Modeling and simulation of bivariate distribution of shear strength parameters using copulas - Risk and Reliability in Geotechnical Engineering - page 102

2.5.1 retaining wall example
A semigravity retaining wall (Low 2005) shown in Figure 2.7 is employed to investigate
the reliability of a retaining wall. Generally, three failure modes should be considered in
the design of a semigravity retaining wall: (1) overturning of the wall about its toe, (2) slid-
ing along its base, and (3) bearing capacity failure of the foundation soil. The overturning
failure mode is examined below because the relationship between the strength parameters
and factor of safety associated with this failure mode is strongly nonlinear. The existing
deterministic approach evaluates a lumped factor of safety against overturning failure about
the wall's toe as (Low 2005)

M
M

W × rm W + × rm resisting

FS = =

1 1 2 2

(2.31)

P × rm

overturning a a

where M resisting and M overturning denote the actual resisting moments and overturning
moments, respectively; W 1 and W 2 are the component weights of the retaining wall, with
horizontal lever distances Arm 1 and Arm 2 , respectively, measured from the toe of the
wall; and P a is the active earth thrust with a vertical lever distance Arm a . In this chapter,
Rankine's theory is used to compute P a , which is based on the assumption that the back
of the retaining wall is frictionless. For backfill with cohesion c and internal friction angle
ϕ, P a is given by

1
2

2 c

2

P = γ H KcHK

2

− 2 + (2.32)

a soil a a

γ

soil

c , ϕ , γ soil

H

Arm 2

2 c 2

2

Arm 1

P a = γ soil H 2 K a - 2 cH

K a +

γ soil

W 2

3 2 c

H 0 = H -

γ soil K a

W 1

O

a

b

Figure 2.7 Geometry of the analyzed retaining wall.