Geoscience Reference
In-Depth Information
Using (5.8), one finds
l
=
e
/(1+
e
0
), so that from (5.14) one obtains
l
=
l
=
(
C
c
/(1+
e
0
))
10
log(1+
'/
0
'
)
(5.15)
Comparison of (5.15) and (5.12) yields a relation between the original empirical
compression index
C
c
and the theoretical index
, according to
C
c
=
2.3
(1+
e
0
) = 2.3
v
0
(5.16)
The compression index
C
c
is extensively measured and reported in literature.
Some values are given in Table 5.1.
TABLE 5.1 RANGE OF COMPRESSION INDEX VALUES FOR VARIOUS SOILS
soil type
C
c
value
soil type
C
c
value
gravel
sand
silty sand
loam
sandy loam
0.002 - 0.009
0.002 - 0.020
0.005 - 0.019
0.030 - 0.170
0.055 - 0.092
clay
sandy clay
organic clay
peat (preloaded)
0.126 - 1.360
0.069 - 0.756
0.420 - 1.690
0.900 - 1.800
In many textbooks, unloading and reloading behaviour is expressed by
C
c
'
, also
referred to by recompression or swelling index. It is usually 2 to 5 times less than
C
c
, or even smaller.
The representation of the compressibility index
C
c
with regard to voids ratio
e
0
and
10
log is historic. As a reference, the voids ratio incorporates the solids volume,
which was considered a stable factor, and in the early times only
10
log
-
graphic
paper was available for outlining test results. It is nowadays convenient to use
measured data directly, like
in particular, because
C
c
/(1+
e
0
) shows less variation
than
C
c
itself.
Settlement of soils is the accumulated vertical displacement at the ground
surface, and it is related to strain summed for each layer, according to
S =
l
dz
(5.17)
As stated before, when using (5.11) the natural strain concept is satisfied. It
applies for large strains as well, and so does (5.17).
In conclusion, for small strains one may use (5.12), for small load steps (5.13),
and for large strains one should use (5.11). Using (5.11) avoids missing the
advantage of large strain concept. The compression index or compressibility
coefficient is easily converted using the relation mentioned in (5.16).
application 5.1
Consider a stratified soil consisting of sand, clay, sandy clay, peat and stiff sand.
The groundwater table and some specific soil properties are given in Table 5.2.
When loaded by 100 kPa, the settlement
S
is calculated and the effect of using the
linear and the natural strain concept is evaluated.
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