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Abstract

The measurement and study of the stress-strain-strength behavior of soils in general stress states involving principal stress rotation are necessary and valuable. To investigate the strength behavior under principal stress rotation, a series of undrained tests on compacted hollow cylinder specimens of completely decomposed granite (CDG) was carried in hollow cylinder apparatus. Tests were conducted using constant inside and outside pressures and maintained a fixed angle of rotation of principal stress with the vertical (α). Seven different angles of major principal stress orientations were used to cover the entire range of major principal stress directions from vertical to the horizontal. Two different confining stresses were used to find out the variations of the experimental results. It is observed that the deviator stresses as well as excess pore pressures decrease with the angle α. It is also observed that specimens were getting softer with the increase of α. The results also show a significant influence of principal stress direction angle on the strength parameters. It is found that the angle α is related to the occurrence of cross-anisotropy and the localization which resulted in a pronounced influence on the strength parameters of the CDG specimens.
FACTA UNIVERSITATIS
Series: Architecture and Civil Engineering Vol. 8, No 1, 2010, pp. 79 - 97
DOI: 10.2298/FUACE1001079K
INFLUENCE OF PRINCIPAL STRESS DIRECTION ON
THE STRESS-STRAIN-STRENGTH BEHAVIOUR OF
COMPLETELY DECOMPOSED GRANITE
UDC 691.212:531.47+539.211+539.42(045)=111
Md. Kumruzzaman1, Jian-Hua Yin2
1Department of Civil Engineering, Rajshahi University of Engineering & Technology,
Bangladesh, E-mail: kzzaman2001@hotmail.com
2Department of Civil and Structural Engineering, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong, China, E-mail: cejhyin@polyu.edu.hk
Abstract. The measurement and study of the stress-strain-strength behavior of soils in
general stress states involving principal stress rotation are necessary and valuable. To
investigate the strength behavior under principal stress rotation, a series of undrained
tests on compacted hollow cylinder specimens of completely decomposed granite
(CDG) was carried in hollow cylinder apparatus. Tests were conducted using constant
inside and outside pressures and maintained a fixed angle of rotation of principal
stress with the vertical (α). Seven different angles of major principal stress orientations
were used to cover the entire range of major principal stress directions from vertical to
the horizontal. Two different confining stresses were used to find out the variations of
the experimental results. It is observed that the deviator stresses as well as excess pore
pressures decrease with the angle α. It is also observed that specimens were getting
softer with the increase of α. The results also show a significant influence of principal
stress direction angle on the strength parameters. It is found that the angle α is related
to the occurrence of cross-anisotropy and the localization which resulted in a
pronounced influence on the strength parameters of the CDG specimens.
Key words: Hollow cylinder, principal stress rotation, friction angle, failure surface,
cross anisotropy.
1. INTRODUCTION
Rotation of principal stress directions are common features in many geotechnical en-
gineering problems and may have significant influences on the behavior of soils. Axial-
torsional loading on hollow cylinder specimens can better simulate this condition in the
laboratory. Distribution of stresses and the rotation of principal stress on hollow cylinder
Received February, 2010
MD. KUMRUZZAMAN, JIAN-HUA YIN 80
specimen are shown in Fig.1. Broms and Casbarian (1965) first investigated the effects of
the rotation of principal stress axes on the shear strength and pore pressure in kaolin clay.
Experimental findings revealed that the rotation of principal stress causes the increase of
pore pressure coefficient as well as the decrease of deviator stresses. Similar to Broms
and Casbarian (1965), Saada and Zamini (1973) found that the effective stress paths, pore
pressure coefficients and the effective friction angles are functions of the inclination of
the principal stresses for kaolin clay. In addition to that experimental results, Saada and
Townsend (1980) explained in details the state of stresses in hollow cylinder specimens
under axial-torsional loading and described the stress non-uniformities in the hollow cyl-
inder specimens. It was recommended to use the appropriate dimensions of the specimen
to avoid the nonuniform stresses. Saada (1988) further described the advantages and
limitations of testing a hollow cylinder specimen under axial-torsional loading. The effect
of principal stress rotation on kaolin clay was also investigated by Hong and Lade (1989).
The experimental results concluded that the isotropic elasto-plastic theory may be suitable
to model K0 consolidated clay during principal stress rotation. Lin and Penumadu (2005)
presented the effective friction angles, undrained shear strengths, stress-strain relation-
ships, pore water pressures and stress-paths as a function of the angle of principal stress
rotation. Strong anisotropy for kaolin specimens under principal stress rotation was also
concluded using the experimental results.
p
i
p
o
T
W
σ
θ
σ
z
σ
r
τ
θz
σ
1
α
Fig. 1 Elements in a hollow cylinder specimen with forces, pressures, and stresses
Albert et al. (2003) conducted rotation of principal stresses on Bothkennar clay and
found that the effective stress paths are not very brittle as those observed in triaxial com-
pression tests. It was also pointed out that the shearing resistance from torsional shear
tests is similar to the values that obtained in triaxial compression and extension tests.
Lade et al. (2008) performed stress rotation tests on Santa Monica beach sand. It is con-
cluded that the strength parameters are influenced by the cross-anisotropic behavior of
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 81
sand as well as shear banding. Most of the previous test studies were carried out on sedi-
mentary soils like sand and clay. Less previous study has been done to investigate the in-
fluence of the principal stress rotation on the stress-strain behavior of residual soils which
are abundant in many countries and regions, for example; Malaysia, Japan, Korea, Hong
Kong, Taiwan, USA.
In Hong Kong, approximately 90% of the rock is granite. The weathering of the
granite in situ produced a lot of Completely Decomposed Granite (CDG) soils, for exam-
ples, in most soil slopes in Hong Kong. The CDG soils may be cut and used as fill materi-
als (compacted) for land formation works, marine reclamations, as back fills of retaining
walls, etc. Therefore, re-compacted CDG soils are often encountered in most of infra-
structural projects, building projects, and slope stabilization project. As pointed out be-
fore, normally these CDG soils are subjected to a rotation of principal stress. Therefore,
the measurement and study of the stress-strain-strength behavior of CDG soils in 3-D
stress states are necessary and of academic interests and importance.
This paper presents an experimental study to investigate the influence of principal
stress directions on the stress–strain and strength behavior of completely decomposed
granite (CDG) of Hong Kong. Tests have been performed using a hollow cylinder testing
system that has been developed by Geotechnical Consulting and Testing System (GCTS,
2007). The results of consolidated undrained tests with various principal stress directions
on completely decomposed granite (CDG) are presented and discussed.
2. TESTING APPARATUS AND SPECIMEN
The hollow cylinder apparatus that has been employed in this testing program are de-
veloped by GCTS. The apparatus comprises of axial-torsional loading system, pressure
controllers, triaxial cell, and the electronic system. The axial torsional loading system and
pressure system are briefly described below.
2.1 Axial-Torsional Loading
The axial-torsional loading system is shown in Fig.2. The loading frame is relatively
light weight but highly stable and has a small tabletop footprint. The cross head beam
supports the double acting load cylinders used to apply the axial load and torque. These
two GCTS loaders offer low start up pressure, extreme sensitive response, very low fric-
tion and low breakaway force for smooth action. These loaders are servo electro-actuated
with hydraulic pressure. The loading system is capable of applying axial load or torque
separately or both of them simultaneously. The maximum load of 22.25 kN and the
maximum torque of 225 N-m can be applied by using this loading system. The loading
platens (Fig.2) are the interface between the pressure /volume control unit and the testing
specimen. The loading platens can accommodate a specimen having the dimensions: 200
mm in height, 100 mm in outer diameter and 50 mm in inner diameter. Each of the load-
ing platens (cap and base) has eight porous disks (14mm in diameter) and eight lips
(1.7mm in width and 3 mm in height), those can make the specimens saturated and can
produce the smooth torque without any slippage.
MD. KUMRUZZAMAN, JIAN-HUA YIN 82
Load cell
Frame for torque and
angular deformation
Triaxial cell
LVDT for axial
deformation
Top cap
Base
Triaxial cell and loadin
g
p
lates
Fig. 2 Loading frame and triaxial cell for HCA
2.2 Pressurization system
The pressurization system (Fig.3) consists of five electro-hydraulically actuated com-
puter servo controlled pressure/volume controllers, transducers for the direct measure-
ments of volumes and pressures. The five controllers are responsible for the outer cell
pressure, inner cell pressure, top back pressure, bottom back pressure and base pore water
pressure. The system utilizes the hydraulic digital servo control for maintaining necessary
test conditions. Each pressure/volume controller has a capacity of 280 cc and is capable
of providing controls and measurements of volume changes as small as 0.01cc. The
maximum pressure of 1000kPa can be applied through these pressure controllers that are
accurate to pressure of 0.1 kPa. The pressure transducer and an external LVDT supply a
direct feedback response used in the control process. System operation is integrated with
the easy to use CATS (GCTS 2007) software which has the flexibility to follow simple or
complex test conditions.
All the parameters that need to control for maintaining the fixed principal stress ori-
entations are worked with PID control system. So the control achievement is good enough
and PID control makes almost accurate adjustments of the stresses. The advantages of
PID controls have been discussed briefly in Mandeville and Penumadu (2004).
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 83
Fig. 3 Pressure system for hollow cylinder apparatus
2.3 Basic Properties of Completely Decomposed Granite
The Completely Decomposed Granite (CDG) soil used in this study was taken from a
slope site in Hong Kong. Specific gravity tests, particle size distribution tests, Atterberg
limit tests, and standard compaction tests were done on the disturbed CDG soil. The per-
centage of soils finer than the No.200 sieve is about 52%. According to the Unified Soil
Classification System (USCS), the CDG soil is classified as CL. A summary of basic
properties from these tests is presented in Table 1. The grain size distribution curve is
shown in Fig. 4. It is noted that the maximum dry density of 1.80 Mg/m3 was obtained by
the standard compaction tests (using Proctor compaction tests). The dry density in the
most compacted fill slopes is 95% of the maximum dry density, that is, 1.71 Mg/m3. The
dry density of 1.71 Mg/m3 (void ratio= 0.55) was used to prepare all specimens.
Table 1. Properties of the Completely Decomposed Granite (CDG) fill
Parameters Unit Value
Specific gravity (Gs) 2.65
The maximum dry density (ρdmax) Mg/m3 1.80
The optimum moisture content % 15.5
Plastic limit (wp) % 22.7
Liquid limit (wl) % 32.8
Gravel content % 1.0
Sand content % 47.0
Fine content % 52.0
MD. KUMRUZZAMAN, JIAN-HUA YIN 84
0
20
40
60
80
100
0.001 0.01 0.1 1 10 100
Particle size (mm)
Percent finer (%)
Fig. 4 Particle size distribution curve for CDG
2.4 Preparation of specimens and testing procedures
Recompacted CDG soil specimens were used in this testing study. A split mould of
inner diameter 100mm was used for the preparation of specimens. A rigid plastic bar of
diameter 50mm was fixed with a gridded base plate. Wax was used to the inner surface of
mould, outer surface of the plastic rod and the base plate before placing the split mould
on the base plate. The CDG soil was compacted to 95% of the maximum dry density, that
is, 1.71 Mg/m3 with initial water content of 13% to 14%. The soil was compacted in
seven layers in the mould following the procedure described in ASTM standard D4767-
95. At first, the oven dried soil mass was mixed thoroughly with water and then divided
into seven portions. Each portion of soil was then poured into the mould and was tamped
gently to fill up the required volume. The top of each layer was scarified prior to the ad-
dition of material for the next layer. The tamper was used to compact the soil in layers in-
side the mould. After a specimen was formed, the inside plastic rod was pushed and taken
it out. The specimen was placed on the base platen of the triaxial cell and the outer mould
assemble was carefully removed from the specimen so that there is no disturbance of the
specimens. The inner membrane was fixed to the base of the triaxial cell before placing
the specimen. Placing of the top cap and filter strips, outer membrane was then fixed. The
thickness of the rubber membrane was 0.35mm. Triaxial cell was then set by placing the
top cover plate. It is noted that there were two drainage lines (opposite to other) on the
top cap which were connected to single drainage line for drainage of water to or from the
top of the specimens. Fig.5 shows (a) an split mould, solid plastic rod, the top and base of
the mould (left side), (b) a specimen fully enclosed by rubber membrane with water tube
connector (right side) for water drainage or water pressure measurement.
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 85
Fig. 5 (a) Mold assembles for sample preparation and
(b) Specimen placed in hollow cylinder triaxial cell
Setting the whole assemble of the triaxial cell, de-aired water was then used to flush
from the bottom outlet and out of the upper outlet tube to remove entrapped air in the
specimen while maintaining an effective confining cell pressure of 8 kPa (inner and outer
cell pressure 15kPa and back pressure from the bottom of the specimen is 7kPa). The top
drainage valve was open to remove the trapped air. After 3hrs flushing and passing water
through the upper drainage, a back pressure of 200 kPa was applied in all the tests.
Skempton's B-value of 0.96-0.98 was obtained for all specimens.
After saturation, specimens were then consolidated isotropically by applying the same
inner and outer pressures. Two different consolidation pressures of 400 kPa and 200 kPa
were used to consolidate the specimens in this experimental program. The step was fol-
lowed up by a controlled stress path. Seven different stress paths with constant angles of
principal stress rotation (α) of 0o, 23o, 30o, 45o,60o, 67o and 90o were carried out to ob-
serve the effect of principal stress rotation, by means of adjusting the vertical stress, Δσv
and the shear stress, Δτ so that 2α= tan-1(2Δτ/ Δσv) is kept a constant. With a same inner
and outer pressure in a hollow specimen, combination of axial and torsional load can
rotate the principal stress and introduce the coefficient of intermediate principal stress si-
multaneously. The relationship between principal stress direction with the vertical (α) and
the coefficient of intermediate principal stress (b) is expressed as; b = sin2α.
Data acquisition and control loops were performed with updating intervals of 60 secs.
Data from the experiments are logged electronically by a computer. All the transducers in
the setup are connected to a controller through the computer interface unit for data acqui-
sition and control. The controller itself is also connected to the computer. CATS software
(GCTS, 2007) is used to automate various phases of testing such as saturation, consolida-
MD. KUMRUZZAMAN, JIAN-HUA YIN 86
tion, and application of stresses for applying a predetermined stress path or strain path.
The setup of hollow cylinder system is shown schematically in Fig. 6.
Computer
interface unit
Signal conditioning
To/ From
sensors
Load cell
LVDT
deformation sensor
Double
acting
actuator
Connected to the
double acting
actuators
Servo valve
Pressure line
Solenoid valve
Servo amplifier
Computer Controller
(
A
/
D
)
o
r
(
D
/
A
)
Hydraulic
pressure system
Fig. 6 Setup of the hollow cylinder system
3. STRESS AND STRAIN PARAMETERS
The specimens were isotropically consolidated by applying the same inner and outer
pressures. The vertical load and torque were then applied on the specimens to rotate the
major and minor principal stresses. The intermediate principal stress is always fixed to the
horizontal direction and equal to the radial stress. The angle of major principal stress with
the vertical, α can be obtained by the equation: 2α= tan-1(2Δτ/ Δσv).
Neglecting the membrane effects and considering the uniform distribution of stresses
across the cross sectional area (Lin and Penumadu, 2002), the change of vertical stress
and horizontal stresses were calculated as Δσv =W/A and Δτθz= 3T/2π(ro3-ri3), where W is
the axial load, A the cross-sectional area of the specimen, T the torque applied on the
specimen, ro and ri are the outer and inner radius respectively.
The principal stresses and the principal strains were calculated using the following
equations presented in Saada and Townsend (1980) and further extended in Lin and Pe-
numadu (2002):
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 87
γ+εε
ε+ε
=ε
γ+εε+
ε+ε
=ε
ε+θΔ=γ
εε=ε
ε=ε
Δ=ε
σΔτΔ=
+σΔ=σΔ
=σΔ
++σΔ=σΔ
θθ
θ
θθ
θ
θ
θ
22
3
22
1
2
3
2
2
1
)()(
2
1
2
)()(
2
1
2
)1(/.
1)]1/(1[
)]1/(1[1
/
/
2/]411[
0
2/]411[
zz
z
zz
z
zoiz
zz
zr
ovz
v
v
v
Hr
Hu
k
k
k
(1)
Where, Ho is the initial height of the specimen. Δuν and Δθ are the change of vertical
and angular displacements, respectively.
Experimental results for axial and torsional stresses were corrected with the real values
of inner and outer radius. The realtime updated values of inner and outer radius ( Ri and Ro)
during shearing were calculated using the equations used by Tatsuoka et al. (1986)
ε
=
ε
=
i
z
i
o
z
o
rR
rR
1
1
1
1
(2)
where εz is the axial strain. The deviator stress and the mean stresses are calculated as the
followings;
σ
+σ
+σ
=
σσ+σσ+σσ
=
3
2
)()()(
321
2
13
2
32
2
21
p
q
(3)
3.1 Loading paths
For α=0o and α=90o, a test was carried out in stress control mode with compression or
extension at the same speed of 0.1 kN/hr while angular deformation was restrained. Re-
straining of angular deformation generated some torsional stresses and the values were
about ± 3.0kPa, which might be neglected in respect to larger compression (or extension)
stresses (Lin and Penumadu 2005). For α=45o, vertical piston load was controlled to be
zero value, while the torsional stress was applied at the rate of 4.7kPa/hour. Due to the
zero piston loading control in a vertical direction, the loading ram moved and developed
MD. KUMRUZZAMAN, JIAN-HUA YIN 88
some axial strain after a little shear strain. Therefore, the stress and strain were not coax-
ial. For α =23o, 30o, 60o and 67o, vertical and shear stresses were applied as a proportion
of k =Δ
τ
/Δσz. The controller of the hollow cylinder system precisely applied the prede-
fined ratio of vertical and shear stresses. However, the strain paths for α =23o and 30o
were not coincided with the stress paths. Therefore, non-coaxiality has also been observed
for these two stress paths. As the compacted CDG is cross-anisotropic, the cross-anisot-
ropic nature of compacted CDG probably affected the strain paths. In the case of α = 60o
and 67o, such a deviation of strain paths was not found for the CDG. The control of the
loading for α=30o and 60o are shown in Fig.7.
0
15
30
45
60
75
0 5000 10000 15000 20000
Time (sec)
Angle of rotation (degree)
Fig. 7 Directions of principal stresses for α = 30o and 60o (pc= 400kPa)
4. TEST RESULTS AND DISCUSSION
4.1 Stress-Strain Behaviour
The main test results from a series of tests with different inclinations of major princi-
pal stress for two different consolidation stresses are presented and discussed in this sec-
tion. Fig.8 shows measured curves of (a) normalized deviator stress (q/pc) versus shear
strain (ε1 ε3), (b) normalized excess pore water pressure (εν) versus shear strain (ε1 ε3)
and (c) effective stress paths (q-p space) for α-values of 0O, 23O, 30O, 45O, 60O, 67O, and
90O respectively from consolidated undrained tests on the CDG soil specimen for the
consolidation stress of 400 kPa. Fig.9 also shows the same types of curves from undrained
hollow cylinder tests on the CDG soil specimen for pc of 200 kPa. It shall be explained
that curves in Figures 8 and 9 do not have data points since these curves are too close to
each other in most regions. If data points were shown, any small difference of the curves
could not be seen clearly.
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 89
0
0.25
0.5
0.75
0 5 10 15
q/p
c
023
30 45
60 67
90
ε
1
-ε
3
(%)
α- values (degree)
0
0.2
0.4
0.6
0.8
0 5 10 15
Δ
u/
p
c
ε
1
-ε
3
(%)
0
100
200
300
400
0 200 400
p' (kPa)
q (kPa)
0o
90o
(a)
(b)
(c)
α =
Fig. 8 Measured curves of (a) normalized deviator stress (q/p) versus shear strain (ε1- ε3),
(b) normalized excess pore water pressure (εν) versus shear strain (ε1- ε3), and
(c) effective stress paths (q-p space) for consolidation pressure of 400kPa
MD. KUMRUZZAMAN, JIAN-HUA YIN 90
0
0.2
0.4
0.6
0.8
0 5 10 15
Δu/p
c
ε
1
-ε
3
(%)
0
0.25
0.5
0.75
1
051015
q/p
c
023
30 45
60 67
90
ε
1
-ε
3
(%)
α- values (degree)
0
100
200
0 100 200 300
p' (kPa)
q (kPa)
0
o
90
o
(c)
(a)
(b)
α =
Fig. 9 Measured curves of (a) normalized deviator stress (q/p) versus shear strain (ε1- ε3),
(b) normalized excess pore water pressure (εν) versus shear strain (ε1- ε3), and
(c) effective stress paths (q-p space) for consolidation pressure of 200kPa
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 91
From Figures 8and 9, a number of characteristics are observed and are explained as
follows:
(a) The curves of the normalized deviator stress (q/pc) versus shear strain (ε1 ε3)
increase with the decrease of consolidation pressure. The deviator stresses show a
gradual ductile behaviour with the increase in shear strain. Higher deviator stresses
have been observed for α=0 in both two consolidation pressures. The deviator
stresses gradually decrease with increasing α-values from 0O to 90O and the mini-
mum deviator stresses have been observed for α=90 O.
(b) The curves of normalized excess pore pressure (Δu/pc) versus shear strain (ε1 ε3)
show shear compression. Development of excess pore pressure (Δu) decreases
with the increase of major principal stress inclinations from 0O to 90O. The nor-
malized excess pore water pressure is little bit lower under lower consolidation
pressure than that under higher consolidation pressure.
(c) Effective stress paths clearly show the decreasing of shear stress with the increase
of the principal stress inclinations. The contractions of the specimens are similar in
fashion for all inclinations of major principal stresses. It is important to note that
the p values at failure for all inclinations of principal stress are more or less the
same.
Decreasing of deviator stresses as well as the excess pore pressures with the increase
of major principal stress directions to the vertical is reported by previous researchers,
(Luan et. al, 2007; Lin and Penumadu, 2005). It should be noted that the deviator stress
for α=90o has been observed little bit higher than that for α=60 o
in Lin and Penumadu
(2005). But the pore water pressure has the gradual decreasing trend with the increase of
major principal stress directions.
4.2 Friction Angles, Pore pressure coefficient and the Failure surface
The Mohr-Coulomb failure criterion is expressed in terms of the major and minor
principal stresses as for zero effective cohesion:
)(sin '
3
'
1
'
3
'
1
1'
σ+σ
σσ
=φ (4)
where the frictional angle φ' is independent of intermediate principal stress σ'2. In Eqn.(4),
effective cohesion is assumed zero here for easy explanation. The friction angle obtained
is considered to be the secant frictional angle with zero cohesion.
The failure of specimens in this test series has been considered as the peak deviatoric
stress (q/pc) or the point of 15% shear strain. The Mohr-Coulomb friction angles meas-
ured at failure plotted with respect to the value of α are shown in Fig.10. The friction an-
gle initially increases with increasing the value of α up to 30O, after which the friction
angle decreases for α >30O. The difference of friction angle is about 9O in the range of α
from 0O to 90O. Lade et. al. (1994) has been reported the similar trend friction angles for
sands with a variation of about 8O. Towhata and Ishihara (1985) using the cyclic rotation
of principal stress has also been reported the similar trend that has been observed in the
present study. The Skempton's pore pressure parameter, Af at failure is shown in Fig. 11.
There is a monotonic increase of the Af value with the increase of the α from 0O to 90O.
MD. KUMRUZZAMAN, JIAN-HUA YIN 92
The maximum and minimum values of Af have been obtained for α =0O and α =90O. The
maximum and minimum values of Af are consistent to the conventional triaxial compres-
sion and extension.
20
30
40
50
0 306090
200 kPa
400 kPa
Major principal stress inclination, α ( degree)
Friction angle,φ ( degree)
Fig. 10 Secant friction angles versus major principal stress directions
0
0.5
1
1.5
2
0306090
200 kPa
400 kPa
Major principal stress inclination, α ( degree)
Pore pressure coefficient, A
f...
Fig. 11 Pore pressure coefficient versus major principal stress directions
Most of the failure envelopes from axial torsional loading on the sedimentary soils
have been shown in (σz σθ)/2 and τzθ space. The failure envelope presented in
(σz σθ)/2 and τzθ space is simple and clear to describe the stress state of a specimen
(Nishimura et al. 2007). Fig. 12 shows the failure surface obtained in this test series in
(σz σθ) / (2pc) and τzθ / pc space. The shape of the failure envelopes is similar for both
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 93
the two different consolidation stresses, but has some effects of the consolidation stresses.
Stress paths for higher consolidation stress are also plotted in this figure. The stress paths
accurately follow the inclinations of principal stress values.
-0.1
0.1
0.3
0.5
0.7
-0.3 0.0 0.3 0.6
200
400
(σ
z
-σ
θ
)/2p
c
τ
θz
/ p
c
Fig. 12 Failure envelop and the stress paths
5. COMPARISON OF FRICTION ANGLES
The strength behavior of the CDG specimens in torsional shear is compared to that ob-
tained from true triaxial compression as well as the strength from well known 3D failure
criterion for soils. In torsional shear tests where inside and outside pressures are maintained
at the same value, the inclination angle α of the major principal stress relative to the vertical,
direction is related to the parameter b as b = sin2α. The parameter b represents the relative
magnitudes of the intermediate principal stress and expressed as b = (σ2 σ3) / (σ1 σ3). It
should mention here that no direct comparison between these two test conditions is possible.
The author wanted to find out the cause of the lowering of strength parameters in torsional
shear tests at the higher angle of principal stress rotation that has been addressed in Lade et
al. (2008). Fig. 13 shows the friction angles measured from torsional shear tests together
with the friction angles from true triaxial tests, all plotted with respect to the b-value. The
true triaxial compression test results in Fig.12 represent the results in the first sector of π
plane, that is, 0 < θ < 600, here θ is Lode's angle Lade et al. (2008) pointed out that the effect
of cross-anisotropy in true triaxial results may not be pronounced in the first sector. The
curves are also plotted using the three dimensional failure criteria for frictional materials de-
veloped by Lade and Duncan (1975). The parameter of the failure criteria was calculated
using the friction angles from the same triaxial compression tests (α=0) performed on speci-
mens consolidated at two different consolidation pressures.
MD. KUMRUZZAMAN, JIAN-HUA YIN 94
20
30
40
50
0.0 0.2 0.4 0.6 0.8 1.0
b
200 400 TT PS
Lade and Duncan
Friction angle,φ ( degree)
Fig. 13 Comparison of friction angles of CDG in TT and HC specimens
The failure criterion matches the true triaxial test results better than the torsion shear
tests, although the friction angles in true triaxial experiments are lower than the predicted
one. The friction angles from torsional shear tests follow the predicted friction angles
from triaxial compression (b=0.0) to b=0.25. The average of friction angles in plane strain
compression tests of CDG was 42.1 and the corresponding b value is 0.21, which is very
close to the b value of 0.25 (shown in Fig.13). Therefore, the study confirms the findings
of Lade et al. (2008) that the strength parameters in three dimensional cases increase from
triaxial compression to the plane strain condition. The dotted line in Fig.13 shows the
trend line of the friction angles in torsional shear tests. The trend line is much lower than
the predicted friction angles after b=0.25. This is probably due to the cross-anisotropic
behaviour of completely decomposed granite or the strain localization at failure. Lade et
al. (2008) pointed out this type of differences in friction angles obtained from similar tests
on Santa Monica beach sand and described that the occurrence of shear banding or the
cross-anisotropy may cause this lowering of friction angles for b after the condition of
plane strain or b>0.3. Fig.14 shows that no visible shear band has been observed in tor-
sional shear testing on CDG for b0.5. Strain localization occurred in the form of the
necking of the specimens for b>0.5. Therefore, the cross-anisotropy may have consider-
able effect to cause these strength parameters much lower in high range of b up to 0.5.
The experimental results observed for higher ranges of b (b > 0.5), cross-anisotropy to-
gether with the formation of necking may also have significant effect on the lowering of
friction angles of CDG specimens. It needs more in-depth investigation of shear bands or
necking rather than the visual inspection.
Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 95
Fig. 14 Specimens after testing (a) for α=45o, (b) for α=67o and (c) for α=90o
6. CONCLUSIONS
A laboratory study has been carried out to investigate the stress-strain-strength be-
haviour of completely decomposed granite (CDG) for different principal stress directions
from hollow cylinder tests on specimens under consolidated undrained conditions. The
influence of the principal stress direction on the strength behaviour of CDG was com-
pared with the result obtained from the same CDG soil in true triaxial condition. It is ob-
served that the deviator stresses as well as excess pore pressures decrease with the in-
crease of principal stress directions. Shear strength parameters and the coefficient of pore
pressures are also affected by the inclinations of the principal stress. Significant influence
of consolidation pressures have been observed on the failure of the soil. Friction angle
initially increases with the increase of the principal stress inclination up to 30o. After that,
a gradual decrease of the friction angle has been obtained for higher range of inclinations
from 30 o to 90 o. Comparison of strength parameters in principal stress rotation with that
of true triaxial testing shows pronounced effects of cross-anisotropy for inclinations
higher than 30 o. Strain localizations may also have contributed to lower strength parame-
ters of the soil in the higher range of inclinations.
α= 45o α= 67o α= 90o
MD. KUMRUZZAMAN, JIAN-HUA YIN 96
Acknowledgements Financial supports from The Hong Kong Polytechnic University and a grant
from Research Grants Committee (RGC: PolyU 5174/04E) of the Hong Kong Special Administra-
tive Region Government of China are gratefully acknowledged.
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Influence of Principal Stress Direction on the Stress-Strain-Strength Behaviour of Completely Decomposed Granite 97
UTICAJ PRAVCA GLAVNIH NAPONA NA PONAŠANJE
ČVRSTOĆE NAPON-DILATACIJU- KOD POTPUNO
RASPADNUTOG GRANITA
Md. Kumruzzaman, Jian-Hua Yin
Merenja i proučavanja napona-dilatacije čvrstoće tla u opštim stanjima napona uključujući
glavni napon rotacije su neophodna i dragocena. Da bi se istražilo ponašanje čvrstoće pod glavnim
naponom rotacije, sproveden je niz opita na uzorcima raspadnutog granita (CDG) sabijenim u
šupljem cilindru. Opiti su sprovedeni uz stalne unutrađnje i spoljne pritiske uz održavanje fiksnog
ugla rotacije glavnih napona sa vertikalom (α). Korišćeni su sedam različitih uglova orjentacije
glavnih napona za da se pokrije opseg pravaca glavnih napona od vertikale do horizontale. Dva
različita ograničavajuća napona korišćena su za iznalaženje varijanti eksperimentalnih rezultata.
Primećeno je da devijator napona kao i prekoračenje pornog pritiska opada sa uglom α. Takođe je
primećeno da su uzorci sve mekši sa povećanjem ugla α. Rezultati takođe pokazuju značajan uticaj
ugla glavnih napona na parametre čvrstoće. Uočeno je da je ugao α vezan za pojavu poprečne
anizotropije i lokalizaciju koja je rezultirala izraženim uticajem na parameter čvrstoće CDG uzoraka.
Ključne reči: šuplji cilindar, glavni napon rotacije, ugao trenja, površina loma, poprečna anizotropija
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This study concerns the effects of continuous rotation of principal stress axes on excess pore water pressure development during cyclic loading. Continuous rotation of principal stress axes has been known to exert some influence on the development of excess pore water pressure and failure of sand during cyclic loading. In an effort to investigate this aspect of the problem, several series of cyclic undrained tests were carried out in a static manner on saturated sampes of sand using a triaxial torsion shear apparatus. In this test apparatus, a hollow cylindrical soil specimen is subjected to a simultaneous application of both triaxial and torsional modes of shear stresses, which brings about the continuous rotation of principal stress axes. The test results indicated that, while the angle of internal friction remains unaffected, the continuous rotation of principal stress axes substantially reduces the resistance of sand to liquefaction by generating a greater amount of excess pore water pressure than in the case without the rotation. Some special tests were also performed to examine the effects of previous liquefaction on the undrained behavior of sand during the subsequent cyclic loading. The results show that the sand having previously experienced large deformations due to liquefaction exhibit a highly anisotropic stress-strain characteristics, whereby reducing the resistance of the sand drastically when sheared in certain directions.
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In order to investigate the fundamental deformation behavior of sand under the more general stress condition involving the rotation of principal stress axes, a series of drained tests was carried out on a dense anisotropic sand using a hollow cylinder torsional shear apparatus. The hollow cylindrical specimens have an anisotropic fabric formed by the parallel alignment of particles induced during deposition, and are tested under the prinsipal stress axes rotation keeping the values of three principal stress constant. The experimental results showed that the shear deformation of sand due to the rotation of principal stress axes are not negligible as compared with that due to the shear with fixed principal stress axes and the effects of inherent anisotropic fabric on the shear deformation and volume change behavior are considerably large. The mode of anisotropic effects on the deformation characteristics depends strongly on whether the rotation of principal stress axes are involved or not. It was also indicated that the anisotropic deformation characteristics under the principal stress rotation can be explained by taking account of the predominant sliding occurring on the bedding plane, irrespective of whether the principal stress axes rotate or not. This consideration is supported by the fact that the bedding plane has the lowest value of the resistance against shear stress according to the horizontal alignment of subelongated sand particles.
Article
A flexible boundary electro-pneumatic true triaxial system has been developed for testing cohesive soil. The system is capable of applying principal stresses on each face of a cubical specimen using a Proportional-Integral-Differential (PID) based closed loop control algorithm. This device has the ability to measure both the internal and external pore pressures for a 102-mm cubical specimen and uses custom developed Butyl rubber membranes. Measurement of the internal pore pressure is accomplished using a needle piezometer. Appropriate software has been developed that can automatically perform saturation, isotropic or Ko consolidation, and shear testing under stress or strain control along various stress or strain paths. Using this system, results from isotropically consolidated triaxial compression and triaxial extension stress paths are presented for cubical kaolin specimens. Comparative tests using conventional cylindrical specimens using lubricated ends were also performed. Issues related to the interference of the flexible membranes, uniformity of strains and bifurcations, interpreted friction angles, and undrained shear strength are discussed.
Article
laboratory experiments involving oedometer and triaxial stre ss path apparatus. Consequently, the undrained shear strength prof iles with depth for triaxial compression and extension are well established. This paper presents results from hollow cylinder
Article
A combined axial-torsional testing system was developed to investigate the effect of rotation of principal stresses on the three-dimensional mechanical behavior of Kaolin clay. Uniform and reproducible cohesive specimens having a specimen shape of a hollow cylinder were obtained using a two-stage slurry consolidation technique. Precise stress paths (triaxial compression to pure torsional shear to triaxial extension), corresponding to a fixed rotation of the major principal stress axis, were achieved by using the proportional-integral-derivative (PID) feedback control technique. Kaolin clay specimens were tested under a variety of stress paths associated with a constant principal stress rotation angle (β) under undrained conditions. Typical test results, such as effective friction angle, undrained shear strength, stress-strain relationship, pore pressure evolution, and stress paths are presented as a function of β. During shearing, the procedure to use advanced servo-hydraulic control (using PID algorithm in this study) to maintain a fixed β value that involves updating specimen geometry in real-time is described. A new approach for data analysis and visualization is presented for providing a convenient way of incorporating the effect of major principal stress rotation angle considering the degradation of stiffness as a function of stress path in three dimensions. Journal of Geotechnical and Geoenvironmental Engineering