Pseudodynamic Analysis of Three-Dimensional Fissured Slopes Reinforced with Piles

Data Availability Statement

Notation

a_h

horizontal seismic acceleration;

B

total width of slope;

$B_{max}^{\mathrm{\prime }}$

maximum width of the 3D portion;

b

effective width of inserted portion of the piles;

c

soil cohesion;

c′

critical soil cohesion;

D_c

internal energy dissipation rate generated by soil resistance;

D_c−c

internal work rate generated by soil resistance;

D_cr

internal energy dissipation rate along crack;

D_p

internal energy dissipation rate generated by antislide piles;

D₁

center-to-center interval of adjacent piles;

D₂

clear interval of adjacent piles;

d

diameter of single pile;

F

safety factor;

f

amplification factor;

f_c

uniaxial compressive strength;

f_t

uniaxial tensile strength;

G

shear modulus;

g

acceleration due to gravity;

H

slope height;

H′

crack height;

h_max

maximum crack depth;

k_h

seismic coefficient;

L

length of AD, as shown in Fig. 1;

L′

length of AB, as shown in Fig. 1;

L_s

horizontal distance between slope toe and slope crest;

n

coefficient of pile location;

p

lateral force of piles;

R

circle radius;

r

upper log-spiral;

r′

lower log-spiral;

r_h

length of OE, as shown in Fig. 1;

r_m

distance between circle center and rotation center;

r_M

length of OM, as shown in Fig. 1;

r₀

length of OA, as shown in Fig. 1;

$r_0^{\mathrm{\prime }}$

length of OA′, as shown in Fig. 1;

S

area of failure surface;

S_cr

area of crack surface;

T

vibration period;

u_h

horizontal displacement;

u_hb

horizontal displacement at slope base;

u_h0

horizontal displacement at slope crest;

V

volume of failure blocks;

V_s

shear wave velocity;

v

magnitude of velocity at considered point;

w

effective width of piles in 3D portion;

W_s

external work rate generated by seismic force;

W_s−c

external work rate generated by seismic forces;

$W_{\gamma }$

external work rate generated by self-weight of soils;

W_γ−c

external work rate generated by soil weigh;

w_p

effective width of piles;

X_p

horizontal distance between slope toe and pile;

z_i

distance between considered point and slope base;

β

slope angle;

γ

unit weight of soils;

δ

angle between vertical crack and velocity vector;

θ

polar angle at considered point;

θ_C, θ_h, θ_M, θ_N, θ₀

angles to describe 3D failure mechanism, as shown in Fig. 1;

λ_s

wavelength of shear wave;

μ

soil viscosity;

ξ

soil damping ratio;

ρ

polar radius at considered point;

ρ_d

soil density;

φ

internal friction angle;

φ′

critical internal friction angle;

ω

angular velocity about axis passing through Point O;

$\overline{\omega }$

angular velocity of shear wave; and

${\overline{\omega }}_n$

natural frequency of soils.

References