2045
Technical Committee 207 /
Comité technique 207
shows the
K
A
value resulting from finite element analyses for an
elastic-perfectly plastic soil following the Mohr-Coulomb
failure criterion (M-C analyses) with friction angle
equal to
the critical state friction angle value
c
of each sand for plane
strain conditions and dilatancy angle
equal to zero (consistent
with the constant volume response at critical state).
7
6
5
4
3
2
1
0
depth (m)
0 10 20 30 40 50 60 70
horizontal stress
h
(kPa)
initial (K=K
0
)
u
c
=4.0cm
K=0.38K
0
u
c
=2.0cm
K=0.57K
0
u
c
=68.8cm
K=0.49K
0
u
c
=37.6cm
K=0.47K
0
Ottawa sand, D
R
=45%
rotation+translation
(a)
7
6
5
4
3
2
1
0
depth (m)
0 10 20 30 40 50 60 70
horizontal stress
h
(kPa)
initial (K=K
0
)
u
c
=2.4cm
K=0.25K
0
u
c
=1.2cm
K=0.35K
0
u
c
=31.8cm
K=0.42K
0
u
c
=15.0cm
K=0.38K
0
Toyoura sand, D
R
=60%
rotation+translation
(b)
As expected,
K
A,min
decreases with increasing relative density
and, consequently, peak friction angle. The crest displacement
required for reaching the MPS is in the 0.003
H
to 0.006
H
range,
regardless the
D
R
value. On the other hand, attainment of
K
A,cr
requires
u
C
larger than 0.10
H
.
Figure 3. Examples of horizontal stress distribution acting on the wall
backface at different stages during the analysis.
Interestingly,
K
A,cr
seems also to depend on the relative
density despite the fact that
c
is independent of
D
R
. Only the
curves for loose sand appear to attain
K
A,cr
values that are in
agreement with the
K
A
from the analyses with a perfectly plastic
soil with material parameters consistent with critical state. This
is because the inclination of the sliding plane delimiting the
wedge depends on the dilatancy that the soil exhibits during the
early stages of the wall movement, since the theoretical value of
the shear band inclination with respect to the minor stress (i.e.
horizontal) axis is equal to
(Vardoulakis 1980)
The sliding wedge forms at MPS, when the soil mass close to
the wall is strongly dilative for all except very loose sand . Once
the main inclined shear band forms, it tends to stay more or less
at that location because of strain localization.
In most of the analyses, the
u
C
values required to cause
bearing capacity failure of the wall foundation is in the 0.01
H
to
0.09
H
range, corresponding to toe displacement of 0.01
B
to
0.065
B
. Hence, the foundation is expected to fail before full
development of the residual active earth pressure state.
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
u
C
/H
0.0
0.2
0.4
0.6
0.8
1.0
K/K
0
H=7m, B=1.5m, D=0.5m
H=7m, B=2.0m, D=0.5m
H=7m, B=2.5m, D=0.5m
H=8m, B=1.5m, D=0.5m
H=6m, B=1.5m, D=0.5m
H=7m, B=1.5m, D=0.2m
Figure 4. Variation of normalized lateral earth pressure coefficient with
wall crest displacement from analyses with medium dense Toyoura sand
(
D
R
=60%).
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
u
C
/H
0.0
0.2
0.4
0.6
0.8
1.0
K/K
0
D
R
=30%
D
R
=45%
D
R
=60%
D
R
=75%
D
R
=90%
Toyoura sand
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
u
C
/H
0.0
0.2
0.4
0.6
0.8
1.0
K/K
0
D
R
=30%
D
R
=45%
D
R
=60%
D
R
=75%
D
R
=90%
Ottawa sand
perfectly plastic with
c
perfectly plastic with
c
(a)
(b)
Figure 5. Variation of normalized lateral earth pressure coefficient with
wall crest displacement from analyses of a wall with
H
=7m,
B
=1.5m
and
D
=0.5m.
3.3
Mobilized resistance along the wall-soil interface
The mobilized friction coefficient
μ
(=tan
on the wall
backface reaches a peak value at very early stages of the
analyses, before the attainment of the MPS. After the peak,
decreases quickly towards a residual value
c
that is consistent
with development of critical state inside the thin shear band that
runs parallel to the wall backface. Despite this, it can be seen
that the mobilized friction angle
mob
at MPS ranges from 1.0 to
1.25 times the
c
(Fig. 6). The
c
values are 30.8
o
and 29.6
o
for
Toyoura sand and Ottawa sand, respectively. These are
consistent with the theoretical
c
values calculated as
arctan(sin
c,PS
), where
c,PS
is the critical state friction angle for
plane strain conditions. For Toyoura and Ottawa sands, this
takes the values of 36.6
o
and 34.6
o
, respectively, which are
