List of Symbols

A_im, A_om

surface areas of the specimen covered by the inner and outer membranes

A_MP

surface area of membrane

b=(σ₂-σ₃)/(σ₁-σ₃)

parameter that measurers the relative magnitude of the intermediate principal stress

C_MP

parameter that depends on specimen size and density for membrane penetration correction

C_u

uniformity coefficient(D₆₀/D₁₀)

D_r

relative density

D ₅₀

mean grain size

D ₁₀

effective grain size

e

void ratio

e_c

void ratio after consolidation

e _max

maximum void ratio

e _min

minimum void ratio

E_m

Young's modulus of membrane

G_S

specific gravity

H

height of apparatus

M_T

torque

n

inner and outer cell radius ratio n=r_i/r_o

O.D

outer diameter of apparatus

I.D

inner diameter of apparatus

P_i

internal cell pressure

P_o

outer cell pressure

P=(σ₁+σ₂+σ₃)/3

mean total stress

P′=(σ′₁+σ′₂+σ′₃)/3

mean effective stress

P_c

mean stress at final consolidation state

q=σ₁-σ₃

deviator stress

r_i,r_o

inner and outer cell radius

R

stress ratio, R=σ′₁/σ′₃

R _max,R_min

maximum and minimum stress ratios

t_m

thickness of membrane

ν_MP

unit membrane penetration

V _soil

volume of soil sample

W

axial load

α

inclination of the major principal stress

α_ε

inclination of the major principal strain

α_dε

inclination of the major principal strain increment

β ₁

normalized parameter

β ₃

parameter to quantify the level of stresses non-uniformity

β_R

stress non-uniformity coefficient

γ_θz, ε_z, ε_r and ε_θ

shear,axial,radial and circumferential strains

ε_m

the unit membrane penetration

ε ₁, ε₂ and ε₃

major,intermediate and minor principal strains

ε_v=ε₁+ε₂+ε₃

volumetric strain

σ ₁,σ₂ and σ₃

major,intermediate and minor total principal stresses

σ′ ₁, σ′₂and σ′₃

major,intermediate and minor effective principal stresses

σ_z, σ_θ, σ_r

axial,circumferential and radial stress

τ_θz, τ_zθ

shear stress

ΔV_sr,ΔV_ir

measured volume changes of the inner chamber and the specimen