Improvement of fine-grained and cohesive soils 139
permeability in clays is generally up to 15 times larger than in vertical direction. Consequently, it is sufficient to assess the consolidation time by neglecting the effect of vertical consolidation and to rely only on radial consolidation.
The relevance of this proposal can easily be verified by the following
consideration. Let us assume that an infinite pattern of stone columns with
diameter d = 1 m is placed in a triangular grid with distances of a = 3 m,
yielding the unit cell diameter d e = 3.15 m. Column length is 10 m, equal to
the vertical drainage path length. Let us calculate the degree of combined
consolidation at time t when the vertical consolidation U v has reached just
10%. Assuming conservatively a ratio of 1 for horizontal to vertical permeability, and using Equations 4.36 and 4.37 at time t, we get an expression
for the time factor of radial consolidation T r as follows:
T
h
d
c
c
T
r
e
h
v
v
=
⋅
⋅
2
(4.39)
and with (Equation 4.38)
T
h
d
k
k
T
T
T
r
e
h
v
v
v
v
=
⋅
⋅ =
⋅ =
⋅
2
2
10
3 15
10 08
.
.
(4.40)
From Figure 4.22, we obtain, for U v = 10%, the time factor T v = 0.01 for vertical consolidation, which when used in Equations 4.39 and 4.40 leads to T r =
0.1. From Figure 4.22 follows now with d/d e = 3.15 = ~3, the degree of radial
consolidation U r = 90%. With Equation 4.34 the combined consolidation
ratio is then U = 91%. Accordingly, at the chosen time t, the contribution of
vertical consolidation represents only 1% of the combined total consolidation.
U = − −
⋅ −
=
1 (1 0.1) (1 0.9) 0.91
(4.41)
This example was used to demonstrate that the vertical drainage flow can
be neglected under normal conditions since radial consolidation generally governs the rate of combined consolidation of soil improved by stone
columns. This also shows that this simplification is a safe assumption.
When adopting the dry bottom feed method for the stone column construction, a zone of reduced column permeability may develop at its perimeter as a result of mixing of disturbed soil with the column material. In
order to account for this smear effect, as it is called, it is recommended to
reduce the column diameter by 5% and to use this effective diameter in the
relationships presented above. Regardless of the construction method, it is
important to ensure the vertical flow of water in the stone columns, and
this requires a permeable granular blanket to be placed over the column
heads on ground surface that has good horizontal drainage characteristics.
When stone columns are installed in nonliquefiable cohesive soils, they
can take considerable horizontal earthquake loads. These horizontal
permeability in clays is generally up to 15 times larger than in vertical direction. Consequently, it is sufficient to assess the consolidation time by neglecting the effect of vertical consolidation and to rely only on radial consolidation.
The relevance of this proposal can easily be verified by the following
consideration. Let us assume that an infinite pattern of stone columns with
diameter d = 1 m is placed in a triangular grid with distances of a = 3 m,
yielding the unit cell diameter d e = 3.15 m. Column length is 10 m, equal to
the vertical drainage path length. Let us calculate the degree of combined
consolidation at time t when the vertical consolidation U v has reached just
10%. Assuming conservatively a ratio of 1 for horizontal to vertical permeability, and using Equations 4.36 and 4.37 at time t, we get an expression
for the time factor of radial consolidation T r as follows:
T
h
d
c
c
T
r
e
h
v
v
=
⋅
⋅
2
(4.39)
and with (Equation 4.38)
T
h
d
k
k
T
T
T
r
e
h
v
v
v
v
=
⋅
⋅ =
⋅ =
⋅
2
2
10
3 15
10 08
.
.
(4.40)
From Figure 4.22, we obtain, for U v = 10%, the time factor T v = 0.01 for vertical consolidation, which when used in Equations 4.39 and 4.40 leads to T r =
0.1. From Figure 4.22 follows now with d/d e = 3.15 = ~3, the degree of radial
consolidation U r = 90%. With Equation 4.34 the combined consolidation
ratio is then U = 91%. Accordingly, at the chosen time t, the contribution of
vertical consolidation represents only 1% of the combined total consolidation.
U = − −
⋅ −
=
1 (1 0.1) (1 0.9) 0.91
(4.41)
This example was used to demonstrate that the vertical drainage flow can
be neglected under normal conditions since radial consolidation generally governs the rate of combined consolidation of soil improved by stone
columns. This also shows that this simplification is a safe assumption.
When adopting the dry bottom feed method for the stone column construction, a zone of reduced column permeability may develop at its perimeter as a result of mixing of disturbed soil with the column material. In
order to account for this smear effect, as it is called, it is recommended to
reduce the column diameter by 5% and to use this effective diameter in the
relationships presented above. Regardless of the construction method, it is
important to ensure the vertical flow of water in the stone columns, and
this requires a permeable granular blanket to be placed over the column
heads on ground surface that has good horizontal drainage characteristics.
When stone columns are installed in nonliquefiable cohesive soils, they
can take considerable horizontal earthquake loads. These horizontal