Geoscience Reference
In-Depth Information
the double-sliding model (see Chapter 9), an extension of the Mohr-Coulomb
model.
TABLE 7.1 VALUES FOR
K
0
type of soil
correlation
Remark
sand
1 - sin
Jaky's formula
clay
0.19 + 0.23log(
I
p
)
I
p
: plasticity index
peat
0.83 - 0.67
OC
OC
: organic matter content (%)
For a given vertical effective stress
v
'
, e.g. equal to vertical weight, the passive
effective earth pressure
h
'
is found, when soil experiences maximum horizontal
compression. The following holds (see Fig 7.4)
h
' + c
cotg
= m
p
(1
+
sin
)
(7.3a)
v
' + c
cotg
= m
p
(1
sin
)
(7.3b)
Elimination of
m
p
yields
1
sin
1
sin
1
sin
1
sin
h
' =
v
'
+ c
cotg
(
- 1)
=
v
'
+
2
c
(7.4)
1
sin
1
sin
1
sin
1
sin
And the passive earth pressure becomes
1
sin
=
tan
2
(45
o
+
h
' = K
p
v
' +
2
c
K
p
with
K
p
=
/2)
(7.5a)
1
sin
In a similar manner, the active earth pressure
h
is found, when soil experiences
minimum horizontal compression. One finds
1
sin
=
tan
2
(45
o
h
' = K
a
v
'
2
c
K
a
with
K
a
=
/2)
(7.5b)
1
sin
=
0
o
, formula (7.5) yields the
Obviously,
K
a
=
1
/ K
p
. For cohesive soils with
following possible variation of
h
' within the Tresca yield limit
k
v
'
- 2k <
h
' <
v
'
+ 2k
(7.6)
For non-cohesive soil,
c =
0, formula (7.5) expresses the Rankine stress states.
For example,
= 30
o
gives with (7.5), dependent on the deformation, the following
possible variation of
h
'
v
' <
h
'
<
3
v
'
(7.7)
Horizontal stresses are important for stability of earth retaining structures (see
Chapter 11). The range of some practical values of
K
0
is given in Table 7.2.
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