Title of Thesis: Effects of anisotropic stress states on deformation characteristics of sand in small strain range（砂の微小ひずみ変形特性に与える異方応力状態の影響）
Name: Mangone Sambe
Supervisor: Hirofumi Toyota

1. Introduction
The real ground formed by sands and/or clay has
usually anisotropic mechanical behavior. Two typesof anisotropy, as shown in Fig. 1, are defined in
Geotechnical Engineering: inherent anisotropy
which develops from orientation of soil particles
during sedimentation, and induced anisotropy whicharises when anisotropic stress is applied to the soil.
A deep understanding about the anisotropy and theeffects on deformation characteristics of soils arevery important when analyzing ground deformationin engineering earthworks. Accurate initial shear
modulus of soils is a key parameter to design andconstruct the underground structures rationally.
The purpose of this research is to study the effectof anisotropic stress states on deformation
characteristics of sand in small strain range(represented by the stiffness = initial shear modulus

that Toyoura sand is a sub-angular to angular poorly
graded fine quartz rich sand (Fig. 2). The physicalparameters of the sand are shown in Table 1. A
container with movable walls (Fig. 3) was employed
to create a soil fabric at different deposition angle (0,45 and 90 degrees). Air pluviation method was used
to make the specimen. The processes of making thespecimen (Fig. 4) are: 1. to pour the sand into thecontainer, 2. To immerse it into water. Then the water
was dehydrated from the soil bloc and then aspecimen of 125 mm and 50 mm respectively inheight and diameter was trimmed to conduct theexperiment.

ρs (g/cm3)

emaxeminUc

D50 (mm)

2.650.990

0.597

1.48

0.2

Table 1: Physical parameters of Toyoura sandG0).

Figure 1: Definition of two types of anisotropy
2. Experiments
2.1. Testingmaterialandspecimen
preparation
Toyoura sand, a Japanese standard sand, was used
for this study. The particle size distribution shows

Figure 2: Particle size distribution of Toyoura sandPage 1|6

(a): Local small strain

Figure 3: Container with movable walls(b): Bender element

Figure 4: Process of making the specimen
2.2. Tests conducted with the triaxial
apparatus
The monotonic triaxial compression/extension test
on small strain triaxial apparatus was used for thisstudy. Two tests namely local small strain (LSS) andbender element (BE), shown in Fig. 5, wereconducted to determine the deformation
characteristic of the sand represented by the stiffness

Figure 5: Tests conducted and parameters obtainedwith the triaxial testing apparatus
2.3. Representative stress paths
Monotonic compression loading and monotonic
extension loading tests were conducted to carry out
this study. Figures 6 and 7 show the differerent stresspaths of the tests.

(or initial shear modulus, G0).
Parameters of axial strain (a) and radial strain (r)were obtained with the LSS test. Then shear strain(s) and initial shear modulus (G0) were calculated
from these two parameters.
In BE test, the parameter of wave travel time (t)
was obtained. Then the shear wave velocity (Vs) andinitial shear modulus (G0) were calculated.

(a): Saturated sandelementP a g e 2 | 6

sand, specimens were consolidated at effective
pressure of 150 kPa. The stress ratio, K, was definedas the ratio between the radial stress and the axial(b): Unsaturated sandFigure 6: Stress paths of compression tests

stress (K = σr/σa). The conditions of the anisotropy
during consolidation were defined as follows:
K=1: isotropic consolidation;
K<1: Compressional anisotropic consolidation(K=0.25, 0.4, and 0.6 in this study);
K>1: Extensional anisotropic consolidation(K=2 and 3 in this study).
The difference between the compression andextension tests is recognized as the shearing process
shown in Fig. 8. In compression shearing, the lateralstress (σr) was constant, the axial stress (σa)
increased and the specimen was expanding laterally.
In extension shearing, the lateral stress (σr) wasconstant, the axial stress (σa) decreased and thespecimen was expanding vertically.

Compression shearing(a): Saturated sand

Extension shearing(b): Unsaturated sandFigure 7: Stress paths of extension tests
Drained q-loading was conducted for saturated
sand at effective pressure of 50 kPa while drying wasconducted for unsaturated sand by applying suctionof 50 kPa. Then for both saturated and unsaturated

Figure 8: Shearing process

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3. Results and discussion
3.1. Bender element results
Bender element results of compression tests,presented in Fig. 9, show that the same tendency isobserved on saturated and unsaturated sands for both
depositional angles (0°, 45°, and 90°).
Under compressional anisotropic consolidation(K<1), the initial shear modulus (G0) decreases when
the stress ratio becomes larger from K=0.4 to K=1.
Then, under extension anisotropy consolidation(K>1), it increases from K=1 to K=2. However, fromK=0.4 to K=0.25 and K=2 to K=3, G0 decreases. G0of unsaturated sand is greater than those obtained on(c): Deposition angle 90°

Figure 9: Bender element results

saturated sand.
3.2. Local Small Strain results
Local small strain (LSS) results are presented in Fig.
10. The compression tests show that the secant shear
modulus (Gsec) becomes greater when the stress ratio
is larger, from K=0.25 to K=0.4. Then it decreases
from K=0.4 to K=3.
LSS results of extension tests show that the secant
shear modulus (Gsec) is decreasing when the stressratio becomes larger from K=0.25 to K=2.

(a): Deposition angle 0°(a): Compression tests(b): Deposition angle 45°

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(b): K=0.4(b): Extension tests

Figure 10: Local small strain results
3.3. Comparison between compression andextension testing results
The comparison between the results obtained incompression and extension tests are shown in Fig. 11.
The secant shear modulus is almost same forcompression and extension tests at very small strain(smaller than 0.001%). From the strain of 0.001% to0.1%, the secant shear modulus of extension tests isgreater than that obtained in compression tests.
The difference between compression andextension becomes smaller when the stress ratio
increases and reaches K=1.

(c): K=0.6

Figure 11: Comparison between compression andextension testing results
4. Conclusions
The following conclusions are made for this study:
Bender element results of compression tests
show that the initial shear modulus (G0) on
unsaturated sand is greater than those obtained(a): K=0.25

with the saturated sand. Under compressional
anisotropic condition (K<1), G0 decreases when
the stress ratio becomes larger from K=0.4 to
K=1. Then, under extensional anisotropiccondition (K>1), it increases from K=1 to K=2.
Local small strain results show that the secant
shear modulus, Gsec, becomes greater when thePage 5|6

stress ratio increases from K=0.25 to K=0.4.
Then it decreases from K=0.4 to K=3.
In extension tests, local small strain results showthat the secant shear modulus (Gsec) isdecreasing when the stress ratio becomes larger
from K=0.25 to K=2.
The comparison shows that the shear modulusof extension tests is greater than that obtained in
the compression tests when the strain increases.
The difference becomes smaller when the stressratio reaches K=1.

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