Stability Analysis of Inhomogeneous Slopes in Unsaturated Soils Optimized by a Genetic Algorithm

Data Availability Statement

Notation

a

distances from the centerline of the conical volume to the slope crest;

B

maximum width of the rotational failure mechanism;

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

maximum width of the 3D portion;

b

width of plane insert block;

c′

effective cohesion strength;

c_app

apparent cohesion;

c₀

effective cohesion strength of the slope base;

c_f

effective cohesion strength of the slope face;

c^3D and c^2D

effective cohesion in 3D and 2D portions of slope, respectively;

$D_{c^{\mathrm{\prime }}}^{3\mathrm{D}}$ and $D_{c^{\mathrm{\prime }}}^{2\mathrm{D}}$

rate of the internal energy dissipation of 3D and 2Ds portion achieved by soil cohesion, respectively;

$D_s^{3\mathrm{D}}$ and $D_s^{2\mathrm{D}}$

rate of the internal energy dissipation of 3D and 2D portions achieved by apparent cohesion, respectively;

d

distances from the centerline of the conical volume to the slope face;

e

distance from the centerline of the conical volume to the slope base;

F_s

factor of safety of slope;

G_s

specific gravity of soil;

H

slope height;

H′

auxiliary height of slope;

h_f

distance from the slope face to the slope crest;

h_s

distance from the slip face to the slope crest;

k_s

saturated hydraulic conductivity;

n

distribution of the soil’s pore size;

n^w and n^d

pore size distribution parameter of wet and dry paths, respectively;

n₀

inhomogeneous coefficient;

q

vertical steady flow rate;

R

radius of the conical volume;

r and r′

radius of log spiral and inner log spiral, respectively;

r₀ and $r_0^{\mathrm{\prime }}$

initial radius of log spirals OA and OA′, respectively;

r_f

distance from the slope face to the center of rotation O;

r_h

final radius of the log spiral;

r_m

average radius of both spirals;

S

degree of pore water saturation;

S_e

normalized degree of saturation;

S_r

residual degree of saturation;

$(u_a-u_w)$

matric suction;

u_a

pore air pressure;

u_w

pore water pressure;

$W_{{\gamma }^{\mathrm{\prime }}}^{3\mathrm{D}}$ and $W_{{\gamma }^{\mathrm{\prime }}}^{2\mathrm{D}}$

rate of external forces achieved by the effective soil weight of the 3D and 2D parts, respectively;

$W_{{\gamma }^{\mathrm{\prime }}}^{3\mathrm{D}}$, $W_{{\gamma }^{\mathrm{\prime }}}^{2\mathrm{D}}$

rate of external forces achieved by the effective soil weight of the 3D and 2D parts, respectively;

z₀

vertical distance from the water table to the slope toe elevation;

z_3D

vertical distance from any one point of failure block to the water table level;

z_2D

vertical distance from the point on the sliding surface of the plane insert block to the water table level;

α

inverse of air entry pressure;

α^w and α^d

inverse of air entry pressure of wet and dry paths, respectively;

β

slope inclination angle;

β′

auxiliary slope inclination angle;

γ′

effective unit soil weight;

γ_sat

unit weight of saturated soil;

γ_w

unit weight of water;

γH/c

stability factor of slope;

σ

total stress;

σ′

effective stress;

σ^s

suction stress;

ϕ′

effective internal friction angle;

τ_f

shear strength;

θ

rotational angle;

θ₀

initial rotational angle;

θ_B and θ_c

rotational angles from horizontal line to the line that passes through points B and C, respectively;

θ_h

final rotational angle of log spiral;

θ_s

saturated volumetric water content; and

θ_r

residual volumetric water content.

References