Nonlinear Response of Micropile Groups Stabilizing Landslides Considering Pile–Soil Interactions

Data Availability Statement

Acknowledgments

Notation

A_i1–G_i7

influence function values under Modes A and C;

a_i and $a_i^{\mathrm{\prime }}$

constant coefficients;

b₀

calculated width of the pile;

c

cohesion;

D

width or outside diameter of the pile;

D_r

relative density;

EI

pile bending stiffness;

F_s

slope safety factor;

f_m

p-multiplier;

f_mn

p-multiplier, a constant used to scale values of landslide thrust;

$f_{mn}^{\mathrm{\prime }}$

p-multiplier, a constant used to scale values of soil resistance;

G_s

specific gravity;

H_i1–O_i7

influence function values under Mode B;

I

inertial moment;

LL

liquid limit;

l

pile length;

l₀

pile length above the sliding surface;

l_c

pile length below the sliding surface;

M_0n

bending moment of the nth row pile top;

M_an

bending moment of the nth row pile in the loaded section under Modes A and C;

$M_{an}^{\mathrm{\prime }}$

bending moment of the nth row pile in loaded section Mode B;

M_cn

bending moment of the nth row pile in the anchored sections under Modes A and C;

$M_{cn}^{\mathrm{\prime }}$

bending moment of the nth row pile in the anchored section under Mode B;

m

row number of piles;

PL

plastic limit;

p_a

group-pile soil resistance;

p_s

single-pile soil resistance;

Q_0n

shear force of the nth row pile top;

Q_an

shear force of nth row pile in the loaded section under Modes A and C;

$Q_{an}^{\mathrm{\prime }}$

shear force of nth row pile in the loaded section under Mode B;

Q_cn

shear force of nth row pile in the anchored section under Modes A and C;

${\phi }_{cn}^{\mathrm{\prime }}$

rotation angle of the nth row pile in the anchored section under Mode B;

$Q_{cn}^{\mathrm{\prime }}$

shear force of nth row pile in the anchored section under Mode B;

q_n(z)

distribution function of residual landslide thrust on the nth row piles;

p_n(z)

distribution function of soil resistance acting on the nth row piles;

S

center-to-center spacing between piles in the loading direction;

S_u

undrained shear strength;

w_s

water content;

X_an

displacement of the nth row pile in the loaded section under Modes A and C;

$X_{an}^{\mathrm{\prime }}$

displacement of the nth row pile in the loaded section under Mode B;

X_cn

displacement of the nth row pile in the anchored section under Modes A and C;

$X_{cn}^{\mathrm{\prime }}$

displacement of the nth row pile in the anchored section under Mode B;

x_0n

displacement of the nth row pile top;

β and γ

pile deformation coefficients;

γ_s

unit weight of soil;

ρ_d

dry density;

φ

friction angle;

φ_0n

rotation angle of the nth row pile top;

φ_an

rotation angle of the nth row pile in the loaded section under Modes A and C;

${\phi }_{an}^{\mathrm{\prime }}$

rotation angle of the nth row pile in the loaded section under Mode B;

φ_cn

rotation angle of the nth row pile in the anchored section under Modes A and C;

ϕ₁, ϕ₂, ϕ₃, and ϕ₄

effect function value of the K method;

ξ, η, and ψ

coefficients of the landslide thrust distribution function; and

ξ′, η′, and ψ′

coefficients of the soil resistance distribution function.

References