Three-Dimensional Stability of Unsaturated Soil Slopes Strengthened through Frame Beam Anchor Plates under Steady Seepage Conditions

Data Availability Statement

Acknowledgments

Notation

1, 2, …, i, …, m

serial numbers of anchor plates;

B

slope width;

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

maximum width of the 3D horn failure part;

b

width of the plane strain section;

c

total cohesion;

c′

effective cohesion;

c″

capillary cohesion –σ^stanφ′;

D

internal energy dissipation;

D_a

energy dissipation rate caused by anchor plates;

D_c′

energy dissipation rate caused by effective cohesion;

D_c″

energy dissipation rate caused by capillary cohesion;

E

elastic modulus;

F_i

shear resistance between the anchor plate's side and the soil mass;

F_h

seismic inertia force acting horizontally;

Fs

safety factor;

f_a

acceleration amplification factor;

f_y, A_s

yield strength and cross-sectional area of tie rod;

G_s

soil-specific gravity;

H

slope height;

h_i

burial depth of anchor plates;

K₀

coefficient of earth pressure at rest;

K_a

coefficient of active earth pressure;

K_p

coefficient of passive earth pressure;

k_h

horizontal seismic coefficient;

k_h(z, t)

pseudodynamic horizontal seismic coefficient;

k_s

saturated hydraulic conductivity;

L

length of Line segment AB in Fig. 3;

L_a, L_b, L_h

length, width, and thickness of anchor plate;

n

soil pore size distribution parameter;

P_i

resistance generated at the front end of the anchor plate;

Q

uniformly distributed load at the top of a slope;

q

steady flow rate;

R

radius of the 3D horn failure mechanism cross sections;

R_int

strength reduction coefficient;

r, r′

polar diameters of log-spiral lines AC and A′C′, respectively;

$r_0^{\mathrm{\prime }}$, r₀

polar diameters of log-spiral lines AC and A′C′ corresponding to angle θ₀, respectively;

r_m

distance between Point O and the rotational axis of the 3D spiral mechanism;

r_Ti, θ_Ti

polar diameter and rotation angle of anchor plates, respectively;

S

pore-water degree of saturation;

S_e

effective degree of saturation;

S_h, S_v

horizontal and vertical spacing of anchor plates, respectively;

S_r

residual degree of saturation;

T₀

seismic period;

T_i

anchoring force;

T_pi

ultimate pullout resistance of anchor plate;

T_s

ultimate pullout resistance of tie rod;

t

time;

t_i

number of anchor plates per row in the failed mechanism;

u_a

pore-air pressure;

u_w

pore-water pressure;

u_a–u_w

matrix suction;

v_s

shear-wave velocity;

W

external work rate;

W_Q

external work rate caused by slope top overload;

W_s

external work rate caused by seismic force;

W_γ′

external work rate caused by soil weight;

z

vertical distance from a point in the slope body to the toe;

z₀

vertical distance from the toe to the water table;

α

inverse of the air entry pressure;

β

slope inclination angle;

γ′

effective unit weight of unsaturated soils;

γ_w

unit weight of water;

γ_s

unit weight of saturated soil;

θ

rotation angle of failure mechanism;

θ_B

rotation angle corresponding to Point B;

θ₀, θ_h

minimum and maximum rotation angle of failure mechanism;

ν′

Poisson's ratio;

ξ

lateral pressure coefficient;

σ

total stress;

σ′

effective stress;

σ_s

suction stress;

τ_f

shear strength of unsaturated soil;

τ_fi

interface shear strength;

φ′

effective internal friction angle; and

ω

angular velocity.

References