ARMA 08-204
The role of oversize particles on the shear strength and deformational
behavior of rock pile material
Fakhimi, A.
Associate Professor, Department of Mineral Engineering, New Mexico Tech, Socorro, NM, USA &
Department of Civil Engineering, University of Tarbiat Modarres, Tehran, Iran
Hosseinpour, H.
Graduate Student, Department of Mineral Engineering, New Mexico Tech, Socorro, NM, USA
Copyright 2008, ARMA, American Rock Mechanics Association
nd
This paper was prepared for presentation at San Francisco 2008, the 42
July 2, 2008.
nd
US Rock Mechanics Symposium and 2
U.S.-Canada Rock Mechanics Symposium, held in San Francisco, June 29-
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presented.
ABSTRACT: Large rock fragments were encountered during the in situ shear testing on the Questa mine rock pile materials, New
Mexico, USA. The in situ shear boxes used in the field were 30 cm × 30 cm and 60 cm × 60 cm in size. In order to evaluate the
effect of these oversize particles on the friction angle and cohesion of the rock pile material, several laboratory shear tests with a
box 6 cm × 6 cm in size were conducted where the oversize particle was simulated using stainless steel spheres that were placed
along the shear plane. The experimental findings suggest that the presence of the oversize particle causes an increase in friction
angle while the cohesion can either decrease or increase depending on the size of the oversize particle with respect to the size of
shear box and the location of the oversize particle along the shear plane.
1. INTRODUCTION
The effect of oversize particles on shear strength of soil
has been studied by some researchers with emphasis on
the role of scalping on the mechanical behavior of rock
fill dam material. Holtz and Gibbs [1] conducted several
triaxial tests on river sand and gravel and quarry material
to investigate the effect of the density, maximum particle
size, particle shape, and amount of gravel on the shear
strength of the material. All specimens were saturated
before testing and the loading rate was slow enough to
allow free drainage of the material without generating
any excess pore water pressure. To study the effect of
specimen size on the shear strength, very small (34.9
mm × 76.2 mm), small (82.5 mm × 206.4 mm), medium
(152.4 mm × 381 mm), and large (228.6 mm × 571.5
mm) specimens were tested. Test results on sand
specimens (passing No. 4 sieve size) compacted at 70%
relative density showed similar friction coefficients
irrespective of the specimen size except for the very
small specimen that showed marked increase in shear
strength. The authors attributed this increase in shear
strength to the appreciable coarse sand of 4.763 mm
(3/16-inch) maximum size that resulted in a maximum
particle size to cell diameter ratio of 0.14. Hennes [2]
investigated the effect of particle size, shape, and
grading on the friction angle of dry, rounded gravel and
crushed rock. The shear test apparatus was 152.4 mm ×
304.8 mm (6-inch × 12-inch) in size. He concluded that
as the maximum particle size increases, the friction angle
increases. The same conclusion was made as some
complementary triaxial tests were conducted by this
author. Note that in this research work, the specimens
were compacted following identical vibration and
tapping of the materials without verifying the resulting
porosity of the specimens.
Vallerga et al. [3] did not observe any change in friction
angle of granular materials using traixial tests for the
situation that the specimen diameter to maximum
particle size ratio was larger than about 15. In the series
of tests conduced, the compaction of specimens were
controlled to achieve a fixed void ratio irrespective of
the maximum particle size.
Rathee [4] in his study of granular soils, using a 30 cm ×
30 cm shear box and maximum applied normal stress of
about 300 kPa, concluded that the ratio of specimen
width to maximum particle size that will not affect the
shear strength is in the order of 10 to 12 for sand-gravel
mixture. Based on this author, the friction angle of sandgravel mixture increases with the increase in the
maximum particle size while for almost uniform size
gravel, the friction angle was almost constant with
increasing the maximum particle size. Su [5] performed
triaxial tests and suggested that the static strength of a
soil with oversize particles in the floating state is mainly
determined by the soil matrix in the far field; tests
should be performed on the soil matrix alone at the dry
density of far field matrix to obtain the shear strength of
the soil with the floating oversize particles. Cerato and
Lutenegger [6] studied the scale effect of direct shear
tests on sands. Their study showed that the friction angle
measured by direct shear testing can depend on
specimen size, and that the influence of specimen size is
also a function of sand type and relative density. They
concluded that for dense sand, the friction angle
measured by direct shear testing reduces as the box size
increases and that a box width to maximum particle size
ratio of 50 or beyond should be used in order to
minimize the size effect on the friction angle of sand.
Furthermore, these authors claim that the thickness of
shear zone in a direct shear test is not only a function of
the mean particle size (D50) but also it depends on the
height and width of the box.
While the above research works illustrate no change or
increase in friction angle with the increase in the
maximum particle size or the ratio of maximum particle
size to the box width, there have been reports that
suggest reduction in friction angle with increase in
particle size. For example, Becker et al. [7] used a
biaxial apparatus to measure the friction angle of earth
dam material in a plane strain condition. They concluded
that in general the friction angle decreases as the
maximum particle size is increased but the difference in
friction angle between the small size material and the
large size material reduces as the confining pressure
increases. Nieble et al. [8] conducted direct shear tests
on uniform crushed basalt and showed that as the
maximum particle size increases, the friction angle
decreases. His study showed that a maximum particle
size less than 5% of the shear box width should be used
to avoid size effect in measuring friction angle.
Kirkpatrick [9] studies on Leighton Buzzard sand with
uniform particle sizes using triaxial tests showed
reduction of friction angle as the mean particle size was
increased while the porosity was kept a fixed value.
Large triaxial tests on gravelly soils with parallel
straight-line grading curves and with maximum particle
sizes of minus sieve No. 10, 6.35 mm, 12.7 mm, 25.4
mm and 50.8 mm were conducted by Leslie [10]. All
gradings had a uniformity coefficient of 3.3. Based on
these series of tests, he concluded that the intermediate
particle sizes rather than the large particles had a greater
influence on the shear strength and that the influence of
oversize particles may not be as important as was
suspected.
To eliminate or reduce the effect of oversize particles on
the shear strength, ASTM standard D3080-98 [11]
recommends that the maximum particle size in a shear
test must be no larger than one tenth of the shear box
width and one sixth of the specimen height.
The above literature survey indicates that there is no
general agreement on the effect of oversize particles on
the shear strength of soil. Note also that almost all the
research work in this field has been concentrated on
cohesionless material. Furthermore, the authors of this
paper are not aware of any research work that studied the
effect of one oversize particle on the shear strength of
rock pile material. All the above studies seem to be
related to earth rock fill dam or sandy-gravelly materials
and the effect of scalping on their shear strength.
In order to measure the shear strength of the near surface
material in some of the rock piles at the Questa mine,
New Mexico (USA), several in situ shear tests using
boxes 30 cm × 30 cm and 60 cm × 60 cm were
conducted. The details of the shear box apparatus and its
accessories have been reported elsewhere [12]. In
majority of the in situ tests, one or two oversize particles
were encountered in the rock pile block along the shear
plane that can modify the shear strength and
deformational behavior of the material. To address this
issue, laboratory studies were performed on Questa rock
pile material with oversize particles whose results are
reported in this paper.
2. SAMPLE PREPARATION
Experimental studies were conducted on the material
collected from Spring Gulch rock pile that passed
through sieve No. 6 using a 6 cm × 6 cm shear box. The
original and scalped gradation curves are shown in
Figure 1. To reduce the errors associated with material
variations, the rock pile material retained on sieve
numbers 10, 16, 30, 40, 50, 70, 100, and passed sieve
No. 100 were collected in separate containers and mixed
together according to the gradation curve of Figure 1 for
direct shear testing. The air dried material was mixed
thoroughly with water to result in 6% water content.
This water content is about the average value of the
unsaturated rock pile materials that was measured in the
field. Each sample was compacted in three layers in the
shear box by tapping it carefully to result in a dry
density of 1670 kg/m3. Note that in all shear tests, the
dry density of the soil matrix was kept equal to 1670
kg/m3 irrespective of the size of the oversize particle.
The normal stresses used for shear testing were 20.5
kPa, 42.3 kPa, and 68.2 kPa that are similar to those
used for in situ shear testing. The oversize particles were
simulated by using stainless steel spheres or balls having
diameters of 0.66 cm, 1.28 cm, and 1.90 cm. The reason
for using spherical particles was to reduce the number of
In-situ
1
80
Lab
20.5
Left
70
60
42.3
68.2
40
20.5
20
10
Middle
30
42.3
10
10.000
1
1.000
0.1
0.100
0.01
0.010
20.5
Right
Fig. 1. Gradation curves (in situ and lab) of the material used
for experimental study.
42.3
68.2
Left
20.5
Direction of
applied force
42.3
68.2
Middle
1.28
42.3
68.2
Right
20.5
42.3
68.2
Fig. 2. A photo of the shear box showing tilting of the top
plate, direction of applied shear force, and right (R) and left
(L) sides of the box.
Left
42.3
68.2
6
7
8
9
10
11
2
2
2
13
15
16
17
18
19
20
21
22
23
24
25
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
42.3
Right
20.5
42.3
68.2
20.5
42.3
68.2
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
Peak Shear Stress
(kPa)
65.8
89.2
90.7
30
30
50.2
51.2
74.6
83.4
3
3
3
3
30.7
30.7
32.2
54.1
54.1
51.2
77.5
80.9
79
29.3
31.9
30.7
2
2
2
2
2
2
3
3
2
2
2
47.2
48.3
72.8
77.2
30.7
26.3
51.2
54.6
74.6
72.8
29.3
25.6
45.8
50.2
43.9
70.2
73.1
73.6
24.9
27.5
45.3
43.9
70.2
68.8
25.3
3
53
68.2
N/A
52
70.2
81.9
3
51
20.5
Middle
0.66
In total, 68 direct shear tests were conducted. To assure
the consistency and repeatability of the shear tests
results, normally more than one test was performed for a
fixed ball size, ball location, and applied normal stress.
Table 1 shows the results of all the shear tests. All the
shear tests were conducted at a displacement rate of
approximately 0.5 mm/min. Figure 3 shows the resulting
Mohr-Coulomb failure envelopes. Each envelop is a
regression line passing through all the points of shear
20.5
No Ball
3. DIRECT SHEAR TEST RESULTS
5
36.6
35.1
2
26
20.5
R
4
14
0.001
0.001
Grain Size (mm)
L
39.2
3
12
68.2
100
100.000
2
3
50
0
1000
1000.000
Number of Tests
90
Test Number
30 40 50 60 100 200
Normal Stress (kPa)
4 6 10 16
1.90
Percent Passing by Weight
100
3/8
Table 1. The results of laboratory direct shear tests.
Ball Location
U.S. Standard Sieve Size
3 2 1.5 1 3/4
test results with the same ball size and ball location. The
average shear stress-shear displacement curves for the
shear tests at the normal stress of 68.2 kPa are shown in
Figure 4. Figures 3 and 4 suggest that the presence of the
oversize particle changes the shear strength of the
material, and that this effect is more pronounced when
the largest oversize particle (1.90 cm in diameter) is
used.
Ball Diameter (cm)
parameters involved in this study; non- spherical
particles can have different degrees of sphericity and
angularity that add to the complexity of the problem.
The oversize particles were accommodated along the
shear plane at the center and the left and right sides of
the shear box to investigate whether the location of
oversize particle modifies the shear strength. Figure 2
shows a photo of the shear box in which the left and
right sides of the box with respect to the location of
applied shear force have been depicted by letters L and
R, respectively.
26.3
27.8
2
2
1
1
1
3
2
3
49.7
52.7
66.6
68.8
24.9
43.9
67.3
27.8
29.3
29.3
52.7
48.3
68.8
73.1
70.2
To investigate the dilatational behavior of the material,
the average normal displacements at the center of top
plate versus the shear displacement for the normal stress
of 68.2 kPa are shown in Figure 5. Except for the largest
ball, the dilatational behavior of the material remained
almost unchanged. As expected, the test with largest ball
shows more dilatation, indicating that more energy is
needed to shear the material that is consistent with the
higher peak shear stress in Figure 4. Note that in Figure
5 the points corresponding to the peak shear stresses are
shown with larger symbols, suggesting that a greater
shear displacement corresponding to the peak shear
stress is observed for the shear tests with the two largest
balls.
100
100
Shear stress (kPa)
Peak shear stress (kPa)
Left
80
60
40
No Ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
20
0
0
20
40
Normal stress = 68.2 kPa
80
60
40
No Ball
Ball diameter = 0.66 cm
20
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0
0
2
4
6
8
10
12
Shear displacement (mm)
60
80
Normal stress (kPa)
(a)
(a)
100
100
Shear stress (kPa)
Peak shear stress (kPa)
Right
80
60
40
No Ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
20
0
0
20
40
Normal stress (kPa)
60
Normal stress = 68.2 kPa
80
60
40
No Ball
Ball diameter = 0.66 cm
20
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0
0
2
4
6
8
10
12
Shear displacement (mm)
80
(b)
(b)
100
100
Shear stress (kPa)
Peak shear stress (kPa)
Middle
80
60
40
No Ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
20
0
0
20
40
60
Normal stress = 68.2 kPa
80
60
40
No Ball
Ball diameter = 0.66 cm
20
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0
0
2
4
6
8
10
12
Shear displacement (mm)
80
Normal stress (kPa)
(c)
Fig. 3. Mohr-Coulomb failure envelopes for the ball located at
the a) left side, b) right side, and c) middle of the shear box.
(c)
Fig. 4. Shear stress vs. shear displacement for ball located at
the a) left side, b) right side, and c) middle of the shear box.
Table 2. The measured friction angles, dilation angles, and
cohesions in the direct shear tests.
Normal stress = 68.2 kPa
1.3
1.1
4
6
8
10
12
Shear displacement (mm)
(a)
Normal stress = 68.2 kPa
Left
48.2
9.0
15.8
Middle
46.5
10.1
7.6
Right
45.1
8.7
10.6
Left
42.8
5.9
10.8
Middle
43.3
5.1
10.5
Right
43.4
7.4
7.4
Left
42.3
6.1
7.1
Middle
41.1
6.8
10.1
Right
42.8
6.9
8.9
N/A
41.2
7.1
11.5
D = 1.28
Normal displacement (mm)
1.5
c (kPa)
2
Dilation angle (Degree)
(Normal stress 68.2 kPa)
-0.1 0
1.3
1.1
0.9
0.7
0.5
No ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0.3
0.1
-0.1 0
2
4
6
8
10
12
(Degree)
0.1
Location of the ball
No ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0.3
Ball diameter (cm)
0.5
D = 1.90
0.7
D = 0.66
0.9
No Ball
Normal displacement (mm)
1.5
Shear displacement (mm)
(b)
tan( ) =
Normal displacement (mm)
1.5
Normal stress = 68.2 kPa
1.3
1.1
0.9
0.7
0.5
No ball
Ball diameter = 0.66 cm
Ball diameter = 1.28 cm
Ball diameter = 1.90 cm
0.3
0.1
-0.1 0
2
4
6
8
10
12
Shear displacement (mm)
(c)
Fig. 5. Normal displacement vs. shear displacement for the
ball located at the a) left side, b) right side, and c) middle of
the shear box.
4. DISCUSSION OF THE RESULTS
The friction angles (G), dilation angles (H) and cohesion
intercepts (c) from direct shear tests are reported in
Table 2. The dilation angles corresponding to the peak
shear stresses and a normal stress of 68.2 kPa were
obtained from Figure 5 using the following equation
[13]:
d
d
yy
xy
=
dv
du
(1)
where Jyy and Kxy are normal and shear strains, and v and
u are vertical (normal) and shear displacements,
respectively. Note that this equation is valid only if the
shear plane is assumed to be a zero extension line. As
expected, the data in Table 2 show that in general with
increase in friction angle, the dilation angle increases.
The friction angles, dilation angles, and cohesions of the
material with and without the oversize ball shown in
Table 2 indicate how the shear strength and
deformational characteristics of the material are affected
with the ball size. In Figure 6a, the variation of friction
angle as a function of normalized ball diameter with
respect to box width is shown. It is clear that with
increase in the ball diameter, the friction angle increases.
The maximum increase in the friction angle is for the
test with the largest ball located in the left side of the
box that shows a friction angle of 48.2° compared to the
no ball situation whose friction angle is 41.2°. The
friction angle of 48.2° is higher than those of 46.5° and
45.1° for the situations where the largest ball is
accommodated in the middle and right side of the box,
respectively. Preliminary observations suggest that
depending on the location of the oversize ball in the
shear box, different kinematical constraints in the box
deformation are realized that affect the shear strength of
the material. For example, even though the final vertical
A hybrid discrete-finite element analysis is underway by
the authors to investigate the effect of oversize particles
in more detail. This numerical investigation should help
to elucidate the shear band formation and the
deformation pattern around the oversize particle in order
to better interpret the experimental findings reported in
this paper.
48
ASTM recommended limit
46
44
42
40
38
36
34
0
There is no general agreement in the literature on the
effect of oversize particles on the shear strength of soil.
To study this problem, several direct shear tests with
specimens 6 cm × 6 cm in size were conducted on the
Questa mine rock pile materials. This study should help
to interpret the in situ shear tests conducted in the mine
area where oversize particles along the shear plane were
encountered. To simulate the oversize particles,
spherical balls made of stainless steel with different
diameters were placed along the shear plane. The results
of direct shear tests suggest that in general both the
friction angle and dilation angle increase due to the
presence of the oversize particle, even though the effect
of an oversize particle is much more pronounced on the
0.1
0.2
0.3
0.4
Ball diameter/box width
(a)
18
16
14
12
10
8
6
4
5. CONCLUSION
Ball at the left of box
Ball in the middle of box
Ball at the right of box
ASTM recommended limit
Figure 6b illustrates the cohesion intercept versus the
normalized ball diameter. Except for the largest ball
located at the left side of the box, the cohesion reduced
due to presence of oversize particle. Depending on the
location of the ball and its size, the decrease in cohesion
intercept could be 10 to 40% with an average of about
15%. Nevertheless, cohesion in general is more sensitive
to soil remoulding compared to friction angle, and its
measurement in the lab might be questionable.
50
Friction angle (degree)
It is important to realize that the increase in friction
angle due to presence of oversize ball is only a couple of
degrees even when the normalized ball diameter is equal
to 20%. This indicates that the recommendation
regarding the maximum allowable particle size in a
direct shear tests by ASTM (maximum particle size /
box width < 0.1) can be somewhat relaxed, at least for
the rock pile material in this study and the given range of
low normal stresses.
friction angle compared to that on the dilation angle. The
recommendation made by ASTM regarding the
allowable maximum particle size seems to be too
conservative for the case studied, i.e., for the low normal
stress used and the rock pile material investigated.
Instead of a limit of 0.1 for the ratio of maximum
particle size to box width, a ratio of 0.2 can be applied
with only minimal increase in friction angle (about 2
degrees). The results of this study show also that
cohesion is normally underestimated if oversize particles
are present in the shear box.
Cohesion (kPa)
displacement of the center of top platen was almost the
same in all the three tests shown in Fig. 5, the tilting of
top platen (Fig. 2) was slightly different depending on
the location of the oversize ball. Discrete element
numerical modeling of the shear box is currently
underway to better clarify the reason for the change of
friction angle with the location of oversize ball. Note
also that tilting of the top platen causes a non-uniform
distribution of soil density and normal stress within the
deformed specimen and that can be another reason for
sensitivity of the shear tests results with the largest ball
to the ball location.
2
0
0
Ball at the left of box
Ball in the middle of box
Ball at the right of box
0.1
0.2
0.3
0.4
Ball diameter/box width
(b)
Fig. 6. Friction angle (a) and cohesion (b) vs. normalized ball
diameter. The allowable maximum particle size / box width
recommended by ASTM is shown with the dashed line.
AKNOWLEDGMENTS
This project was funded by Chevron Mining Inc.
(formerly Molycorp Inc.), and the New Mexico
Bureau of Geology and Mineral Resources
(NMBGMR), a division of New Mexico Institute of
Mining and Technology (New Mexico Tech). David
Jacobs, and Dirk Van Zyl reviewed an earlier
version of this manuscript and their comments are
appreciated.
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2.
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3.
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