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(the peak response occurs earlier than the peak loading). Already in 1904 Honda
noticed a negative delay in the potential tidal response in Yokohama and in 1916
Friedrich observed the same in Lubeck. Unknown subsoil water streams were
thought to be the cause! In 1933 a similar behaviour was noticed during
construction of the Park sluice in Rotterdam. No explanation was offered then.
Today, the phenomenon can be understood after a close inspection of the physical
process that takes place; in fact, it is a consequence of the effective stress principle.
C
WAVES ON BREAKWATERS
Internal set-up
Regular storm waves and tides characterised by amplitude
H
and period
T
generate groundwater flow and transient pore pressures in porous dams and dikes.
The induced internal water table height
h
shows a decay and delay, which are
usually expressed by the well-known cyclic solution for a dam with a permeability
k
and effective porosity
n
, according to
h = H
exp(
x/
2
)
cos(
2
t
x/
2
)
(16.28)
))
0.5
, and wave period
T
= 2
with the cyclic leakage factor
.
This formula explains that at distance
x
from the boundary (outer slope), where
the free water moves with
H
cos(
2
= (
KDT/
(
n
/
2
2
t
)
,
the local amplitude decays with
H
exp(
x/
2
) and delays with
t = x/
2
. The average still water level
D
remains
unchanged in this example (Fig 16.12).
T
H
D
2
x
Figure 16.12 Cyclic porous flow in a breakwater
Geometric nonlinear effects occur which are related to the water depth
D
and the
angle
of the outer slope of the dam or dike. They may cause the average water
level
h
inside the dam to rise significantly more than expected, according to
equation (16.28), which is addressed as internal set-up (Barends). The inflow
surface along a slope at the moment of high water level (wave top) is significantly
larger than the outflow surface at the moment of low water level (wave trough).
Moreover, the average seepage path for inflow is significantly shorter that the
outflow path. Hence, during cyclic water level changes, water will enter the
structure more easily than it will leave. Consequently, there will be a state in which
the corresponding inflow surplus is balanced with an extra outflow drive, i.e. by a
groundwater table set-up.
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