Active Earth Pressure against Cantilever Retaining Walls with the Long Relief Shelf Rotating about the Bottom

Acknowledgments

Notation

b

length of relief shelf (m);

b₁

length of wall toe (m);

b₂

thickness of vertical wall (m);

b₃

length of wall heel (m);

c

cohesion of backfilled soil (kPa);

c′

cohesion of foundation soil (kPa);

dw

weight of soil slice (kN/m);

E

Young’s modulus of wall (MPa);

E_a

total earth pressure (kN/m);

E_r

earth pressure at the end of relief shelf (kN/m);

E_s

Young’s modulus of backfilled soil (MPa);

$E_s^{\mathrm{\prime }}$

Young’s modulus of foundation soil (MPa);

E_s2

total earth pressure on the second failure surface (kN/m);

E_s3

total earth pressure on the third failure surface (kN/m);

E_w

earth pressure at the end of wall heel (kN/m);

E₃

earth pressure on the third failure surface (kN/m);

$E_3^{\mathrm{\prime }}$

earth pressure on the extension surface of the third failure surface (kN/m);

E₂₁

earth pressure on the second failure surface (kN/m);

E₂₂

earth pressure on the second failure surface (kN/m);

$E_{22}^{\mathrm{\prime }}$

earth pressure on the extension surface of the second failure surface (kN/m);

e₃

earth pressure on the third failure surface (kPa);

e₂₁

earth pressure on the second failure surface (kPa);

e₂₂

earth pressure on the second failure surface (kPa);

e₂₃

earth pressure on the second failure surface (kPa);

H

total height of wall (m);

H₁

height of upper wall (m);

H₂

thickness of relief shelf (m);

H₃

height of lower wall (m);

H₄

thickness of bottom plate (m);

l

relative length of relief shelf;

l_E

moment arm of total earth pressure (m);

m

relative height of upper wall;

n

relative length of wall heel;

q

ground overload (kPa);

R₁

force between the failure wedges (kN/m);

R₂

force between the failure wedges (kN/m);

W

weight of the wedge (kN/m);

Z_E

distance between the total earth-pressure application point and the bottom of the wall (m);

z_r

distance between the application point of E_r and backfilled soil surface (m);

z_s2

distance between the application point of E_s2 and backfilled soil surface (m);

z_s3

distance between the application point of E_s3 and backfilled soil surface (m);

z_w

distance between the application point of E_w and backfilled soil surface (m);

α_E

angle of the total active earth pressure (°);

α₁

first failure surface inclination (°);

α₂

first failure surface inclination (°);

α₃

second failure surface inclination (°);

α₄

third failure surface inclination (°);

δ

friction of the soil–wall interface (°);

δ′

friction of the soil–wall interface (°);

γ

unit weight of backfilled soil (kN/m³);

γ′

unit weight of foundation soil (kN/m³);

σ_w

horizontal stress of earth pressure (kPa);

σ_n

normal stress of earth pressure (kPa);

υ

Poisson’s ratio of backfilled soil;

υ′

Poisson’s ratio of foundation soil;

φ

internal friction of backfilled soil (°); and

φ′

internal friction of foundation soil (°).

References