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Effects of Specimen Size and Some Other Factors on the Strength and
Deformation of Granular Soil in Direct Shear Tests
Article in Geotechnical Testing Journal · January 2008
DOI: 10.1520/GTJ100773
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Geotechnical Testing Journal, Vol. 31, No. 1
Paper ID GTJ100773
Available online at: www.astm.org
Po-Kai Wu,1 Kenichi Matsushima,2 and Fumio Tatsuoka3
Effects of Specimen Size and Some Other
Factors on the Strength and Deformation of
Granular Soil in Direct Shear Tests
ABSTRACT: Four direct shear (DS) apparatuses having different sizes with the specimen lengths ranging from 40 to 800 mm were constructed in
the study. The vertical and shear stresses acting on the shear zone were measured as accurately as possible confirming its importance. Noticeable
effects of specimen shape were observed. The effects of specimen size were evaluated by performing constant pressure DS tests on a fine poorly
graded sand (Toyoura sand) in the small, semimedium, medium and large DS apparatuses and a well-graded sandy gravel in the medium DS
apparatus. The residual shear strength of Toyoura sand was independent of the specimen size and initial density. Due likely to specimen size effects
on both progressive failure and boundary mechanical restraint, the peak strength decreased with an increase in the specimen size. As the specimen
size increased with dense Toyoura sand and as the particle size increased in the medium DS tests, the shear displacement at the peak stress and the
ultimate volume increase at the residual state consistently increased while the postpeak strain softening became slower. These specimen size effects
can be attributed to the thickness of shear zone and the number of shear bands included in the shear zone.
KEYWORDS: Direct shear test, Granular material, Scale effect, Shear band, Shear strength, Shear zone, Dilatancy
Introduction
The direct shear (DS) test (or the shear box test) using a pair of rigid
shear boxes has been and is widely employed in Geotechnical Engineering practice and research to evaluate the shear strength as
well as the shear stress, shear displacement and volume change relations of geomaterial. Such a popular use as above is due mainly to
its relatively simple apparatus and test operation while it represents
many typical shear failure modes in the field. Furthermore, it is
usually considered that the interpretation of results from the DS
tests is rather straightforward. Despite the above, the DS test has the
following inherent drawbacks:
a.
b.
c.
In the DS test, the peak angle of the stress obliquity along the
horizontal shear plane, ␾DS, which is in the zero-extension
direction, is defined as the frictional angle. However, Pradhan
et al. (1988a & b) showed that the ␾DS value is considerably
smaller than the angle of internal friction, ␾, defined in terms
of the effective major and minor principal stresses in simple
shear tests on Toyoura sand. This serious problem with the DS
test is usually not recognized, as it is not possible to evaluate
the ␾ value mobilized in the shear zone in the DS test.
Usually local strains in the shear zone cannot be accurately
evaluated, as it is usually very difficult to evaluate reliably the
shear zone thickness and the deformation pattern of shear
zone.
The stress and strain conditions in the shear zone become in-
Manuscript received August 23, 2006; revised March 9, 2007; accepted for
publication May 23, 2007; published online August 2007.
1
Assistant Professor, Department of Construction Engineering, National
Yunlin University of Science and Technology, Yunlin, Taiwan, R.O.C. Corresponding author; electronic mail:wupokai@yuntech.edu.tw
2
Research Engineer, National Research Institute of Rural Engineering, Kannondai, Tsukuba City, Ibaraki, Japan.
3
Professor, Department of Civil Engineering, Tokyo University of Science,
2641, Yamazaki, Noda City, Chiba, 278-8510, Japan.
evitably nonuniform in the shear direction resulting in a sort
of progressive failure. This factor is affected by the specimen
size (i.e., one type of size effect) and not well understood.
d. The free development of shear zone may be restrained by
boundary effects to a larger extent with a smaller specimen
size relative to the particle size. Perhaps by this factor, the
measured relationships among the shear stress, the shear displacement and the volume change of a given type of granular
material are prone to significant effects of the specimen size
relative to the particle size (e.g., Palmeira and Milligan,
1989). This is another type of size effect, and not well understood either.
In addition, the following two artificial factors often become important:
e.
f.
The stress and strain conditions become more nonuniform by improper boundary mechanical conditions of
the shear boxes, which can have significant effects on the
measured strength and dilatancy characteristic (Mikasa,
1960; Jewell and Worth, 1987; Shibuya et al., 1997).
It is often very difficult to accurately evaluate the average normal and shear stresses acting on the shear zone.
Related to problems e and f, three types of direct shear boxes are
currently in use (Fig. 1, Shibuya et al., 1997). Figure 2 schematically shows the standard commercial small-size DS apparatus according to ASTM D3080. This type, which is categorized into type
A in Fig. 1, has the following major inherent drawbacks (Jewell and
Worth, 1987). That is, as the normal load is applied to the center of
the top loading platen that is not fixed against rotation, no moment
is applied about its center of the top loading platen. Then, when the
soil specimen inside the top shear box is subjected to compressive
load from the sidewall of the top shear box, the distribution of vertical (i.e., normal) stress along the shear zone (at the mid-height of
specimen) becomes inevitably biased (so does the shear stress) to
maintain the equilibrium of moment within the specimen (for ex-
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2 GEOTECHNICAL TESTING JOURNAL
FIG. 1—Three types of direct shear boxes currently in use (modified from Fig. 4
of Shibuya et al., 1997).
ample, about the center of the shear zone, denoted by the letter ‘C’
in Fig. 2), which results in a more progressive mobilization of the
peak shear strength along the shear zone. Furthermore, the vertical
load applied to the top loading platen becomes different from the
vertical load acting on the shear zone due to the friction acting
along the inner surface of the top shear box caused by the volume
changes of the specimen.
To alleviate these problems described above and others, Mikasa
(1960) proposed a modified DS apparatus which rigidly fixes the
top platen against rotation (Takada, 1993). This type of DS apparatus is categorized into “type C measuring the normal load acting at
the top platen, Wupper” in Fig. 1. Later, Shibuya et al. (1997) showed
that, in case the upper shear box is fixed against vertical movement,
the value of Wupper still underestimates the true value acting on the
shear zone when the specimen is dilating. For this reason, Shibuya
et al. (1997) proposed to measure the whole vertical load acting at
the bottom box (type C measuring Wlower in Fig. 1). With this type,
the relative movement between the specimen and the lower shear
box is very small. It is not known whether the vertical load acting
on the upper face of the bottom loading platen, Winner, is free from
the effects of side wall friction.
Type B in Fig. 1 is another type of DS apparatus, which has the
top loading plane and the upper shear box that are rigidly connected
to each other forming one unit in such a way that they can move
vertically together and freely without rotation relative to the lower
shear box (e.g., Jewell and Worth, 1987; Qiu et al., 2000). To accurately evaluate the value acting on the shear zone, they measured
the normal load, W, acting at the top platen, while taking into account the self weight of the specimen and the upper shear box. This
stress measuring method is in principle the same as “type C measuring Wlower.” The relative movement between the specimen and
the shear boxes is smallest with the type B. Unlike a constant spacing between the upper and lower shear boxes with type C, the spacing changes according to volume changes of specimen with type B.
With respect to the specimen size effect (problems c and d),
Scarpelli et al. (1982) showed that multiple shear bands developed
due to a large freedom for strain localization to take place in a long
specimen of a fine sand. Jewell and Worth (1987) defined the shear
box size by a ratio of the specimen length to the mean particle diameter, L / D50. Despite that they suggested that the proper ratio of
L / D50 is in a range from 50 to 280, they did not show a rationale for
that. Palmeira and Milligan (1989) used three shear boxes having
ratios of L / D50 ranging from 75 to 1,250. They reported that, within
the test conditions they examined, the shear box size did not significantly affect the peak friction angle and peak dilation angle of Silver Leighton Buzzard sand 共D50 = 0.8 mm兲, but it had large effects
FIG. 2—Schematic diagram of a direct shear test according to the guidance of
ASTM D3080-90.
on the shear zone thickness and associated volumetric change.
However, the detailed and direct observations of the shear zones
that developed in the shear boxes having different sizes were not
reported.
Moreover, different specimen shapes (i.e., disk-shaped with a
circular cross section in most cases and cubic or rectangular prismatic in the other cases) are used. However, reports on the effects of
this factor cannot be found in the literature.
In view of the above, the present study was performed to evaluate:
1.
2.
3.
effects of some mechanical configurations of the shear box,
which is in particular important to find the relevant method
to accurately measure the vertical load acting on the shear
zone (by using a small DS apparatus);
effects of specimen shape (by using a small size DS apparatus); and
specimen size effects on the measured strength and deformation characteristics by using four DS apparatuses having
largely different sizes (40, 120, 300, and 800 mm in length)
while using fine and coarse granular materials.
Figure 3 shows the relationships between the specimen length,
L, and the mean diameter, D50, for the DS tests performed in the
present study. The numbers of shear band indicated in this figure
FIG. 3—Relationships between specimen length L and particle mean diameters
D50 in the present study, compared with the one in the study of Palmeira and
Milligan (1989).
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TABLE 1—DS apparatuses with four different sizes used in the present study
Specimen sizea
(unit: mm)
Disk-shaped
Type in Fig. 1
Type C
(upside down
configuration)
Notes
Two versions; i.e., simple [Figs. 4(a) and 4(b)] and complicated
[Figs. 4(c) and 4(d)].
L = W = 40; & H = 20
L = W = H = 120
Type B
Medium
L = W = H = 300
Type B
Large
L = 800; W = 500;
& H = 600
Type B
The same design principles as the
medium DS apparatus.
Modified from Qiu et al. (2000).
See Figs. 5 and 6.
The same design principles as the
medium DS apparatus.
DS apparatus
Small
␾ = 60; & H = 20
Rectangular
Semimedium
␾: diameter. W: width. L: length. H: height.
a
are explained later in this paper. The employed range of the ratio
L / D50 was from about 235 to about 4700 for Toyoura sand
(D50= about 0.17 mm). The difference is a factor up to about 20,
which is larger than the pervious studies that can be found in the
literature as far as the authors know. The range of L / D50 employed
by Palmeira and Milligan (1989) is also indicated in Fig. 3. In the
present study, the shear zones were carefully observed in some
typical tests to evaluate the thickness of shear zone as well as the
number of shear bands involved and strain nonuniformity in and
around the shear zone. The specimen size effects seen in the
strength-deformation characteristics from the DS tests with different values of L / D50 were analyzed based on these observations of
shear zone.
Direct Shear Apparatuses
The following four DS apparatuses (Table 1) were used.
Small DS Apparatus (Simple and Complicated
Versions)
Two versions (simple and complicated) of small DS apparatus (Fig.
4), which are Type C in Fig. 1, were designed modifying the one
proposed by Mikasa (1960). The vertical load (i.e., the normal
load) that is produced by using an air cylinder is transmitted
through a loading platen located below the lower shear box (note
that the configurations of the shear boxes presented in Figs. 1 and 4
are described upside down). The upper shear box is laterally pushed
by using a gear system driven by an AC motor. The total shear load
applied to the upper shear box is measured with a load cell (No. 4 in
Fig. 4).
With the simple version [Figs. 4(a) and 4(b)], the inner normal
load acting at the top of the specimen (i.e., Winner in type C, Fig. 1)
was measured with an internal load cell, LC-1 (No. 1 in Fig. 4), set
at the inside face of the top part of the upper shear box. With the
complicated version (Figs. 4(c) and 4(d)), in addition to the internal
load cell LC-1 described above, the external vertical load (i.e.,
Wlower in type C, Fig. 1) was measured with a pair of external load
cells, LC-2 and LC-3 (Nos. 2 and 3 in Fig. 4(c) and 4(d)) that were
arranged between the axial loading piston (above the specimen)
and the reaction frame. A pair of linear guides consisting of highprecision ball bearings (No. 9) was arranged between these two
load cells and the reaction frame so that essentially no shear load
acts on the external load cells. Two external load cells are necessary
to measure the normal load under the action of large moment
caused by shear load applied to the upper shear box. Moreover, the
two external load cells are of two-component type, each measuring
the normal and shear load. Any redundant horizontal frictional
shear force acting in the linear guides of high-precision ball bearings (No. 9) was measured with the external load cells and used to
accurately evaluate the shear load acting on the shear zone in the
specimen.
The vertical load measured with the external load cells is free
from any friction that may be activated along the vertical side faces
inside the upper shear box, which may affect the reading of the
inner load cell, LC-1. However, the arrangement of these two external load cells made the DS apparatus much more complicated,
therefore much more expensive, than the simple version. It was examined in the present study whether even the inner load cell can
measure the normal load acting on the shear zone rather accurately
enough because of a small inner wall height of the upper shear box,
equal to 10 mm, and essentially zero gross relative vertical movements of the specimen relative to the upper shear box.
The simple version small DS apparatus was originally designed
to accommodate a disk-shaped specimen having a circular cross
section with a diameter of 60 mm and a height of 20 mm. On the
other hand, the semimedium, the medium and the large DS apparatuses (described below) use cubic or rectangular prismatic specimens. To evaluate the specimen size effects under otherwise the
same test conditions, the complicated version small DS apparatus
was modified to accommodate prismatic specimens having dimensions of 40 mm⫻ 40 mm in the rectangular cross section and
20 mm in height by arranging auxiliary metal pieces inside the
shear boxes of the small DS apparatus. It is shown later in this paper
that the specimen shape has noticeable effects on the test results,
resulting from the fact that the length in the shear direction is not
uniform in the transversal direction with disk-shaped specimens.
Only Toyoura sand was used in the tests using these two versions
of small DS apparatus. A piece of sponge was glued on the circumference of the top face of the lower shear box to prevent the leakage
of sand particles at large shear displacements. With this treatment,
the opening between the upper and lower shear boxes was fixed,
equal to 1.0 mm, during shearing. A series of DS tests were performed at an average vertical stress equal to 50 kPa at a constant
shear displacement rate equal to 0.5 mm/ min.
Semi-Medium DS Apparatus
A semimedium DS apparatus (type B in Fig. 1) was designed and
constructed at the Tokyo University of Science (Hirakawa, 2005)
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4 GEOTECHNICAL TESTING JOURNAL
FIG. 4—Simple and complicated versions of small DS apparatus. (a) Cross view of small DS (simple version); (b) plane view of small DS (simple version); (c) cross
view of small DS (complicated version); (d) plane view of small DS version (complicated version)
based on the same design philosophy as the medium DS apparatus
described below. The specimen was cubic with a length equal to
120 mm in each side. Only Toyoura sand was used. The initial
opening between the upper and lower shear boxes was 1.8 mm and
the shear displacement rate was 0.31 mm/ min. The details of the
apparatus and results from a comprehensive series of DS tests using
this apparatus are reported by Duttine et al. (2007).
Medium DS Apparatus
Figures 5 and 6 show the medium DS apparatus (type B in Fig. 1)
used in this study. The specimen was cubic 共300 mm⫻ 300 mm
⫻ 300 mm兲. The apparatus was first designed and used by Qiu et al.
(2000) and modified as follows in the present study. That is, the
level at which the horizontal shear load is applied to the upper shear
box was moved lower from the level of the loading platen (No. 11)
to a level close to the opening between the upper and lower shear
boxes to reduce the rotational moment. Not only Toyoura sand but
also a sandy gravel with D50 = 2.0 mm was used in the tests using
this apparatus.
The lower shear box (No. 9 in Figs. 5 and 6) is rigidly fixed to the
loading frame. The upper shear box (No. 8) is rigidly fixed to the
top loading platen (No. 11 in Fig. 6). The top loading platen is fixed
to two pairs of air cylinders (in total four; No. 1 in Fig. 6). Independently controlled air pressures were supplied to these pairs of air
cylinder to keep the total vertical load to a specified value while
supplying the compensating moment necessary to keep the top
loading platen horizontal, as at the initial stage, during shearing.
The tilting tolerance of the top loading platen was only
0.05– 0.1 mm for a length of 450 mm, which was determined to be
as small as possible based on the attainable accuracy of the displacement measurements and the maximum feedback response
speed of the loading system. The vertical load acting to the top
loading platen was measured with four load cells (Nos. 2a and 2b),
fixed between the four air cylinders and the top loading platen. The
respective load cell measures both normal and shear loads. The four
air cylinders were fixed to the upper reaction bearing platen (No.
12), which can travel laterally freely without any restraint along a
pair of linear guides consisting of high-precision ball bearings. To
accurately measure the normal load with load cells Nos. 2a and 2b,
the frictional horizontal shear force acting between the upper reaction bearing platen (No. 12) and the reaction frame was minimized
as described above. Any redundant shear force was measured with
load cells Nos. 2a and 2b. The inner faces of the shear boxes were
not lubricated. Despite the above, as the upper shear box was supported in the vertical direction only with the four load cells, Nos. 2a
and 2b (fixed to the top loading platen), the total vertical load activated to the shear zone at the level of the opening can be obtained
precisely from the vertical load measured with the load cells while
accounting for the self weight of the specimen and the upper shear
box.
The shear load was applied to the upper shear box at a level
45 mm above the mid-height of the specimen by using a pair of
screw jacks (No. 6) having a load capacity of 5 ton (i.e. 49 kN)
each. The two screw jacks were independently driven and controlled in an automated way by using two electric AC motors pre-
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WU ON DIRECT SHEAR TEST
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FIG. 5—Medium DS apparatus.
venting any horizontal rotation of the upper shear box relative to the
lower shear box. The screw jacks were fixed to the reaction frame
via a ball-bearing guide (d in Fig. 6) while being counterbalanced
so that it can move vertically without any restraint following vertical displacements of the upper shear box. The shear load applied to
the upper shear box was measured with a load cell (No. 5) arranged
between the upper shear box and the shear loading ram. The shear
load working along the shear zone can be obtained precisely by
correcting the shear load measured as above for the shear load measured with four load cells (Nos. 2a and 2b), which was actually very
small.
The initial opening between the upper and lower boxes was adjusted by placing a set of spacers with a desired thickness between
the upper and lower shear boxes. The initial opening before consolidation was 8 mm in the tests using Toyoura sand and a sandy
gravel. To prevent the leakage of soil particles from the opening
during shearing, a piece of sponge and a smooth metal plate were
placed between the upper and lower shear boxes. The front lateral
side of the upper and lower shear boxes is transparent, made of
Acrylic platens, to observe the deformation of the specimen during
shearing. However, it was not possible to confidently define the detailed deformation of the shear zone from these external observa-
FIG. 6—Boundary conditions of the medium DS apparatus shown in Fig. 5.
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6 GEOTECHNICAL TESTING JOURNAL
TABLE 2—Physical properties of tested soils.
Soil type
Toyoura sand
Sandy gravel
D50 (mm)
0.17
2.0
Uc
1.70
2.2
Gs
2.64
2.74
tions. The shear displacement rate was kept to be 0.75 mm/ min in
all the tests. Other details of the medium DS apparatus are described in Qiu et al. (2000).
emax
0.977
0.99
emin
0.597
0.48
Grain shape
Angular to sub-angular
Angular
The other type of granular material is a well-graded sandy
gravel of crushed sandstone from a quarry in the Kuzuu mountain
area, the Tochigi Prefecture, Japan. The original material was
sieved to between 0.84 and 4 mm with D50 equal to 2.0 mm.
Large DS Apparatus
A large DS apparatus was designed and constructed at the National
Research Institute of Rural Engineering, fully following the design
principle for the medium DS apparatus described above. The specimen dimensions are 800 mm in length, 500 mm in width and
600 mm in height. Only Toyoura sand was used in the present
study. The initial opening between the upper and lower shear boxes
was 10 mm and the shear displacement rate was 0.26 mm/ min. Results from a comprehensive series of DS tests using this large DS
apparatus will be reported by the authors in the near future.
Experimental Program
The experimental program and part of the test data are summarized
in Table 3. Dense specimens of Toyoura sand were prepared by pluviating air-dried particles from a hopper covering the whole area of
the shear box keeping the falling height equal to 30 cm. The hopper
consisted of six sieves with a mesh size equal to 1.5 mm. Air-dried
sandy gravel specimens with a relative density of around 80 % were
prepared in 9 sub-layers by manual tamping using a small hammer.
Observation of Shear Zones
Test Materials and Experimental Program
Test Materials
The physical properties of Toyoura sand and a sandy gravel used in
the present study are summarized in Table 2 and the grading curves
are presented in Fig. 7. Toyoura sand is a quartz-rich sand, originated from the weathered granite in the Yamaguchi Prefecture,
Japan. Toyoura sand has been extensively used in laboratory stressstrain tests, including those performed at the University of Tokyo:
i.e., drained plane strain compression (PSC) tests (e.g., Tatsuoka et
al., 1986a; Park and Tatsuoka, 1994; Yasin et al., 1999; Yasin et al.,
2000), drained triaxial compression (TC) tests (e.g., Fukushima
and Tatsuoka, 1984; Goto, 1986; Tatsuoka et al., 1986b), drained
torsional shear tests on isotropically consolidated specimens (e.g.,
Tatsuoka et al., 1986c), drained torsional simple shear (TSS) tests
on K0-consolidated specimens (e.g., Pradhan et al., 1988a and
1988b) and drained DS tests (Qiu et al., 2000). The strength of
dense Toyoura sand from the DS tests obtained from the present
study is compared with those from these previous tests later in this
paper.
FIG. 7—Grain size distribution curves of the tested soils.
Toyoura Sand—To observe the shear zones in the mediumsize dense Toyoura sand specimens, six vertical thin piles of blackdyed Toyoura sand particles with a square cross section 共5 mm
⫻ 5 mm兲 and seven solder cords with a diameter equal to 0.6 mm
were arranged at the central vertical section in parallel to the shearing direction of the specimen (Figs. 8 and 9). To minimize the skin
friction, the surface of the solder codes were smeared with silicon
grease (Shin-etsu Silicon KS63G) and then wrapped with a piece of
tissue paper. The solder codes in guide pipes were first arranged in
the shear boxes before pluviating Toyoura sand into the inside of
the shear boxes in the same way as the tests without this shear zone
observation. Uppermost attentions were paid during the sand pluviation to keep the solder codes vertical as the original place. After
the sand surface reached the top level of the upper shear box, it was
leveled off by removing extra sand particles using a straight edge.
Then, the piles of black-dyed Toyoura sand particles were inserted
into the completed specimen by using thin (0.8-mm-thick) guide
pipes made of aluminum. Subsequently, these pipes were extracted
very carefully and slowly protecting the surrounding zones from
any significant disturbances. The subsequent test procedures for assembling the shear boxes and other parts and performing onedimensional compression and DS shearing were the same as the DS
tests without observing the shear zone.
After the respective shearing process of medium DS test had
been performed, the upper and lower shear boxes were rigidly fixed
to each other. Then the specimen was made saturated by infiltrating
water through the holes at the bottom of the lower shear box. It took
about 10 hours or more to complete this saturation process. Then,
the vertical planes containing deformed solder cords and blackdyed sand piles were carefully exposed by hand excavation, as
shown in Figs. 8 and 9. Thereafter, photographs of these excavated
planes were taken and the coordinates of deformed solder cords and
colored sand were mapped by the photogrammetric method.
The dry densities of the specimens were calculated taking into
account a very small volume of the solder cords, only 0.0019 % of
the total volume of the specimen. It was also the case with the sandy
gravel specimen explained below. Negligible effects of this ar-
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WU ON DIRECT SHEAR TEST
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TABLE 3—Experimental program and part of the data of DS tests using four different size DS apparatuses
Measured values
Peak state
e ia
␶vh / ␴v
Test code
Soil type
Size ratioc
Test group a (simple version small DS tests, disk specimen)
CPT03S
Toyoura
353
0.663
0.970
sand
CPT07S
0.639
0.969
CPT10S
0.649
0.961
CPT14S
0.663
0.974
Test group b (complicated version small DS tests, disk specimen)
CPT20S
Toyoura
353
0.650
0.947
sand
0.634
1.008
CPT47Sb
Test group c (complicated version small DS tests, rectangular specimen)
CPT27S
Toyoura
235
0.627
0.986
sand
CPT37S
0.654
1.030
Semi-medium DS tests, cubic specimen
Test 7
Toyoura
706
0.698
0.804
sand
Test 8
0.721
0.753
Test 9
0.659
0.893
Test 10
0.638
0.918
Medium DS tests, cubic specimen
Toyoura
1765
0.677
0.830
CPT06b
sand
0.683
0.828
CPT10Rb
CPG02b
Sandy
150
0.591
1.314
gravel
Large DS tests, rectangular specimen
Test 65
Toyoura
4706
0.641
0.881
sand
Residual state
Figure of
共␶vh / ␴v兲 versus
shear disp.
␾DS (deg)
␶vh / ␴v
␾DS (deg)
44.1
44.1
43.9
44.3
0.741
0.809
0.707
0.740
36.5
39.0
35.2
36.5
Figs. 13 and 16
43.4
45.2
0.720
0.680
35.8
34.2
Figs. 13, 14, and 16
44.6
45.8
0.689
0.680
34.9
34.2
Fig. 14
38.8
37.0
41.8
42.6
0.705
0.690
0.701
0.739
35.2
34.6
35.0
36.5
Fig. 17
39.7
39.6
52.7
0.688
N/A
0.774
34.5
N/A
37.7
Fig. 18
41.3
0.660
33.4
Fig.18
a
The void ratio of soil specimen after sample preparation while before consolidation.
The shear zone patterns were observed in these tests.
c
Size ratio =共␾ / D50兲 or 共L / D50兲, where ␾ and L are the diameter and length of shear box, respectively.
b
rangement on the test results were confirmed by comparing the
shear stress—shear displacement—volume change relations of the
specimens with and without this shear zone observation.
The shear zone in a disk-type small size dense Toyoura sand
specimen was observed by inserting thin piles of black-dyed sand
particles with a diameter of 5 mm in the specimen (Fig. 10) in the
similar way as the medium-size specimens. The solder cords were
not used. Negligible effects of this treatment on the test results were
confirmed.
FIG. 8—Cross-section at s = 5 mm of Toyoura specimen in the medium DS apparatus (Test CPT10R).
FIG. 9—Cross-section at s = 45 mm of Toyoura specimen in the medium DS apparatus (test CPT06).
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8 GEOTECHNICAL TESTING JOURNAL
FIG. 10—Cross-section at s = 6 mm of Toyoura specimen in the small DS apparatus (test CPT47S).
Sandy Gravel—Nine solder cords with a diameter of
0.8 mm were arranged at the central vertical section of a gravel
specimen (Fig. 11), without using black-dyed sand particles. Larger
diameter solder cords were used to maintain as much as possible its
original straight shape when compacting the specimen. As with
Toyoura sand, the surface of the solder cords was smeared with silicon grease and then wrapped with a piece of tissue paper. To prevent excessive permanent deformations during the compaction process of specimen, the cords were placed inside the guide pipes of
aluminum with an external diameter of 4 mm, which were then
fixed to a guide metal platen with a thickness of 0.2 mm. Before the
start of specimen preparation by compaction, the guide plate was
placed vertical at the central section in the shear boxes (Fig. 11).
During the compaction process, the guide platen was pulled out
step by step, not leaving any unprotected height between the bottom
of the platen and the transient surface of compacted specimen. This
procedure was repeated until the whole height of specimen was
compacted to the top of the upper shear box. The subsequent test
procedures were the same as the Toyoura sand specimens.
After the DS test, the upper and lower shear boxes were rigidly
fixed to each other and then rotated 90° to make the vertical plane
containing the solder cords horizontal. Then, the specimen was
hand-excavated carefully to expose the plane containing the deformed solder cords (Fig. 12). Photographs of the excavated plane,
which was horizontal at this stage, were taken and the coordinates
of deformed solder cords were also mapped by the photogrammetric method.
FIG. 12—Cross-section at shear displacement equal to 45 mm of sandy gravel
specimen in the medium DS apparatus (test CPG02).
Accurate Measurement of Vertical Load in Small DS
Tests
Figures 13 and 14 show the relationships between the stress ratio,
␶vh / ␴v, and the shear displacement, s, and between the vertical displacement, d, and s from the following DS tests on small size specimens of dense Toyoura sand having similar dry densities performed
at a constant vertical pressure, ␴v = 50 kPa (see Table 3):
Test group a: Tests CPT03S, CPT07S, CPT10S and CPT14S on
disk-shaped specimens using the simple version small DS apparatus, in which the feedback control for constant ␴v was made based
on the value measured with the inner load cell, LC-1 (hollow data
points in Fig. 13).
Test Results and Discussions
The shear and vertical stresses from all the DS tests referred to
below were calculated based on the respective initial crosssectional area.
FIG. 11—Guide pipe and platen for inserting solders during the preparation of
a gravel specimen.
FIG. 13—Results of small DS tests on disk specimens of Toyoura sand.
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9
FIG. 15—Peak stress ratios of Toyoura sand in DS tests with different specimen
sizes.
FIG. 14—Effects of specimen shape in small DS tests on Toyoura sand.
Test group b: Tests CPT20S and CPT47S on disk-shaped specimens using the complicated version small DS apparatus, in which
the feedback control for constant ␴v was made based on the value
measured with the external load cells, LC-2 and LC-3, and these ␴v
values are used to calculate ␶vh / ␴v (solid data points presented in
Fig. 13).
Test group c: Tests CPT27S and CPT37S on rectangular prismatic specimens using the complicated version small DS apparatus
(square data points presented in Fig. 14).
It may be seen from Fig. 13 that the ␶vh / ␴v − s − d relations from
the tests on disk-shaped specimens using the simple and complicated versions small DS apparatus (test groups a and b) are very
similar until some moment during the post-peak softening regime.
The peak stress ratios, 共␶vh / ␴v兲peak, from these and other similar DS
tests (explained later in this paper) are plotted against the initial
void ratio 共ei兲 before consolidation in Fig. 15. It may be seen that
the 共␶vh / ␴v兲peak values obtained by using the simple version small
DS apparatus (group a) are essentially the same with those obtained from external measurements of the vertical load using the
complicated version small DS apparatus (group b), which are basically more reliable. This result indicates that, apart from the specimen size effects on the peak strength explained later in this paper,
the peak strength can be evaluated rather accurately even by using
the simple version small DS apparatus using a disk-shaped specimen measuring the vertical load with a load cell installed in the top
platen of the upper shear box (group a).
On the other hand, the stress ratio, ␶vh / ␴v, at the residual stress
state in group a becomes larger than the one in group b, which becomes more significant with an increase in the shear displacement.
To better understand this trend of behavior, the following ␶vh / ␴v
− s relations from test group a and b are compared in Fig. 16(a) and
the corresponding d − s relations in Fig. 16(b).
i.
␶vh / ␴v − s relation with the ␴v value measured with the
inner load cell (LC-1) from test CPT03S using the
simple version small DS apparatus (group a);
ii.
␶vh / ␴v − s relation with the ␴v value measured with the
inner load cell (LC-1) from test CPT20S using the complicated version (group b); and
iii.
␶vh / ␴v − s relation with the ␴v value measured with external load cells (LC-2 & LC-3) from the same test above
(test CPT20S).
Figure 16(c) compares the vertical stresses, ␴v, measured with the
inner and external load cells from a single test (test CPT20S). The
following trends of behavior may be seen from these figures:
1.
2.
3.
In Fig. 16(a), the ␶vh / ␴v − s relations with the ␴v value measured with the inner load cell from the two tests using the
simple and complicated versions small DS apparatuses are
very similar to each other. The d − s relations [Fig. 16(b)]
are also very similar. These test results indicate a high reproducibility of DS test in the present study.
In test CPT20S using the complicated version small DS apparatus, the ␶vh / ␴v − s relations based on the ␴v value measured with the inner load cell and the external ones are very
similar until some moment during the post-peak softening
regime. However, as s increases at the residual state, the
␶vh / ␴v value based on the ␴v value measured with the inner
load cell gradually increases relatively to the one based on
the ␴v value measured with the external ones.
In Fig. 16(c), in test CPT20S, the ␴v value measured with
the external load cells was kept accurately constant. In
comparison, the ␴v value measured with the inner load cell
shows a large variation during the test. This phenomenon is
due likely to: (a) effects of friction activated at the inner
side face of the upper shear box, caused by contractive then
dilative behavior of sand; and (b) effects of eccentric distribution of the normal stress acting to the inner load cell. A
large reduction in the vertical load measured with the inner
load cell at the residual state is consistent with an apparent
increase in the stress ratio, ␶vh / ␴v, at the residual state obtained based on the ␴v value measured with the inner load
cell.
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10 GEOTECHNICAL TESTING JOURNAL
FIG. 17—Results of semimedium DS on Toyoura sand.
1.
FIG. 16—(a) and (b). Effect of measurement method of vertical stress in small
DS test on Toyoura sand. (c) Vertical loads measured with inner and external
load cells in test CPT20S using the complicated version of small DS apparatus.
This result indicates that, even with such a small and thin specimen having a total height of 20 mm, it is indispensable to measure
the normal load acting to the whole shear box with external load
cells to accurately evaluate the normal load at the residual state, in
particular at large shear displacements.
Specimen Shape Effects in Small DS Tests
Figure 14 compares the ␶vh / ␴v − s − d relations (based on the ␴v values measured with the external load cells) from test group b and c
using respectively disk-shaped and rectangular prismatic specimens of dense Toyoura sand. The peak strength values from test
groups c and b are plotted and compared in Fig. 15. It may be seen
from these figures that the effect of specimen cross-sectional shape
on the peak stress ratio is insignificant, if any. However, the following subtle but noticeable effects may be seen from Fig. 14:
The shear displacement at the peak stress ratio is smaller in
test group c (rectangular prismatic specimens) than in test
group b (disk-shaped specimens)
2. The rectangular prismatic specimens (test group c) exhibit
a faster strain softening in the post-peak regime and
reaches the residual state at a smaller shear displacement
while exhibiting a smaller ultimate volume increase.
It is likely that these trends of behavior are due to more simultaneous failure in the horizontal transversal direction orthogonal to
the shearing direction in the rectangular prismatic specimens
(group c), while the failure is more progressive in the disk-shaped
specimens (group b). For this difference, in the following, the results of test group c are compared with those from semimedium,
medium and large DS tests performed on cubic or rectangular prismatic specimens to evaluate the specimen size effects in the DS
test.
Results from DS Tests using Apparatuses of Different
Sizes
The ␶vh / ␴v − s − d relations from four semimedium DS tests (Tests
7–10) on cubic specimens of dense Toyoura sand having different
initial void ratios are presented in Fig. 17. The results from two of
them (test 9 and test 10) are also shown in Figs. 18 and 19, compared with the typical results from the following seven tests performed at the same vertical stress 共␴v = 50 kPa兲:
i.
ii.
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One small DS test (test CPT37S of group c) on a rectangular prismatic specimen of dense Toyoura sand measuring ␴v with the external load cells.
Two medium DS tests (tests CPT06 & CPT10R) on
cubic specimens of dense Toyoura sand, one that was
WU ON DIRECT SHEAR TEST
11
FIG. 18—Scale effects in DS tests using different specimen sizes and different materials.
iii.
stopped around the peak stress state and the other that
was continued until s became about 45 mm. In these
tests, the shear zone was observed by exposing the central section after the respective test.
One medium DS test (CPG02) on a cubic specimen of
dense sandy gravel. The shear zone was observed after
the test.
iv.
One large size DS test (Test 65) on a rectangular prismatic specimen of dense Toyoura sand. The shear zone
was not observed in this test.
Figure 15 and Fig. 20, respectively, summarizes the peak and residual stress ratios of air-dried Toyoura sand from all the DS tests
performed in the present study as well as those from a series of
medium DS tests on Toyoura sand having a wide range of initial
FIG. 19—Close-up until s = 20 mm of the results presented in Fig. 18.
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12 GEOTECHNICAL TESTING JOURNAL
FIG. 20—Residual stress ratios of Toyoura sand in DS tests with different specimen sizes.
void ratios performed by Qiu et al. (2000) under the same test conditions as test ii) above. It may be seen from Fig. 15 that the peak
strengths from the medium DS tests from the present study are consistent with those from the tests performed by Qiu et al. (2000). It
may be seen from Fig. 20 that the residual strength from the DS
tests on Toyoura sand by Qiu et al. (2000) is essentially independent
of initial void ratio, ei. This trend of behavior is consistent with
other data of Toyoura sand obtained by other types of stress-strain
test, as typically seen from Fig. 21(a). The definition of the angle ␦
is presented in Fig. 21(b). The 共␶vh / ␴v兲res value obtained from a
torsional simple shear (TSS) test on a hollow cylindrical specimen
of dense Toyoura sand performed under otherwise the similar conditions (i.e., test CTSS11: ei = 0.674; ␴v = 196 kPa with ␴3
= 64 kPa at failure, Pradhan et al., 1988b) is also presented in Fig.
20. In their TSS tests on loose specimens, the residual stress state is
difficult to reach due to a limited mechanical capacity of shear distortion that could be applied to the specimens. Therefore, reliable
evaluation of the effects of initial void ratio on the residual strength
is difficult by the TSS tests.
The following two other trends of behavior may be seen from
Fig. 20:
The residual stress ratio, 共␶vh / ␴v兲res, is nearly the same
among the small, semimedium, medium and large DS tests
and independent of initial void ratio except for those obtained by internally measuring the vertical load in the small
DS tests.
2. The 共␶vh / ␴v兲res values from the DS tests and the TSS tests
are consistent with each other.
These results indicate that the different test conditions other than
the specimen size in the present study (such as types B or C, and the
different openings) have negligible effects on the test results. These
facts are therefore the very important basis to reliably evaluate the
specimen size effects on the shear strength and deformation characteristics of Toyoura sand in the DS test.
1.
It may be seen from Fig. 15 as well as Figs. 18 and 19 that, with
dense Toyoura sand, the ␶vh / ␴v − s and d − s relations and the peak
stress ratios obtained from the small, semimedium, medium and
large DS tests performed under otherwise the same test conditions
FIG. 21—(a) Results of typical PSC tests on Toyoura sand (␴3 = 392 kPa; ␦
= 90°; after Tatsuoka et al., 1986a). (b) Definition of angle ␦ of the bedding
plane direction relative to the direction of ␴1 in PSC tests (Tatsuoka et al.,
1986a). (c) Friction angles of Toyoura sand at ␴3 around 50 kPa from different
stress-strain tests (Pradhan et al., 1988a, b).
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WU ON DIRECT SHEAR TEST
13
(externally measuring the vertical load using cubic or rectangular
prismatic specimens) are largely different. That is, with an increase
in the specimen size:
a.
b.
c.
the shear displacement s at the peak stress state increases;
the peak stress ratio, 共␶vh / ␴v兲peak, decreases;
the strain-softening rate becomes slower with the shear displacement increment, ⌬s, in the range between the peak stress
state and the start of residual state becoming larger; and
the ultimate volume increase due to dilatancy becomes larger.
d.
These significant specimen size effects in the DS tests on granular materials described above can be attributed to the following factors, among others, due to the different ratios of the specimen size
to the sand particle size:
FIG. 22—Strength anisotropy of Toyoura sand observed in drained PSC and
TSS tests (Tatsuoka et al., 1986a; 1990).
1.
the stress uniformity (or nonuniformity) in the shear direction in the shear zone;
2. the width and internal structure of the shear zone in terms
of the thickness and the number of shear band involved;
and
3. the degree of restraint by mechanical boundary conditions
to the free development of multiple shear bands; or in other
words, the degree of forced development of a single shear
band at the prescribed level in the specimen by mechanical
boundary conditions.
These factors should be linked to each other.
Specimen Size Effects on the Peak Shear Strength
To evaluate this factor, the shear strength of Toyoura sand from the
DS tests performed in the present study was first compared with
those from other types of shear tests that are free from the abovementioned three factors. Figure 21(c) summarized the following
angles of internal friction of air-pluviated Toyoura sand at
␴3=around 50 kPa obtained from different laboratory stress-strain
tests that were performed under otherwise similar test conditions as
the present study but are free from the effects of these three factors
(Pradhan et al., 1988a, 1988b):
a.
b.
␾SS = arctan
The angles of internal friction defined by Eq. 1 are obtained
from the tests listed below:
␾0 = arcsin
i.
ii.
iii.
冉
冊
␴1 − ␴3
␴1 + ␴3 max
(1)
Drained plane strain compression (PSC) tests performed on specimens when the angle, ␦, of the direction of the effective major principal stress, ␴1, relative to the bedding plane was 90° and 45° (Fig. 21(b);
Tatsuoka et al., 1986a). Figure 22 shows the relationship between the ratio of the ␾0 value at a given angle
␦ to that at ␦ = 90°. The ␾0 value exhibits the maximum and minimum values when ␦ = 90° and
25° – 35°.
Drained TC tests on specimens prepared at ␦ = 90°
(7 cm in diameter and 15 cm in height with lubricated top and bottom ends; Fukushima and Tatsuoka,
1984; Tatsuoka et al., 1986b). The ␾0 values from
these tests are coincidently similar to the values in the
corresponding PSC tests at ␦ = 45°.
Drained torsional simple shear (TSS) tests in which
the inner and external pressures of a hollow cylindrical specimen (10 and 6 cm in inner and outer diameters and 20 cm in height) were automatically controlled during shearing so that the shape and area of
the cross section were kept constant (i.e., the simple
shear strain conditions). As the shear zone in a DS
test is basically under the simple shear strain conditions, the results from the DS tests performed in the
present study should be comparable with those from
these TSS tests. As seen in Fig. 22, the ␦ values at the
peak stress state in these TSS tests are around
40° – 45° and the ␾0 values from the TSS tests are
consistent with those from PSC tests at the same ␦
values.
The simple shear angle of internal friction defined in terms of
the shear stress and normal stress, ␶vh and ␴v, acting on the
horizontal plane [Eq. 2] from the drained TSS tests:
c.
冉 冊
␶vh
.
␴v max
(2)
In a given TSS test, the simple shear angle, ␾ss, is significantly smaller than the ␾0 value [Eq. 1], which is due to the
fact that the plane of the maximum stress obliquity is inclined
by some angle from the horizontal plane, which is in the zeroextension direction (Pradhan et al., 1988a, b). The angle difference is theoretically equal to 共␾0 − ␯d兲 / 2, where ␯d is the
dilatancy angle at the peak stress state, defined as arcsin兵
−共␧˙ 1 + ␧˙ 3兲 / 共␧˙ 1 − ␧˙ 3兲其at peak (␧˙ 1 and ␧˙ 3 are the major and minor
principal strain rates).
The simple shear angles of friction, ␾ss, for the TSS tests
theoretically obtained as:
␾SS = arctan
冉
冊
sin␾0 · cos ␯d
,
1 − sin ␾0 · sin ␯d
(3)
where ␾0 is the measured angle of friction [Eq. 1] (Pradhan et
al., 1988a, b). The theoretically deduced values of ␾SS are
very close to its respective corresponding measured value
(Fig. 21(c)).
In Fig. 23, the values of ␾DS = arctan共␶vh / ␴v兲max of Toyoura sand
at ␴v = 50 kPa from all the DS tests performed in the present study,
using the small, semimedium, medium and large DS apparatuses,
are plotted against the respective initial void ratio, ei. The data from
the medium DS tests from the present study and Qiu et al. (2000)
are plotted in the shaded zone. These ␾DS values are compared with
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14 GEOTECHNICAL TESTING JOURNAL
FIG. 24—Relationship between ␾ds and L / D50 from DS tests on Toyoura sand
specimens with five different sizes.
4.
FIG. 23—Comparison of shear strength among TSS tests and direct shear tests
on Toyoura sand.
the friction angles, ␾0 and ␾SS, from the TSS tests at ␴v = 49 kPa
and those at ␴v = 98 kPa (plotted in Fig. 21(c)). The ␾DS values at
␴v = 49 kPa from the DS tests on Toyoura sand specimens (square in
plan with 150 mm in length and width and 120 mm in height) reported by Shibuya et al. (1997) are also presented in this figure. The
following trends of behavior may be seen:
1.
2.
3.
With dense Toyoura sand, the ␾DS values at ␴v = 50 kPa
from the semimedium, medium and large DS tests are similar to or only slightly higher than the simple shear friction
angles, ␾SS = arctan共␶vh / ␴v兲max, from the drained TSS tests
at ␴v = 49 kPa. On the other hand, these ␾DS values are
much smaller than the angle of internal friction angles, ␾0
= arcsin关共␴1 − ␴3兲 / 共␴1 + ␴3兲兴max, from the drained TSS tests
at ␴v = 49 kPa. These results suggest that the shear zone in a
dense specimen of Toyoura sand in the semimedium, medium and large DS tests underwent basically the simple
shear strain conditions.
For ei larger than about 0.8, the ␾DS value of Toyoura sand
from the medium DS tests becomes larger relative to the
␾SS values from the drained TSS tests with an increase in
the void ratio. A similar trend can be seen with the data of
Shibuya et al. (1997). The reason for the above is not
known to the present authors.
The ␾DS values of dense Toyoura sand from the small DS
tests are consistently higher than those under otherwise the
same conditions from the semimedium, medium and large
DS tests and, therefore, they are consistently higher than
the simple shear friction angles, ␾SS, from the drained TSS
tests. On the other hand, these ␾DS values of dense Toyoura
sand from the small DS tests are comparable with the ␾0
values from TC tests 共␦ = 90° 兲 (plotted in Fig. 21(c)). However, this coincidence is due to incidental balancing among
several factors including the strength anisotropy, effects of
intermediate principal stress, the different definitions of the
friction angle [i.e., Eq. 1 versus Eq. 2] and the specimen
size effects in the DS test and therefore not objective.
The ␾DS values from the semimedium and medium DS
tests are similar to those obtained by Shibuya et al. (1997).
In the DS tests performed by Shibuya et al. (1997), the inside of the shear box was lubricated unlike the DS tests performed in the present study, while the vertical stress was
obtained from Wlower. Furthermore, the spacing between
the upper and lower shear boxes increased when the specimen dilated in the DS tests performed in the present study,
while the spacing was fixed in the DS tests performed by
Shibuya et al. (1997). It seems that the effects of these two
factors are insignificant, if any.
Figure 24 shows the relationships between the ␾DS values of
dense Toyoura sand when ␴v = 50 kPa and an initial void ratio, ei, is
equal to 0.65 from all the DS tests described above. The respective
single data points from multiple tests were obtained by averaging
the measured values for the void ratios less than 0.7. The measured
shear strengths when ei = 0.65 were obtained by referring to the
changing rate of the shear strength with changes in ei of the average
curve for the medium DS tests obtained by Qiu et al. (2000), presented in Fig. 15. In Fig. 24, the average ␾SS value from the two
TSS tests on dense Toyoura sand when ␴v = 49 kPa is also indicated
by a horizontal line. This ␾SS value has been corrected to ei = 0.65
by referring to the average ␾SS − ei relation when ␴v = 98 kPa, presented in Fig. 23. The following trends of behavior may be seen:
1.
2.
With an increase in the specimen size from 40 to 800 mm,
or the ratio L / D50 from 235 共=40 mm/ 0.17 mm兲 to 4700
共=800 mm/ 0.17 mm兲, the ␾DS value of dense Toyoura sand
obtained from the present study tends to decrease. According to Jewell and Worth (1987), the proper range of L / D50
is 50–280. Obviously, this range of L / D50 is too small to
obtain the ␾DS value of dense Toyoura sand that is independent of specimen size effects. In the range L / D50 of 75–
1250 employed by Palmeira and Milligan (1989), the ␾DS
value of dense Toyoura sand noticeably decreases with an
increase in L / D50.
As the specimen size becomes larger, the values of ␾DS
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WU ON DIRECT SHEAR TEST
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FIG. 25—A shear band and the relationships between stress ratio and average and local shear strains from a typical drained TSS on dense Toyoura sand (Pradhan
et al., 1988a).
from the present study tend to approach the ␾SS value from
the TSS tests.
Figure 25 shows a hollow cylindrical specimen at the end of a
typical drained TSS test on dense Toyoura sand. The relationships
between the effective principal stress ratio and the globally averaged shear strain and those between the stress ratio and the local
shear strains inside and outside the shear band at the residual state
are also presented in this figure. In this test, ultimately a single welldefined shear band, which was not forced to develop at a specified
location, was observed (Fig. 25). Tatsuoka et al. (1986c) showed
that multiple shear bands had started developing immediately before the peak stress state in a hollow specimen in a torsional shear
test on dense Toyoura sand. However, only one shear band, which
should be weakest among a number of candidates, developed further in the post-peak regime, despite that the development of a
single shear band was not forced.
On the other hand, only a single shear band is forced to develop
at the prescribed level in the DS test. As shown below, the above
was actually the case with the small DS tests on dense Toyoura
sand, whereas multiple shear bands developed, forming a rather
thick shear zone, in the respective medium DS specimens. These
trends of behavior indicate the following:
1.
2.
Without any mechanical boundary restraint, a shear band
that has once started developing should develop further
without the development of any new shear band(s), as in the
TSS test described in Fig. 25. This is because the shear
band becomes weaker with shear deformation due to associated dilatation. The development of multiple new shear
bands in a medium DS test indicates that the shear band
that has developed first at the level of the opening between
the top and bottom shear boxes becomes stronger relative
to another or other shear band(s) that start(s) developing
subsequently. This means that there are some mechanical
restraints to the further development of the first single shear
band in the DS test.
On the other hand, the development of only a single shear
band in the small DS tests means that there are some mechanical restraints to the development of new shear
band(s).
It is likely that the peak strength measured by a DS test is more-
or-less higher than the value measured without any such mechanical restraining effects. It seems that effects of the mechanical restraint to the development of the first shear band and new multiple
one(s) become smaller with an increase in the specimen size relative to the particle size. On the other hand, the failure of DS specimen is more-or-less progressive in the sense that the local peak
shear strengths are not mobilized simultaneously in the lengthwise
direction of shear zone, resulting into a decrease in the global peak
shear strength. The effects of progressive failure should become
larger with an increase in the specimen size relative to the sand
particle. In comparison, there is no strong mechanical restraint to
the free shear band development in the specimens in the drained
TSS and PSC tests. Furthermore, the degree of progressive failure
in the circumferential direction of a hollow cylindrical specimen in
the TSS test and in the direction of shear band inside the specimen
with well-lubricated top and bottom ends in the PSC test is insignificant. For these two reason, the values of ␾0 from these tests
under otherwise the same conditions are consistent (Fig. 22). Summarizing the above, the following is very likely:
1.
2.
A decrease in the shear strength of dense Toyoura sand with
an increase in the specimen size seen from Fig. 24 is due
likely to both a decrease in the effect of mechanical boundary restraint to the free development of shear band and an
increase in the degree of progressive failure with an increase in the specimen size relative to the particle size.
In the medium and large DS tests on dense Toyoura sand,
the effect of mechanical boundary restraint to the free development of shear band might be still nonzero, but it is
likely that the effect of this factor is balanced by that of
progressive failure, resulting to ␾DS values similar to the
corresponding ␾SS values from the drained TSS tests.
Shear Zone Pattern in DS Tests
Figures 8 and 10 show the exposed central vertical sections of the
small and medium specimens of dense Toyoura sand sheared to
nearly the same shear displacement, s = 5 – 6 mm. At this shear displacement, the stress condition had already reached the residual
state in the small specimen (Fig. 13), while it was still around the
peak stress state in the medium specimen (Figs. 18 and 19). A very
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16 GEOTECHNICAL TESTING JOURNAL
3.
FIG. 26—Zoom up of the central part of shear band at s = 45 mm of Toyoura
sand specimen in the medium DS apparatus (test CPT06).
clearly defined single shear band had developed in the small specimen (Fig. 10), while it was not the case in the medium specimen
(Fig. 8). This difference explains the specimen size effects, at least
partly, that can be seen in the test results presented in Figs. 18 and
19.
Figure 9 shows the exposed central section of the medium specimen of dense Toyoura sand sheared to s = 45 mm (Figs. 18 and 19).
Figure 26 is a close-up of the shear zone. The mapped shear zones
of those seen in Figs. 12 and 26 are, respectively, presented in Figs.
27(a) and 27(b). The following features may be seen from these
photos and figures:
1.
2.
In Figs. 9 and 26, the deformation patterns of the blackdyed sand piles and solder cords are essentially the same.
This result indicates that the deformation pattern of the solder cords is representative of that of the medium DS specimen of Toyoura sand and so with the DS specimen of sandy
gravel (Fig. 12).
The shear zone in the medium specimen of Toyoura sand
consists of multiple shear bands (i.e., highly strainlocalized bands) and multiple local less-sheared thin layers
located in between (Figs. 9, 26, and 27). The shear zone is
thickest and the number of shear band is largest (i.e., four)
at the center in the lengthwise direction of the shear zone.
In contrast to the Toyoura sand specimen, the medium
specimen of sandy gravel exhibits a well-defined single
shear band (Fig. 12). The ratio of the specimen length 共L兲
of the medium sandy gravel specimen to D50 (equal to
300 mm/ 2 mm= 150) is of the same order of magnitude as
the one with the small specimen of Toyoura sand (equal to
40 mm/ 0.17 mm= 235). This similarity may explain similar shear zone patterns in these tests.
The top and bottom boundaries of the respective shear zone are
denoted by hollow circles in Figs. 27(a) and 27(b), which were defined as the locations where the local shear strain, defined below,
was equal to 20 % along the respective black-dyed sand pile and
solder cord.
共␥vh兲local = ⳵ slocal/⳵ y + ⳵ dlocal/⳵ x,
(4)
where slocal is the local shear displacement in the horizontal direction; dlocal is the local vertical displacement due to dilatancy; and y
and x are the vertical and horizontal coordinates. As it was very
difficult to evaluate confidently the values of dlocal along a blackdyed sand pile and a solder cord soil and ⳵dlocal / ⳵x should be much
smaller than ⳵slocal / ⳵y at a given location, Eq. 4 was simplified as
follows:
共␥vh兲local = ⳵ slocal/⳵ y
(5)
It was assumed that the initial axial directions at the start of
shearing of the black-dyed sand piles and solder cords were vertical
and orthogonal to the central horizontal plane of specimen. The average thickness of the shear zone at the residual state observed in
the medium specimen of Toyoura sand is 25.4 mm, which is about
150 times as large as the D50 value. On the other hand, the average
thickness of the shear zone, which consisted of a single shear band,
observed in the medium sandy gravel specimen, was equal to
30.4 mm, which is about 15 times as larger as the D50 value
共=2 mm兲, similar to the ratio with dense Toyoura sand as discussed
below.
The thickness at the residual state of a single shear band observed in the small and medium specimens of dense Toyoura sand
was essentially the same, approximately equal to 3 mm, which is
equal to about 18 times as large as the D50 value 共=0.17 mm兲. This
value is consistent with the one observed in the drained PSC tests
(Yoshida and Tatsuoka, 1997). Figure 28 shows the relationships
between the thickness at the residual state of a single shear band,
Wsb, and the mean particle diameter, D50, of Toyoura sand and the
sandy gravel obtained from the present study together with those
from a series of the drained PSC tests performed by Yoshida and
Tatsuoka (1997) and Okuyama et al. (2003). It may be seen that the
data obtained from the present DS tests are consistent with those
from the previous PSC tests. It may also be seen that Wsb increases
with an increase in D50 while the ratio Wsb / D50 tends to decrease
with an increase in D50.
Analysis of Stress-Displacement Relations Based on
Shear Zone Pattern
FIG. 27—(a) Mapped shear zone of dense gravel specimen shown in Fig. 12. (b)
Mapped shear zone in the dense Toyoura sand specimen shown in Fig. 26.
To better understand the specimen size effects on the strengthdeformation characteristics of granular materials in the DS tests
using shear boxes having largely different sizes, the results presented in Figs. 18 and 19 were analyzed based on the shear zone
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WU ON DIRECT SHEAR TEST
17
FIG. 28—Relationship between mean particle size D50 and shear band thickness Wsb.
patterns observed at the central vertical sections of the specimens.
Figure 29 shows the relationships between the stress ratio, ␶vh / ␴v,
and the normalized shear and vertical displacements, s / Wsz and
d / Wsz, obtained by dividing the shear and vertical displacements
with the aforementioned respective average shear zone thickness at
the residual state, Wsz, observed in the small and medium DS tests
of Toyoura sand and the medium DS of sandy gravel (presented in
Figs. 18 and 19). Therefore, s / Wsz and d / Wsz represent the average
shear and volumetric strains in the respective shear zone. The values of s / Wsz and d / Wsz more or less underestimate the maximum
local strains in the shear bands, because local strains are more intensely localized in shear bands than less-intensely strained layers
in the shear zone. The following trends of behavior may be seen
from Fig. 29:
1.
FIG. 30—DS test results with shear and vertical displacements normalized with
respective to the total shear band thickness NWsb.
2.
As mentioned before, the peak stress ratio, 共␶vh / ␴v兲peak, of
Toyoura sand from the small DS tests is noticeably higher
than the one from the corresponding medium DS tests. It
seems that this phenomenon can be attributed to both larger
boundary mechanical restraint to the free shear band devel3.
FIG. 29—DS test results with shear and vertical displacements normalized with
respective to the thickness of apparent shear zone WSZ.
opment in the small DS test and more progressive development of multiple shear bands in a shear zone in the medium
DS test.
The effects of ratio D50 / L on the strain values at the same
shear stress level relative to the peak value are more insignificant than those in Figs. 18 and 19. In particular, the
stress-strain relations presented in Fig. 29 from a small DS
test on Toyoura sand and a medium DS test on sandy gravel,
in which only a single shear band developed, are very similar to each other. This result indicates that the specimen size
effects on the shear and vertical displacements is controlled
by the ratio D50 / L in that the ratio of the thickness of shear
zone to the particle size increases with an increase in the
ratio L / D50.
However, the normalized ultimate dilatancy, d / Wsz, at the
residual state in the medium DS specimen of dense Toyoura
sand is much smaller than those in the other two tests.
Figure 30 shows the relationships between ␶vh / ␴v and the normalized shear and vertical displacements, s / 共NWsb兲 and d / 共NWsb兲,
obtained by dividing the measured shear and vertical displacements
with the total thickness of the multiple shear bands in the respective
shear zone, N times Wsb, where N is the number of shear bands in
the respective shear zone and Wsb is the thickness observed at the
residual state of a single shear band, which is 3.0 and 30.4 mm for
Toyoura sand and the sandy gravel. The average strains obtained in
this way are more representative of the local strains in the shear
bands into which strains have been intensely localized. It may be
seen that, for the reason given above, the normalized dilatancy,
d / 共NWsb兲, at the residual state in the medium DS specimen of
dense Toyoura sand is very similar to those in the other two tests.
Figure 31 shows the relationships between the shear displacement to reach the peak state, speak, and the shear zone thickness,
Wsz, which is equal to the thickness of a single shear band in case
the shear zone consists of a single shear band, from the small and
medium DS tests on dense Toyoura sand and the medium DS test on
the sandy gravel. In this figure, the relationships between speak and
the total thickness of multiple shear bands that developed in the
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18 GEOTECHNICAL TESTING JOURNAL
FIG. 31—Shear displacement at peak state versus the number of shear band
共N兲 times shear band thickness 共Wsb兲 and shear zone thickness 共Wsz兲.
respective shear zone, NWsb, are also presented. The corresponding
data from medium DS tests on dense Toyoura sand from Qiu et al.
(2000) are included in these data. It may be seen that, with dense
Toyoura sand, the speak value is rather proportional to the average
thickness of shear zone, Wsz, not to the total thickness of multiple
shear bands, NWsb. This means that the deformation of shear zone
is rather uniform at least until the peak stress state and the normalization of shear displacement and volume change based on the average thickness of shear zone, Wsz, is relevant at least until the peak
stress state.
On the other hand, Fig. 32 shows the relationships between the
ultimate volume increase at the residual state, dres, and the average
thickness of shear zone, Wsz, and those between dres and the total
thickness of multiple shear bands, NWsb, corresponding to Fig. 31.
It may be seen that, with dense Toyoura sand, the dres value is rather
proportional to NWsb, not to Wsz. This result indicates that the deformation of shear zone becomes less uniform associated with the
development of multiple shear bands in a progressive way with an
increase in the shear displacement in the post-peak regime. It seems
that, as multiple shear bands start developing in a shear zone,
strains are more localized in the shear bands. This means that the
normalization of shear displacement and volume change based on
NWsb, becomes more relevant with an increase in the shear displacement in the post-peak regime, in particular at the residual
state.
Furthermore, it may be seen that the same speak and Wsz relation
is relevant to both Toyoura sand and sandy gravel in Fig. 31, while
the same dres and NWsb relation is relevant to both Toyoura sand and
sandy gravel in Fig. 32. This consistent result supports the arguments on the reason for the specimen size effects on the stressstrain relations from the DS tests given above.
We can find a number of papers in the literature on the scale
effects in the DS test results of granular materials (e.g., Cerato and
Lutenegger, 2006). However, for either or all of the following reasons, it is very difficult to compare the scale effects observed in the
present study with those from most of these previous other studies
(except for those referred to in this paper) on the same basis:
1.
2.
3.
4.
The detailed structures of DS apparatus and test procedures, of which the effects on test results are one of the
major objectives of the present study, are not fully, or not at
all, reported.
Unlike the present study, the scale effects were analyzed
based on the data from DS tests using the apparatuses of
“type A” or “type C” with measurement of Wupper to obtain
the normal stress (Fig. 1), except for Jewell and Worth
(1987), Palmeira and Milligan (1989) and Shibuya et al.
(1997). There could be a large variance in results from DS
tests using type A (Takada, 1993), while measured values
of Wupper with type C could not be accurate (Shibuya et al.,
1997).
Unlike the present study, the scale effects were not analyzed by comparing the DS test results with those obtained
by using other laboratory stress-strain test types (e.g., TC,
PSC and TSS tests) while taking into account relevant factors (i.e., strength anisotropy, different definitions of friction angle and the effects of intermediate principal stress),
except for Shibuya et al. (1997).
Unlike the present study, the observed scale effects were
not analyzed based on the internal deformation pattern of
specimens having different sizes, except for Jewell and
Worth (1987) and Palmeira and Milligan (1989).
Conclusions
From the data and their analysis presented above, the following
conclusions can be derived:
1.
FIG. 32—Dilatancy at residual state versus number of shear bands 共N兲 multiplying by shear band thickness 共Wsb兲 and shear zone thickness 共Wsz兲.
2.
In the small direct shear (DS) tests on dense Toyoura sand
with a ratio of the specimen length to the mean particle diameter, L / D50, equal to 40 mm/ 0.17 mm, an experimentally correct peak strength could be evaluated by measuring
the normal load acting at the inside face of the top platen of
the upper shear box. However, to accurately evaluate the
stress-displacement relations at large shear displacements
in the post-peak regime, the normal load acting on the shear
zone should be obtained by measuring the total normal load
with load cells located outside the shear boxes.
The failure of dense Toyoura sand was more progressive in
disk-type specimens having a circular cross section than in
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WU ON DIRECT SHEAR TEST
3.
4.
5.
6.
7.
those having a square or rectangular cross section. It is suggested to use the latter shape to more accurately evaluate
the direct shear behavior of granular material.
The peak strength by DS shear tests of dense Toyoura sand
decreased with an increase in the ratio L / D50 from
40 mm/ 0.17 mm= 235 (i.e., conventional small DS tests)
toward 800 mm/ 0.17 mm= 4700 (special very large DS
tests), approaching the value from drained torsional simple
shear (TSS) tests performed under otherwise the similar
test conditions. The DS strength from medium and large
DS tests on dense Toyoura sand was also consistent with
those from drained plane strain compression (PSC) tests
when taking into account the effects of inherent anisotropy
in the strength while based on the same definition for the
angle of internal friction.
The abovementioned agreement of shear strength from the
medium and large DS tests and the TSS tests is due likely to
that, in the medium and large DS tests, the effect of mechanical boundary restraint on the free development of
shear band, which might be still nonzero, is balanced by the
effect of progressive failure in the lengthwise direction of
specimen. The effects of these two factors depend on L / D50
and, due to the former factor, only single shear band was
forced to develop in small dense Toyoura sand specimens
with L / D50 = 235 and a medium sandy gravel specimen
with L / D50 = 300 mm/ 2 mm= 150. On the other hand,
multiple shear bands developed in the shear zone in medium dense Toyoura sand specimens with L / D50
= 300 mm/ 0.17 mm= 1,764.
As a result from the conclusions 3 and 4 above, it seems
that, when only a single shear band develops in the DS
specimen of dense granular material, the peak strength is
overestimated by mechanical boundary restraint when
compared to those from stress-strain tests in which the effect of mechanical boundary restraint as well as the effect
of progressive failure are deemed to be insignificant (e.g.,
TSS and PSC tests).
The specimen size effects on the deformation property of
granular material in DS tests can be explained by the effects of L / D50 on the thickness of the shear zone and the
number of shear bands involved in the shear zone.
The residual strength of Toyoura sand was essentially independent of the specimen size effects in terms of L / D50 as
well as the initial void ratio, and consistent with those from
the TSS tests.
Acknowledgments
The authors would like to acknowledge the cooperation provided
by Dr. Uchimura, T., and Dr. Honda, T., Geotechnical Laboratory,
the University of Tokyo and Dr. Hirakawa, D., and Dr. Kongkitkul,
W., Geotechnical Laboratory, Tokyo University of Science.
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