Slip-Line Solution for the Active Earth Pressure of Narrow and Layered Backfills against Inverted T-Type Retaining Walls Rotating about the Base

Acknowledgments

Notation

b

thickness of the wall stem (m);

b₁

length of the toe (m);

b₁

width of the heel (m);

b₂

length of the heel (m);

b₃

width of the backfill behind the heel bottom plate (m);

C_a

integral constant along a-line;

C_β

integral constant along β-line;

c

cohesion of the backfill (kPa);

E

Young’s modulus (MPa);

H

total height of the wall (m);

h₁

total height of the stem (m);

h₂

total height of the bottom plate (m);

K

interface reduction coefficient;

k_c

inclination of the imaginary wall (°);

M

number of slip-lines passing through stress singularity;

p

average stress of Mohr’s stress (kPa);

R

radius of Mohr’s stress (m);

v

Poisson’s ratio;

X

body load acting in the x-direction (kN/m³);

Z

body load acting in the z-direction (kN/m³);

δ

friction at the soil–wall interface (°);

ɛ

angle between soil element shear surface and major principal stress (°);

γ

unit weight of the backfill (kN/m³);

η

angle between normal stress on the boundary and the z-axis (°);

θ

deflection angle of principal stress (°);

θ_g

deflection angle of principal stress at the backfill surface (°);

θ_w

deflection angle of principal stress at the stem interface (°);

φ

internal friction of the backfill (°);

σ_h

horizontal component of earth pressure strength (kPa);

σ_n

normal stress acting on the boundary (kPa);

σ_v

vertical component of earth pressure strength (kPa);

σ_x

normal stress acting in the x-direction (kPa);

σ_z

normal stress acting in the z-direction (kPa);

σ₁

major principal stress (kPa);

σ₃

minor principal stress (kPa);

τ_nt

shear stress acting on the boundary (kPa); and

τ_xz

shear stress acting in the x-direction (kPa).

References