. 22 corresponds to the lower density region observed in Fig. 21. Using the relationship between the CT values and the densities of the soil particles, the pore water, and the pore air, we can distinguish them in the partial CT images. In the CT image shown in Fig. 22, the black area indicates the volume expansion partly due to dilatancy, while in the partial CT image in Fig. 23 with the higher spatial resolution, it is seen that the void areas in the shear band are larger than those outside of the shear band. It can be seen in the three-dimensional CT image that the intersectional area between the soil particles inside of the shear band is smaller than that outside of the specimen. Figure 24 shows a slice of the partial CT image of Fig. 23 with a thickness of 0.1 mm, corre-

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108

Fig. 21.

CT images and the location of the partial CT scan (Case U-5, axial strain: 20%, before being unloaded)

Fig. 22. Partial CT image (Case U-5, axial cross section, after being unloaded)

sponding to roughly half of the average diameter of a Toyoura sand particle. In Fig. 24, chain-like structures in the shear band, loosely connected particles, are depicted. The structures cross the shear band with small contact areas between the particles. This structure is similar to the ``Columnar structure'' observed in the shear bands of the dry sand specimens after the plane strain compression tests by Oda et al. (2004). The columnar structure developed in the shear band results in a large void ratio and sustains the axial force. A handwritten sketch of the soil particles, the pore water, and the pore air of section B shown in Fig. 22 is illustrated in Fig. 25 to emphasize the boundaries among the three phases. The soil particles in the shear band are denoted by the gray color. A greater area of water meniscus can be seen outside of the shear band than inside of it. Pore water cannot exist as a water meniscus because the soil particles rotate largely and the voids in the shear band

Fig. 23. Three-dimensional partial CT image (Case U-5, after being unloaded)

become large. On the other hand, pore water can easily form a meniscus at the initial state of the dense sand specimen because the soil particles are close to each other and the contact area is much wider than that in the shear bands. The thickness of the shear band is 1.8 mm which corresponds to 10 times the average diameter of Toyoura sand. This ˆnding is consistent with that obtained for dry Toyoura sand by Oda et al. (2004), namely, 10 times the particle diameter. As mentioned above, the microstructures of partially

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND

Fig. 24. Columnar structure in a shear band (Case U-5, white solid lines indicate the outline of the columnar structure, white dotted lines are the boundaries of the shear band)

Fig. 25. Sketch of the soil particles, the pore water, and the pore air (Case U-5, grey: shear bands, blue: water meniscus)

saturated sand and air-dried sand are similar in their shear bands. In addition, the residual states of fully saturated sand, partially saturated sand, and air-dried sand are almost the same. At residual states, in which soils reach the critical state with development of clear shear bands, it can be assumed that most of deformation due to external loading occurs in the shear bands; hence, the stress-strain relation for the whole specimen is governed mainly by the behavior in the shear bands. This suggests that the behavior at the critical state of sand is unique and is almost independent of the initial degree of saturation. As can be seen in Fig. 25, however, it is possible to say that the water meniscus remaining in the shear bands increases the shear strength of the partially saturated sand. Further study is required on this point through comparison among microstructural changes in shear bands for air-dried, fully saturated and partially saturated sands. CONCLUSIONS In this paper, the strain localization behavior and microstructural changes in partially saturated Toyoura

109

sand during and after triaxial compression under drained conditions for air and water have been studied using microfocus X-ray CT through a comparison of the drained triaxial test results for fully saturated sand and for air-dried sand specimens. The main conclusions are as follows: 1) Strain localization behavior in partially saturated and fully saturated sand specimens has been visualized by mX-ray CT scans. Shear bands were seen to have developed more clearly in the partially saturated sand than in the fully saturated or air-dried sand. The stress-strain relations for partially saturated sand exhibited stronger softening behavior than those for the fully saturated or the air-dried sand. 2) The partially saturated specimens with relatively higher initial void ratios have shown the diŠuse failure mode, while clear shear bands have been seen in the specimens with smaller initial void ratios. The eŠect of initial saturation on the triaxial behavior of partially saturated sand is not signiˆcant when comparing with the eŠect of initial void ratio in the present study. 3) The stress levels and the volumetric strain levels at the residual state of fully saturated sand, air-dried sand, and partially saturated sand with various initial void ratios were found to be almost the same. This suggests that the steady state of sand is not in‰uenced by the initial void ratio or by the degree of saturation under the same conˆning pressure. From the microscopic point of view, further studies on localized zones are necessary in order to conˆrm this conclusion. 4) The microstructures of partially saturated triaxial sand specimens have been successfully viewed by partial CT scans. Through a comparison between the microstructures in the shear bands and the initial state and between the microstructures inside of and outside of the shear bands, the voids in the shear bands have been found to be much larger than those at the initial state or outside of the shear bands. 5) The soil particles in the shear bands make contact with each other in a smaller area than those outside of the shear bands and at the initial state. This structure is similar to the ``columnar structure'' observed in the air-dried Toyoura sand specimen reported by Oda et al. (2004). 6) The behavior observed in the partially saturated sand specimen is more brittle than that in the fully saturated or the air-dried sand specimen, because the voids inside of the shear bands are very large and the bonding between the soil particles due to the water meniscus is broken inside of the shear band. Since the residual states of partially saturated sand, fully saturated sand, and air-dried specimens are almost the same and the microstructures in the shear bands of partially saturated sand and airdried specimens are similar, the behavior of the sand in the critical state seems to be uniquely in-

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dependent of the initial degree of saturation. 7) The volume changes in the partially saturated sand specimens during triaxial tests under drained conditions for both air and water can be measured accurately using mX-ray CT scans, although it is di‹cult to measure the volume changes in partially saturated soil by the existing methods, such as the double cell method, direct measurements of the axial and the radial deformation of the specimen using internal LVDT, or the digital image processing technique.

15)

16)

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REFERENCES 1) Alshibli, K. A., Sture, S., Costes, N. C., Frank, M. L., Lankton, M. R., Batiste, S. N. and Swanson R. A. (2000): Assessment of localized deformations in sand using X-ray computed tomography, Geotechnical Testing Journal, 23(3), 274–299. 2) Bishop, A. W. and Henkel, D. J. (1957): Measurement of Soil Properties in the Triaxial Test, Edward Arnold. 3) Cunningham, M. R., Ridley, A. M., Dineen, K. and Burland, J. B. (2003): The mechanical behaviour of a reconstituted unsaturated silty clay, G áeotechnique, 53(2), 183–194. 4) Curry, T. S., Dowdey, J. E. and Murry, R. C. (1990): Christensen's Physics of Diagnostic Radiology, Lea and Febiger, London. 5) Desrues, J., Chambon, R., Mokni, M. and Mazerolle, F. (1996): Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography, G áeotechnique, 46(3), 539–546. 6) Fujii, M. and Uyama, K. (2003): Recent advances on X-ray CT, Xray CT for geomaterials, soils, concrete, rocks, Proc. First International Workshop on X-ray CT for Geomaterials, GeoX2003, Kumamoto, Japan, (eds. by Otani, J. and Obara, Y.), Balkema, 1–12. 7) Gachet, P., Geiser, F., Laloui, L. and Vulliet, L. (2007): Automated digital image processing for volume change measurement in triaxial cells, Geotechnical Testing Journal, 30(2), 98–103. 8) Goto S., Tatsuoka, F., Shibuya, S., Kim, Y.-S. and Sato, T. (1991): A simple gauge for local small strain measurements in the laboratory, Soils and Foundations, 31(1), 169–180. 9) Hall, S. A., Lenoir, N., Viggiani, G., Desrues, J. and B áesuelle, P. (2009): Strain localization in sand under triaxial loading: characterization by X-ray micro tomography and 3D digital image correlation, Proc. First International Symposium for Computational Geomechanics, (eds. by Pietruszczak, S., Pande, G. N., Tamaganini, C. and Wan, R.), ComGeo I, 29 April–1 May 2009, Juan-lesPins, France, (CD-ROM) 447–456. 10) Higo, Y., Oka, F., Kimoto, S., Sanagawa, T., Sawada, M., Sato, T. and Matsushima, Y. (2010): Visualization of strain localization and microstructures in soils during deformation using microfocus X-ray CT, Advances in Computed Tomography for Geomaterials, Proc. 3rd International Conference on X-ray CT for Geomaterials, (eds. by Alshibli, K. A. and Reed, A. H.), March 1–3, 2010, New Orleans, Louisiana, USA, GeoX2010, ISTE Ltd., John Wiley & Sons, Inc., 43–51. 11) Hounsˆeld, G. N. (1972): A method of and apparatus for examination of a body by radiation such as X-ray or gamma radiation, The Patent O‹ce, London, England, British Patent Number GB1283915. 12) Ishihara, K. (1993): Liquefaction and ‰ow failure during earthquakes, G áeotechnique, 43(3), 351–415. 13) Kikuchi, Y. (2006): Investigation of engineering properties of manmade composite geo-materials with micro-focus X-ray CT, Advances in X-ray tomography for geomaterials, Proc. Second International Workshop on X-ray CT for Geomaterials, GeoX 2006, Aussois, France, (eds. by Desrues, J., Viggiani, G. and B áesuelle, P.), ISTE, Ltd., 255–261. 14) Kodaka, T., Oka, F., Otani, J., Kitahara, H. and Ohta H. (2006a):

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Experimental study of compaction bands in diatomaceous mudstone, Advances in X-ray tomography for geomaterials, Proc. Second International Workshop on X-ray CT for Geomaterials, GeoX 2006, Aussois, France, (eds. by Desrues, J., Viggiani, G. and B áesuelle, P.), ISTE, Ltd., 255–261. Kodaka, T., Oka, F., Kitahara, H., Ohta, H. and Otani, J. (2006b): Observation of compaction bands under triaxial conditions for diatomaceous mudstone, Proc. Int. Symp. on Geomechanics and Geotechnics of Particulate Media, Ube Yamaguchi, Japan, Sep. 12–14, (eds. by Hyodo, M., Murata, H. and Nakata, Y.), Taylor & Francis, 69–75. Kolymbas, D. and Wu, W. (1989): A device for lateral strain measurement in triaxial tests with unsaturated specimens, Geotechnical Testing Journal, 12(3), 227–229. Lenoir, N., Bornert, J., Desrues, J., B áesuelle, P. and Viggiani, G. (2007): Volumetric digital image correlation applied to X-ray microtomography images from triaxial compression tests on argillaceous rock, Strain, 43, 193–205. Matsushima, T., Uesugi, K., Nakano, T. and Tsuchiyama, A. (2006): Visualization of grain motion inside a triaxial specimen by micro X-ray CT at SPring-8, Advances in X-ray tomography for geomaterials, Proc. Second International Workshop on X-ray CT for Geomaterials, GeoX 2006, Aussois, France, (eds. by Desrues, J., Viggiani, G. and B áesuelle, P.), ISTE, Ltd., 255–261. Mulilis, J. P., Seed, H. B., Chan, C. K., Mitchell, J. K. and Arulanandan, K. (1977): EŠects of sample preparation on sand liquefaction, Journal of the Geotechnical Engineering Division, ASCE, 103, GT2, 91–108. Oda, M., Takemura, T. and Takahashi, M. (2004): Microstructure in shear band observed by microfocus X-ray computed tomography, G áeotechnique, 54(8), 539–542. Oka, F., Kodaka, T., Ohno, Y., Takato, J., Takyu, T. and Nishimatsu, N. (2002): Observation of eŠectiveness of improvement for sands by permeation grouting under drained triaxial conditions, Proc. JSCE Annual Meeting, Sapporo, III-094, 187–188 (in Japanese). Otani, J., Mukunoki, T. and Obara, Y. (2000): Characterization of failure in sand under triaxial compression using an industrial X-ray CT scanner, Soils and Foundations, 40(2), 111–118. Otani, J., Mukunoki, T. and Obara, Y. (2002): Characterization of failure in sand under triaxial compression using an industrial X-ray CT scanner, International Journal of Physical Modelling in Geotechnics, 1, 15–22. Otani, J., Pham, K. D. and Sano, J. (2006): Investigation of failure patterns in sand due to laterally loaded pile using X-ray CT, Soils and Foundations, 46(4), 529–535. Tatsuoka, F., Ochi, K., Fujii, S. and Okamoto, M. (1986): Cyclic undrained triaxial and torsional shear strength of sands for diŠerent sample preparation methods, Soils and Foundations, 26(3), 23–41. Vardoulakis, I. and Sulem, J. (1995): Bifurcation Analysis in Geomechanics, Blackie Academic & Professional, 1995. Viggiani, G., B áesuelle, P., Hall, S. A. and Desrues, J. (2010): Sand deformation at the grain scale quantiˆed through X-ray imaging, Advances in Computed Tomography for Geomaterials, Proc. 3rd International Conference on X-ray CT for Geomaterials, (eds. by Alshibli, K. A. and Reed, A. H.), March 1–3, 2010, New Orleans, Louisiana, USA, GeoX2010, ISTE Ltd., John Wiley & Sons, Inc., 43–51. Zlatovi ác, S. and Ishihara, K. (1997): Normalized behavior of very loose non-plastic soils: eŠect of fabric, Soils and Foundations, 37(4), 47–56.

APPENDIX: ACCURACY OF THE MEASUREMENT METHOD OF VOLUME OF UNSATURATED SOIL SPECIMENS BY CT IMAGES In order to examine the accuracy of the measurement method of volume of unsaturated soil specimens by CT

MICROSTRUCTURAL CHANGES IN UNSATURATED SAND Table A1.

111

Comparison between the volume of the specimen at the initial state calculated by the CT images and that by the height and the diameter Case no.

3

Vct (cm ): Volume calculated by the CT images Vms (cm3): Volume calculated by the height and the diameter Error (z): (Vct－Vms)/Vms×100

images, comparison between the volume calculated by CT images and that by the height and the diameter is listed in Table A1. The range of error is less than ±1z. In this method, the accuracy is not dependent on the way to choose the threshold value, which divides the specimen and the surroundings, since the threshold value is uniquely chosen as the minimal value between the mode value of the specimen and that of the surroundings. Since partially saturated soils contain pore air in the specimen, one voxel may be occupied by pore air only, namely, the white voxel indicating air may exist in the

U-1

U-2

U-3

U-4

U-5

S-1

D-1

67.03 67.14 －0.16

69.79 69.44 0.50

73.37 72.73 0.87

70.34 69.87 0.67

69.36 69.44 －0.12

68.95 68.90 0.08

67.64 67.90 －0.38

specimen. This results in the underestimation of the volume of the specimens. In this study, however, the white voxels inside the specimen were very few. This is because the voxel size of about 502×80 mm is rather large comparing with the size of pore air formed by the sand grains with D50 of 185 mm and the pore water. When employing much smaller voxel size, a number of white voxels may exist in the specimen. In such case, the boundaries between the specimen and the surroundings are determined ˆrstly, and then the volume can be measured by integrating the voxels inside the boundaries.