Seismic Stability and Permanent Displacement of 3D Slopes with Tension Cutoff

Data Availability Statement

Notation

B

width of a slope;

b

width of a plane insert;

C

displacement coefficient;

C₁, C₂

stress circles;

c

cohesion of soil;

D, D^curve, D^plane

rate of internal energy dissipation: whole mechanism, curvilinear cone portion, plane insert portion;

f_c

uniaxial compressive strength;

f_t, f_3t

uniaxial and triaxial tensile strength;

f_t′

reduced uniaxial tensile strength;

G

weight of the rotating soil mass;

H

slope height;

k_h

horizontal seismic acceleration coefficient;

k_y

yield acceleration coefficient;

L

length between Point C and Point E;

l

distance between Point O and the center of gravity of the rotating soil mass;

r, r′

radius of the log spirals DBF and D′B′F′;

r_c

average radius of upper and lower log spirals;

r_h

radius of the log spirals DBF at θ = θ_h;

r_m, $r_m^{\mathrm{\prime }}$

radius of the log spirals P′CD and P′C′D′ at θ = θ_m;

r₀, $r_0^{\mathrm{\prime }}$

radius of the log spirals DBF and D′B′F′ at θ = θ₀;

r₁, r₂

radii depicting the distance between point O and shadow boundary in Fig. 2;

[T]

traction vector;

u_x

horizontal displacement;

v

magnitude of the velocity discontinuity vector;

[v]

velocity discontinuity vector;

W_s, W_s^curve, W_s^plane

rate of work done by seismic forces: whole mechanism, curvilinear cone portion, plane insert portion;

W_γ, W_γ^curve, W_γ^plane

rate of work done by soil weight: whole mechanism, curvilinear cone portion, plane insert portion;

β

slope inclination angle;

γ

unit weight of soil;

δ

dilatancy angle in the nonlinear portion of the strength envelope;

δ_m

maximum dilatancy angle in the mechanism;

δθ

increment of the rotation angle;

η₀, η_0.2

yield acceleration influence coefficients;

θ

angular coordinate in the polar system;

θ_h, θ_m, θ_tc, θ₀

angles depicting the positions of Point B, C, D, and A in Fig. 2;

$\ddot{\theta }$

rotational acceleration;

μ

displacement influence coefficient;

ξ

reduction coefficient;

ρ

radial coordinate in the polar system;

φ

internal friction angle of soil; and

ω

angular velocity.

References