A Semianalytical Model for Three-Dimensional Stability Analysis of Potentially Rotational Slopes in Unsaturated Soils

Acknowledgments

Notation

c_ap

apparent cohesion;

c′

effective cohesion of soils;

c_t

total cohesion;

COV(i) (i

k_s, φ′, c′, 1/α, n) = variation coefficients of the mechanical and hydraulic parameters;

G_s

specific gravity of soils;

H

slope height;

k_s

saturated hydraulic conductivity;

L_y: (L_z)

autocorrelation distances in the Y (Z) direction;

n

pore size distribution of soils;

q

specific discharge under vertical steady flow condition;

R_i,j

polar radius of the gravity centers of regular triangle T_i,j;

$R_{i,j}^{\mathrm{\prime }}$

polar radius of the gravity centers of inverted triangle T′_i,j;

S

water saturation degree;

S_r

residual degrees of saturation;

S_e

effective degrees of saturation;

S_i,j

area of regular triangle T_i,j;

$S_{i,j}^{\mathrm{\prime }}$

area of regular triangle T′_i,j;

u_w

pore water pressures;

V_i,j

volume of regular triangle T_i,j;

$V_{i,j}^{\mathrm{\prime }}$

volume of regular triangle $T_{i,j}^{\mathrm{\prime }}$;

v_i,j

velocity magnitude of regular triangle T_i,j;

$v_{i,j}^{\mathrm{\prime }}$

velocity magnitude of inverted triangle $T_{i,j}^{\mathrm{\prime }}$;

W

slope width;

${\dot{W}}_D$

internal energy dissipation;

${\dot{W}}_{\gamma }$

work rate done by soil weight;

W₁

width of the initial cross section of the 3D discretized failure mechanism;

z

vertical distance between the water table and the specified point within slopes;

z_u

vertical distance between the slope toe and the location of water table elevation;

α

inverse of the air entry pressure;

β

slope inclination;

δψ

discretization angle between two adjacent points on a radial plane of the 3D discretized failure mechanism;

δθ

discretization angle between two adjacent radial planes of the 3D discretized failure mechanism;

φ′

effective friction angle of soils;

γ_sat

saturated unit weight of soils;

γ_w

water unit weight;

η

radial angle of the maximum cross section of the 3D discretized failure mechanism;

λ_i,j

length parameter of the discretized point P_i,j of the 3D discretized failure mechanism;

μ_i

(i = k_s, φ′, c′, 1/α, n) means of the mechanical and hydraulic parameters;

ρ_i

(i = k_s, φ′, c′, 1/α, n) autocorrelation coefficients of the mechanical and hydraulic parameters;

${\rho }_{c^{\mathrm{\prime }},{\phi }^{\mathrm{\prime }}}^{\ln }$

cross-correlation coefficient of the effective soil cohesion and frictional angles;

${\rho }_{1/a,n}^{\ln }$

cross-correlation coefficient of the pore size distribution coefficient of soils and the air entry pressure;

σ

total stresses of soils;

σ′

effective stresses of soils;

σ^s

suction stress;

τ

shear stress;

ω

rotational angular velocity; and

ψ_i,j

angular parameter of the discretized point P_i,j of the 3D discretized failure mechanism.

References