Improvement of fine-grained and cohesive soils 141
the vertical component a v of the ground acceleration also needs to be considered, the resisting normal stresses σ c in the stone column would have to be
reduced by the vertical design earthquake acceleration a v accordingly and the
expression in Equation 4.42 would then be
SF
v
c
c
c
h
=
⋅ ⋅ ⋅
a n a
a
tan ϕ
(4.44)
The column stress concentration factor n c is in the order of 2 close to foundation level. It can also be estimated with the assumptions of the Priebe
method by first taking the improvement factor β from Figure 4.14 for a c
and φ c , then calculating n and n c with Equations 4.12 and 4.6. However,
as previously indicated, the Priebe method seems to overestimate the effect
of the stone column leading to n c values of about 3 for the infinite grid
with a c = 0.25 and φ c = 45°. Unfortunately, only few data from field measurements exist for n and n c but they indicate n c values between 1.5 and
2.0 only (Kirsch, 2004). It is therefore recommended to conduct field shear
tests in critical cases to establish the allowable shear force that can be
mobilized under actual conditions. In Section 4.6.4, a detailed discussion
of the stress concentration factors can be found which will help to provide
a better understanding of the variation of this parameter with depth t and
relative column length λ.
Provided that sufficient compaction time is allowed, the stone column
installation will also significantly increase the relative density of loose,
clean sand layers, which could be imbedded in the soils to be improved,
and which might liquefy. To ensure that sufficient density was achieved to
prevent liquefaction, the methods described in Section 3.3.3.1 need to be
applied with the earthquake-induced settlements to be estimated according to Section 3.3.3.2.
However, in silty sands that can only marginally be compacted by vibro
compaction, the stone columns will act as gravel drains and will help to prevent the detrimental pore water pressure build-up occurring in cohesionless
soils during an earthquake. Seed and Booker (1976) have developed design
principles for stone or gravel columns acting as drains by which the necessary drain spacing and diameter can be evaluated to avoid liquefaction.
Figure 4.24 gives useful design charts allowing determining the necessary
relative stone column pattern spacing d/d e as a function of the maximum
allowable pore water pressure increase r g , a ratio for the earthquake severity N eq /N l , and the time factor T ad according to the following expressions:
r g = u g / ′
σ v is the greatest pore water pressure ratio allowed in the design
N eq is the equivalent numbers of uniform stress cycles causing a stress
ratio τ av / ′
σ v during time t d (see also Section 3.3.3.1)
N l is the number of stress cycles causing initial liquefaction in the laboratory with τ av
the vertical component a v of the ground acceleration also needs to be considered, the resisting normal stresses σ c in the stone column would have to be
reduced by the vertical design earthquake acceleration a v accordingly and the
expression in Equation 4.42 would then be
SF
v
c
c
c
h
=
⋅ ⋅ ⋅
a n a
a
tan ϕ
(4.44)
The column stress concentration factor n c is in the order of 2 close to foundation level. It can also be estimated with the assumptions of the Priebe
method by first taking the improvement factor β from Figure 4.14 for a c
and φ c , then calculating n and n c with Equations 4.12 and 4.6. However,
as previously indicated, the Priebe method seems to overestimate the effect
of the stone column leading to n c values of about 3 for the infinite grid
with a c = 0.25 and φ c = 45°. Unfortunately, only few data from field measurements exist for n and n c but they indicate n c values between 1.5 and
2.0 only (Kirsch, 2004). It is therefore recommended to conduct field shear
tests in critical cases to establish the allowable shear force that can be
mobilized under actual conditions. In Section 4.6.4, a detailed discussion
of the stress concentration factors can be found which will help to provide
a better understanding of the variation of this parameter with depth t and
relative column length λ.
Provided that sufficient compaction time is allowed, the stone column
installation will also significantly increase the relative density of loose,
clean sand layers, which could be imbedded in the soils to be improved,
and which might liquefy. To ensure that sufficient density was achieved to
prevent liquefaction, the methods described in Section 3.3.3.1 need to be
applied with the earthquake-induced settlements to be estimated according to Section 3.3.3.2.
However, in silty sands that can only marginally be compacted by vibro
compaction, the stone columns will act as gravel drains and will help to prevent the detrimental pore water pressure build-up occurring in cohesionless
soils during an earthquake. Seed and Booker (1976) have developed design
principles for stone or gravel columns acting as drains by which the necessary drain spacing and diameter can be evaluated to avoid liquefaction.
Figure 4.24 gives useful design charts allowing determining the necessary
relative stone column pattern spacing d/d e as a function of the maximum
allowable pore water pressure increase r g , a ratio for the earthquake severity N eq /N l , and the time factor T ad according to the following expressions:
r g = u g / ′
σ v is the greatest pore water pressure ratio allowed in the design
N eq is the equivalent numbers of uniform stress cycles causing a stress
ratio τ av / ′
σ v during time t d (see also Section 3.3.3.1)
N l is the number of stress cycles causing initial liquefaction in the laboratory with τ av