Evolution of Limiting Slope Face in Rock Mass Using the Stress Characteristics Method

Data Availability Statement

Acknowledgments

Notation

A_a

parameter as defined in Eq. (4);

a

dimensionless HB material parameter as defined in Eq. (2a) representing the characteristics of rock mass;

D

disturbance factor of the rock mass;

d

depth of firm stratum from the base of the slope;

F

function defining the yield criterion in Eq. (6);

f

macroscopic yield condition;

H

any typical scalar function of x and y;

h

height of the rock slope;

k

parameter as defined in Eq. (4);

m

parameter as defined in Eq. (12);

m_b

dimensionless HB material parameter as defined in Eq. (2b) related to m_i;

m_i

Hoek‒Brown constant of intact rock representing the hardness of the rock;

N

stability number, that is, σ_ci/(γh·FS);

N_cr

critical stability number corresponding to FS=1.0;

p

average stress, that is, (σ₁ + σ₃)/2;

p_g

magnitude of p along the top surface of the slope (OG);

p_s

magnitude of p along the limiting slope face (OA);

q

uniformly distributed surcharge;

R

radius of the Mohr circle, that is, (σ₁–σ₃)/2;

R_g

magnitude of R along the top surface of the slope (OG);

R_s

magnitude of R along the limiting slope face (OA);

s

dimensionless HB material parameter as defined in Eq. (2c) representing the degree of fragmentation of the rock;

u, v

horizontal and vertical displacement, respectively;

X

body force per unit volume in the x-direction;

x, y

axes in 2D Cartesian coordinate system;

Y

body force per unit volume in the y-direction;

α

horizontal inclination of the ELS;

α_L

horizontal inclination of a linear slope, as reported in the literature;

β_a

parameter as defined in Eq. (4);

γ

unit weight of the rock mass;

ζ_a

parameter as defined in Eq. (4);

θ

orientation of the major principal stress about the positive x-axis;

θ_g

magnitude of θ along the top surface of the slope (OG);

θ_s

magnitude of θ along the limiting slope face (OA);

μ

parameter as defined in Eq. (12);

ρ

instantaneous friction angle as defined in Eq. (16);

ρ_g

magnitude of ρ along the top surface of the slope (OG);

ρ_s

magnitude of ρ along the limiting slope face (OA);

σ⁺, σ⁻

axes in the 2D curvilinear coordinate system representing the positive and negative characteristics, respectively;

σ₁

major principal stress;

σ₃

minor principal stress;

σ_ci

uniaxial compressive strength of the intact rock;

σ_ng

normal stress on the top surface of the slope (OG);

σ_x

normal stress on the x-plane;

σ_y

normal stress on the y-plane;

τ_g

shear stress on the top surface of the slope (OG);

τ_xy

shear stress in the xy-plane; and

ψ

magnitude of θ at O_S.

References