New Instability Criterion for Stability Analysis of Homogeneous Slopes with Double Strength Reduction

Acknowledgments

Notation

c

initial cohesion;

c₁

reduced cohesion;

c₁*

critical cohesion;

E

elastic modulus;

F₁

reduction factor for the internal friction angle;

F₂

reduction factor for cohesion;

F_1crit

critical reduction factor for the internal friction angle;

F_2crit

critical reduction factor for cohesion;

F_1crit*

minimum critical reduction factor for the internal friction angle;

F_2crit*

minimum critical reduction factor for cohesion;

FS

factor of safety;

FS₁

factor of safety by the proposed method;

FS₂

factor of safety by the polar diameter method;

H

slope height;

i, j, l

nature number;

K

reduction ratio factor;

k*

minimum reduction ratio factor;

k_o

initial reduction ratio;

Δk

increment of ratio;

L_min, L_k

trajectory of the strength reduction;

M, M_α, M_β, $M_{\beta }^{\mathrm{\prime }}$

points on a slip line;

M_b, M_ij

points on the critical slope contour;

M_o

point of initial condition;

M_min, M_k

points on the marginal state line;

N

total number of nodes;

N₁

number of calculation steps;

P

surcharge load at the top of the slope;

P_min

minimum load at the top of the slope;

x, x₁, x_b, x_ij, x_α, x_β, $x_{\beta }^{\mathrm{\prime }}$

abscissa values;

Δx

calculation step on the active zone boundary;

y, y_b, y_ij, y_α, y_β, $y_{\beta }^{\mathrm{\prime }}$

ordinate values;

y_min

minimum ordinate values;

α

alpha family slip line;

α₀

slope angle;

β

beta family slip line;

γ

unit weight;

θ, θ_b, θ_ij, θ_α, θ_β, ${\theta }_{\beta }^{\mathrm{\prime }}$, θ_I

intersection angles between the maximum principal stress and the x-axis;

μ

mean angle between two family slip lines;

ν

Poisson’s ratio;

σ, σ_b, σ_ij, σ_α, σ_β, ${\sigma }_{\beta }^{\mathrm{\prime }}$, σ_I

characteristic stresses;

σ₁

maximum principal stress;

φ

initial internal friction angle;

φ₁

reduced internal friction angle; and

φ₁*

critical internal friction angle.

References