208 Ground improvement by deep vibratory methods
and 48.5 Hz (Type B) with a centrifugal force of about 220 kN creating
a maximal double amplitude of 9 mm at their tips. Three test campaigns
were carried out on-site each consisting of three vibro compaction probes
of 7 m depth with five measuring points being placed 50 cm below ground
surface and with distances from the vibrator between 3 and 26.5 m. As can
be seen on the graph, the 5 mm/s PPV threshold for residential buildings
was on average met at about 7–9 m distance from the vibrator.
When vibro compaction works are performed in granular soil behind
retaining structures or inside cofferdams, to make use of the high friction
angle attained from increased density, the design has to take into account
different loading conditions. Initially, the wall has to support a high earth
pressure that derives from a lower density but considerably higher earth
pressure coefficient. Ultimately, the wall is subjected to a reduced earth pressure resulting from the much reduced earth pressure coefficient and in spite
of the higher density.
In the direct vicinity of the wall with a vibro probe, the soil liquefies during compaction and local stresses rise to hydrostatic pressures with densities of approximately 2.25  ton/m 3 for saturated sand. Stress attenuation
follows as pore water pressure declines (Dücker, 1957, 1968). These temporary local stress peaks have to be considered in the design, particularly
where steel sheet piles are concerned.
We have seen that the vibro compaction process leads to a densification
of granular soils, which is accompanied by a volume reduction manifesting
itself in a ground surface lowering. Whenever adjacent structures are within
reach of this deformation that develops during compaction, the structure
may undergo intolerable settlements particularly when its foundations are
situated close to ground surface resting on loose sandy soil. Although such
foundation settlements generally do not occur, except within a distance
from the depth vibrator equal to the probe depth, care should be exercised,
particularly when very powerful machines are being used (cf. e.g., DIN
4150-3, Appendix C).
From the above example in Berlin where vibrations at ground surface
have been measured it is possible to calculate the minimum distance at
which no compaction and thus surface settlements have to be expected.
With the measured PPVs, the maximum shear strain amplitudes γ max are
calculated according to:
γ max
S
=
PPV
c
(6.5)
with measured shear wave velocities between c S  = 104 and 118 m/s for the
different measurement campaigns in the prevailing granular soils. Figure 6.4
shows the results of these measurements accordingly. It can be seen that the
lower volumetric strain level of γ = 5·10 −5 below which no induced compaction of the granular soil occurs (Vucetic, 1994) is reached at a distance of
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