2.1.15
Seismic analysis of a concrete gravity dam
Products:
Abaqus/Standard
Abaqus/Explicit
In this example we consider an analysis of the Koyna dam, which was subjected to an
earthquake of magnitude 6.5 on the Richter scale on December 11, 1967. The example
illustrates a typical application of the concrete damaged plasticity material model for the
assessment of the structural stability and damage of concrete structures subjected to
arbitrary loading. This problem is chosen because it has been extensively analyzed by a
number of investigators, including Chopra and Chakrabarti
(1973), Bhattacharjee and
L茅ger
(1993), Ghrib and Tinawi
(1995), Cervera et al.
(1996), and Lee and Fenves
(1998).
Problem description
The
geometry
of
a
typical
non
-
overflow
monolith
of
the
Koyna
dam
is
illustrated
in
Figure
2.1.15鈥?
.
The
monolith
is
103
m
high
and
71
m
wide
at
its
base.
The
upstream
wall
of
the
monolith
is
assumed
to
be
straight
and
vertical,
which
is
slightly
different
from
the
real
configuration. The depth of the reservoir at the time of the earthquake is
= 91.75
m. Following
the
work
of
other
investigators,
we
consider
a
two
-
dimensional
analysis
of
the
non
-
overflow
monolith assuming plane stress conditions. The finite element mesh used for the analysis is shown
in
Figure
2.1.15鈥?
.
It
consists
of
760
first
-
order,
reduced
-
integration,
plane
stress
elements
(CPS4R). Nodal definitions are referred to a global rectangular coordinate system centered at the
lower
left
corner
of
the
dam,
with
the
vertical
y
-
axis
pointing
in
the
upward
direction
and
the
horizontal
x
-
axis pointing in the downstream direction. The transverse and vertical components of
the
ground
accelerations
recorded
during
the
Koyna
earthquake
are
shown
in
Figure
2.1.15鈥?/p>
3
(units
of
g
=
9.81
m
sec
鈥?
).
Prior
to
the
earthquake
excitation,
the
dam
is
subjected
to
gravity
loading due to its self
-
weight and to the hydrostatic pressure of the reservoir on the upstream wall.
For the purpose of this example we neglect the dam鈥揻oundation interactions by assuming that the
foundation
is
rigid.
The
dam鈥搑eservoir
dynamic
interactions
resulting
from
the
transverse
component of ground motion can be modeled in a simple form using the Westergaard added mass
technique. According to Westergaard (1933), the hydrodynamic pressures that the water exerts on
the dam during an earthquake are the same as if a certain body of water moves back and forth with
the dam while the remainder of the reservoir is left inactive. The added mass per unit area of the
upstream
wall
is
given
in
approximate
form
by
the
expression
,
with
, where
= 1000
kg/m
3
is the density of water. In the Abaqus/Standard analysis
the added mass approach is implemented using a simple 2
-
node user element that has been coded
in user subroutine
UEL
. In the Abaqus/Explicit analysis the dynamic interactions between the dam
and the reservoir are ignored.
The hydrodynamic pressures resulting from the vertical component of ground motion are assumed
to be small and are neglected in all the simulations.
Material properties