Bui, Man T.
(2009)
Influence of some particle characteristics on the small strain response of granular materials.
*University of Southampton, School of Civil Engineering and the Environment, Doctoral Thesis*, 252pp.

## Abstract

The key parameters representing the small strain response of geomaterials are the very
small strain shear modulus, Gmax, shear modulus degradation G/Gmax, and damping
ratio. These are also important parameters in the design of foundations where only small
deformation takes place. A review of the literature suggests that shear modulus and
damping ratio at small strain are significantly influenced by void ratio and mean effective
stress. They are also influenced by other parameters such as confinement time, anisotropy,
number of loading cycles, and OCR, etc. However, there was little evidence in the literature
showing the influence of particle characteristics on the small strain response of
geomaterials.

In this research the effects of some particle characteristics such as particle size and particle
shape on the small strain response of soils are investigated. Granular materials with
different particle shapes, namely glass Ballotini with various diameters, Leighton Buzzard
sand fraction B and E, glass glitter, glass nugget, as well as mixtures of Leighton Buzzard
sand fraction B and 0.1 mm mica, are tested using a fixed-free resonant column apparatus
(RCA).

The test results suggest that particle shape significantly influences the small strain response
of geomaterials. Both particle form and particle roundness have correlations with
the values of Gmax normalised by a void ratio function, F(e). Normalised Gmax increases
with increasing sphericity and roundness of the particle. At the same void ratio, the
stress exponent, n, elastic threshold strain,
e, and shear modulus degradation, G/Gmax,
for granular materials decrease with an increase in sphericity and roundness. Material
damping ratio also increases with increasing sphericity and roundness.

Particle size was also found to significantly influence the small strain response of glass
Ballotini. At the same void ratio and effective stress, Gmax increases with an increase in
particle diameter. Elastic threshold strain,
e, and G/Gmax also increase with an increase
in particle diameter. In addition, stress exponent, n, and material damping ratio decrease
with increasing particle diameter. It can be concluded that fine soils are more susceptible
to an increment in shear strain and effective stress than coarse soils.

The addition of a small proportion of 0.1 mm mica to Leighton Buzzard sand fraction B
(LBSB) considerably reduces Gmax, even though the void ratios of the mixtures are lower
than those of the sand alone. The stiffness reduction of the mixtures of LBSB and 0.1
mm mica can be attributed to the effects of both platy particle shape and fine particle
size of mica.

The effects of particle characteristics on the small strain response of geomaterials can
be explained using the proposed porous discontinuous-solid model. A dry soil elementis assumed to consist of two phases, namely the pore and the discontinuous solid, where
the stiffness of discontinuities is represented by a shear wave velocity through the contact
network, Vcontact, which is a function of particle characteristics. Particle size and particle
shape create both macro effects (e.g. effect of void ratio) and micro effects (at the contact
level) on the small strain response of granular materials. The model postulates that an
increase in void ratio will increase travel length, and hence decrease Vs. The model suggests
that the macro effect of void ratio on Gmax can be normalised using the theoretical
(universal) void ratio function, F(e) = (1 + e)?3, which can be applied for both clays and
sands with various void ratio range. And by doing so, the micro effects of particle shape
and particle size can be observed and taken into account using a particle characteristic
coefficient, Cp, which increases with increasing particle diameter, sphericity, and roundness.

In addition, during testing relatively stiff specimens using the RCA, equipment compliance
was observed, leading to an significant underestimation of the natural frequencies of
the specimens. In order to identify the source of compliance and evaluate the influence
of equipment compliance on the measured data using the RCA, several finite element
(ABAQUS) models were developed. The numerical analysis results suggest that the stiffness
of the drive mechanism, the mass and/or fixity of the test base, and calibration bar
design significantly affect the test results. To correct for the effects of system compliance,
a new model termed two spring model is developed. The model key parameters
i.e. stiffness of the equipment, Kequipment, and mass polar moment of inertia of the drive
mechanism, I0, can be calibrated through testing of a series of aluminium calibration bars.

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