Anisotropy and Non-coaxial Behaviour of Sand Along Different Strain Paths

Anisotropic characteristics of granular soil, consolidated to various initial stress states,

were evaluated under generalized strain paths using hollow cylinder torsional shear

tests. Fraser River sand samples prepared by water pluviation were subjected to

isotropic and anisotropic consolidation stresses and sheared under undrained con-

ditions along specific strain paths characterized by constant intermediate principal

strain parameter (𝑏𝜀) and various fixed principal strain directions (𝛼𝜀). A series of

tests along different inclinations of the major principal strain with respect to the

vertical depositional direction permitted an assessment of the interaction between

principal strain directions and fabric. A decrease in strain hardening tendency is ob-

served as the major principal strain aligned towards the bedding plane. Considering

different levels of anisotropic consolidation stresses also allowed a detailed examina-

tion of how initial static shear affects the responses. In particular, generated principal

stresses and their direction, as well as the pore pressure responses, were closely exam-

ined. Novel findings, that highlight range of intermediate principal stress parameter

(𝑏𝜎) associated with the undrained plane strain condition, and the interaction be-

tween 𝑏𝜎 and 𝑏𝜀 during shearing are presented. It was found that 𝑏𝜎 systematically

decreases with shear strain in constant 𝑏𝜀 tests. The 𝑏𝜎 value in plane strain tests

(𝑏𝜀=0.5) was found to be in the range of 0.2 to 0.4 depending on the loading path,

and the stage of shearing.

The relationship between principal stress directions and plastic-strain increment

directions was assessed to identify the nature of plasticity in the material. In order to

ensure confident assessment of non-coaxiality, total strain was decomposed into elas-

tic and plastic strain. The existence of non-coaxiality in Fraser River sand (FRS) was

observed when the sand was subjected to undrained shear at fixed principal strain di-

rections that do not coincide with the fabric axis of symmetry. Non-coaxiality was not

observed when the principal directions of stress/strain coincided with the fabric axis

of symmetry. It was also noticed that irrespective of the initial condition, the degree of

non-coaxiality reduces with increasing shear strain. The influence of initial fabric

and principal strain direction on the degree of non-coaxiality was analyzed in detail.

Test results show that irrespective of initial condition, the degree of non-coaxiality

reduces as the principal strain direction aligns towards the bedding plane direction.

The degree of non-coaxiality in FRS at the phase transformation (PT) state and the

effect of intermediate principal stress on non-coaxiality were also examined. Different

values of degree of non-coaxiality at PT state indicate that the phase transformation

state can not be thought of as a good representation of the critical state even though

the friction angle at phase transformation has been found to be similar to that at

the critical state. The results revealed that the non-coaxial behaviour of soil is also

influenced by the intermediate principal stress parameter (which could alternatively

be represented by the Lode angle).

The influence of non-coaxiality on stress-dilatancy of sand was investigated under

generalized loading conditions, and it was found that the effect of non-coaxiality

on stress-dilatancy characteristics of the sand was influenced by its initial fabric

anisotropy. The effect of non-coaxiality in stress-dilatancy relationship has been

investigated within the theoretical framework developed by Gutierrez and Ishihara

(Gutierrez and Ishihara, 2000, Soils Found., 40(2):49–59) and Gutierrez and Wang

(Gutierrez and Wang, 2009, Granul. Matter, 11(2):129–137) who extended the Rowe’s

stress-dilatancy relation to the non-coaxial conditions. Our research study verifies this

framework beyond its original context of 2D simple shear tests.