New Simple Breakage Index for Crushable Granular Soils

Acknowledgments

Notation

B₁₀

particle breakage index proposed by Lade et al. (1996);

B₁₅

particle breakage index proposed by Lee and Farhoomand (1967);

$B_N^{\ast }$, $B_N^H$, $B_N^E$

particle breakage index proposed in this study;

B_f

particle breakage index proposed by Nakata et al. (1999);

B_g

particle breakage index proposed by Marsal (1967);

B_p

breakage potential;

$B_r^E$

particle breakage index proposed by Einav (2007);

$B_r^H$

particle breakage index proposed by Hardin (1985);

B_r50

particle breakage index proposed by Xiao and Liu (2017);

B_rI

particle breakage index proposed by Indraratna et al. (2005);

B_t

total breakage;

b_p

potential for breakage of a particle for a given particle size;

D₁₀

effective particle size;

D₁₅

particle size corresponding to 15% in PSD;

$D_{10}^i$ and $D_{10}^f$

effective particle size of the initial and final gradation, respectively;

$D_{50}^i$, $D_{50}^c$, and $D_{50}^u$

mean particle diameters of the initial PSD, current PSD, and ultimate PSD, respectively;

D_m and D_M

minimum and maximum particle sizes, respectively;

df

differential of PSD with percentage finer divided by 100;

F(D)

grain-size cumulative function;

I_D

initial relative density;

I_G

particle breakage index proposed by Muir Wood and Maeda (2008);

M^c

sum of total passing-sieve weights percentage at current state;

Mⁱ

sum of total passing-sieve weights percentage at initial state before test;

M^u

sum of total passing-sieve weights percentage at ultimate state;

P₀

percentage of particles in current PSD smaller than the minimum particle size in the original sand;

$p_k^i$, $p_k^c$, $p_k^u$

cumulative passing-sieve weights percentage corresponding to a particle size for the initial, current, and ultimate states, respectively;

R²

coefficient of determination;

α

fractal dimension; and

ΔP_max

maximum difference between initial PSD and current PSD.

References