1
Oberon Dam – Failure hazard of a buttress dam and its vulnerability to earthquake damage
Wan, Chi-fai1; Hascall, Jason1; Richardson, Andrew2; Sukkar, John2 1Black & Veatch Corporation
2State Water Corporation
Oberon Dam is the major headwork of the Fish River Water Supply Scheme providing bulk water supply to
Oberon Shire and Lithgow City Councils, Sydney Catchment Authority, and Delta Electricity. The dam is
owned and operated by State Water Corporation (SWC).
Located on the Fish River 2km south of Oberon in New South Wales, Oberon Dam was completed in two
stages in 1946 and 1957. In 1996 the dam was upgraded to pass the 1993 Probable Maximum Flood
estimate by raising the dam 1.77m and constructing a 50m wide auxiliary spillway on the left abutment.
The upgraded dam comprises a 232m long, 35.3m high concrete slab and buttress section and a 165m long
earth embankment section.
A typical buttress dam has its inclined upstream face made up of relatively thin reinforced concrete slabs
supported by but not integral with the buttresses, making a relatively flexible dam structure vulnerable to
earthquake damage.
As buttress dams evolved from concrete gravity dams, their structural design follows the same principles
as applied to gravity dams. However, many buttress dams were designed over 60 years ago using outdated
methods that did not consider earthquake loads. Current overseas and local design guidelines do not
provide sufficient guidance for checking the seismic stability of existing buttress dams. For instance, the
simplified seismic analysis, proposed by Fenves and Chopra to investigate the seismic response of gravity
dams to earthquake loads in the upstream-downstream direction, is not applicable to buttress dams which
are also susceptible to damage by earthquake loads in the cross-valley direction.
SWC engaged Black & Veatch to carry out a three-dimensional finite element analysis of Oberon Dam to
better understand the structural behaviour of the dam under earthquakes. The analysis used both the
response spectrum and time history approaches. Due to the uncommon design of Oberon Dam and the
limited discussion found in the literature on the dynamic behaviour of buttress dams, the Authors would
like to share their experience in the assessment of the hazard, and on the use of modern finite element
modelling techniques to investigate the dynamic response of this type of dam.
Keywords: Ambursen dams, Buttress dams, Risk assessment, Time history analysis, Finite element
analysis.
INTRODUCTION
Oberon Dam
Oberon Dam is located on the Fish River 2km south of
Oberon, which is situated approximately 43km south-east
of the closest major regional town of Bathurst. The
concrete section of the dam is located on a north-
west/south-east axis with the downstream side facing a
north-easterly direction. The dam is the major headwork
of the Fish River Water Supply Scheme which provides
the bulk water supply to Oberon Shire Council, Lithgow
City Council, Delta Electricity for the Wallerawang and
Mount Piper Power Stations and the Sydney Catchment
Authority for water supply to the Blue Mountains area.
Oberon Dam was constructed in two stages to suit the
overall development of the scheme. Stage 1 was
completed in 1946 with concrete slabs and buttresses to
an interim height of 16.8m and to a length of 192m. The
storage capacity then was 9,100ML. Before Stage 2 work
commenced, the design was amended by substituting an
earth embankment for the planned installation of
additional buttresses on the left abutment. Stage 2 work
commenced in 1954 and was completed in 1957 raising
the dam to the maximum designed height of 33.5m and
extending the length to 378m consisting of a 232m long
concrete section and a 146m long earth embankment. The
crest of the concrete section was 3m wide with a wave
wall 0.7m high. The height of the earth embankment was
14m with a 6m wide crest and it had a 0.9m high stone
wave wall along the upstream edge of the crest.
At the junction of the concrete and earth sections, the end
concrete buttress was strengthened and strutted against
the three succeeding buttresses by cross-buttresses, and
backfilled with sand to form a cellular structural
component. Both the upstream and downstream slopes of
the earth embankment wrapped around onto the face slab
and behind the buttresses in a general conical form.
Flood security upgrade works were carried out for the
dam in 1996 to enable the dam to safely pass the Probable
Maximum Flood (PMF) and included the following key
elements:
Raising the existing reinforced concrete buttress
crest by constructing a 1.77m high reinforced
concrete parapet wall.
Raising the existing earth embankment by 2.3m.
Structurally strengthening the existing ski jump
spillway in the concrete buttress section and raising
the existing upstream training walls.
Construction of a new auxiliary fuse plug spillway
on the left abutment consisting of three 17m wide
bays separated by concrete dividing walls.
Construction of an enlarged 900mm diameter
outlet scour line, with valves and associated
structures.
The upgraded dam is 397m long, consisting of a 232m
long concrete slab and buttress section and a 165m long
earth embankment section. Figure 1 shows the general
arrangement of Oberon Dam after completion of the 1996
upgrade works. Recent photographs of the upgraded dam
are shown in Figures 2 and 3.
Figure 1 General arrangement of Oberon Dam
Figure 2 Downstream view of the concrete buttress
section.
Objectives of this paper
In 2007 State Water commissioned a Quantitative Risk
Assessment (QRA) for Oberon Dam. The QRA (GHD
2009) concluded that the major hazards of Oberon Dam
were piping through the embankment and piping between
the interface of the concrete slab and buttress section and
the embankment dam, structural failure of the inclined
slabs of the concrete section of the dam, and slab and
buttress failure.
Figure 3 View of the auxiliary fuse plug spillway, the
embankment section, and the concrete buttress section
from the left abutment
The 2009 QRA report recommended the provision of a
downstream filter and weighting zone for the main
embankment section of the dam to reduce the piping
hazard, and to carry out a Finite Element Analysis (FEA)
for the concrete slab and buttress dam to evaluate the
effect of cross valley seismic loading. As a result of the
recommendations, Black & Veatch Pty Ltd were engaged
by State Water Corporation to carry out a three-
dimensional FEA of Oberon Dam subject to earthquake
loads.
Due to the uncommon design of Oberon Dam and the
limited discussion found in the literature on the dynamic
behaviour of buttress dams, the Authors would like to
share their experience in the assessment of the hazard, and
on the use of modern finite element modelling techniques
to investigate the dynamic response of this type of dam.
The challenges of completing the 3D FEA to meet the
objectives of the study will be discussed in this paper.
The 3D FEA will provide essential information for
updating the event tree analysis for Oberon dam as part of
State Water Corporation’s Portfolio Risk Analysis Update
in 2012, mainly by informing members of the risk
assessment panel on the dynamic structural behaviour of
the dam during earthquakes.
The updated risk assessment will then provide the basis to
confirm the present level of risk of Oberon dam within the
overall portfolio of eighteen prescribed dams under the
care of State Water Corporation, and help to evaluate the
potential need to pursue safety upgrade options for the
dam.
PREVIOUS RISK ASSESSMENTS OF OBERON DAM
Consequences of dam failure
In 1992 a dam break study was prepared by the then
Public Works Department to evaluate the population at
risk (PAR) downstream of Oberon dam in order to
determine the consequence category for dam failure.
The results of the 1992 dam break study provided a PAR
for both the Sunny Day (caused by a major earthquake,
3
structural stability issue or piping failure) and Flood
failure and no failure cases in order to understand the
incremental impact. The severity of damage and
economic losses were also estimated, which combined
with the PAR values enabled the respective consequence
categories to be determined for the failure of Oberon
Dam. The dam failure consequence categories were
assessed in accordance with the ANCOLD Guidelines on
Assessment of the Consequences of Dam Failure (May
2000) and the NSW Dams Safety Committee Guidance
Sheet DSC3A (June 2010) on Consequence Categories
for Dams.
In 2009 State Water Corporation carried out an updated
flood and dam break analysis for Oberon Dam to simulate
the failure and the propagation of the resultant flood wave
along the Fish and Duckmaloi rivers. The flood
inundation was mapped for seven failure scenarios. The
2009 dam break analysis, however, did not provide
sufficient information on flood depths, velocities and
flood wave arrival times at various affected properties
within the inundated area to allow for a verification of the
PAR. The Probable Loss of Life (PLL) and the
consequence category for Oberon Dam also could not be
verified.
Currently State Water Corporation is reassessing the PLL
using the best available data sets for various flood and
dam break scenarios as part of its Portfolio Risk
Assessment (PRA) Update Project.
Quantitative Risk Assessment in 2009
Between 2007 and 2009, State Water Corporation
commissioned a QRA for Oberon Dam. As indicated in
the QRA Report (GHD 2009), the main contributors to
individual risk were:
piping through the embankment (39.9%);
piping between the interface of the concrete slab
and buttress section and the embankment dam
(18.2%);
structural failure of the inclined slabs of the
concrete section of the dam (11.9%);and
failure of slab and buttress (8.3%)
The cross-section of the raised embankment, as shown in
Figure 4, indicates that the embankment has a toe drain
but without an intercepting chimney filter to limit
continuation and progression of piping through the
embankment. This explains the relatively high hazard
assessed for piping through the embankment.
The hazard of piping between the interface of the concrete
slab and buttress section and the embankment was
assessed as second highest due to the likelihood of a gap
forming between backfilled soil and the concrete wall,
and the lack of a downstream filter. Figure 5 shows a
plan view of the interface between the concrete slab and
buttress section and the embankment.
The individual and societal risks were evaluated to be
below the ANCOLD limit of tolerability for an existing
dam.
Figure 4 Cross-section of the raised embankment
Figure 5 Plan view of the interface between the concrete
slab and buttress section and the embankment
The Societal Risk was similarly assessed to be below the
limit of tolerability. The F-N curve, indicating the level of
societal risks, was plotted within the ALARP region for
which remedial works are to be considered to ensure the
risk is As-Low-As-Reasonably-Practicable.
The estimated total annual risk cost for Oberon dam was
low, suggesting that upgrade works would be difficult to
justify on a risk cost reduction basis alone.
The 2009 QRA recommended the following remedial
works and study to help mitigate and understand the risks
of dam failure to State Water Corporation:
Provision of a downstream filter and weighting
zone for the main embankment section of the dam,
Carrying out finite element analysis for the
concrete slab and buttress dam to evaluate the
effect of cross valley seismic loading, followed by
updating of the risk assessment to confirm the level
of risk and evaluate the need for any seismic
upgrade options.
THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF OBERON DAM FOR THE EFFECTS OF EARTHQUAKE LOADS
Objectives of the 3D FEA of the concrete slab and buttress section
Following one of the recommendations of the 2009 QRA
Report, State Water Corporation engaged Black & Veatch
Pty Ltd in 2011 to carry out 3D FEA of Oberon Dam
subject to earthquake loads.
The objective of the study, in brief, was to evaluate
Oberon Dam for seismic loading to determine its
behaviour during and vulnerability to earthquakes, and
also to assess its adequacy in meeting the requirements of
ANCOLD 1998 Guidelines for Design of Dams for
Earthquake (ANCOLD 1998).
For the purpose of developing a risk assessment, State
Water Corporation requested Black & Veatch to evaluate
the load effects of four levels of seismic load, each of
different annual exceedance probabilities (AEPs). The
four levels of earthquakes correspond to AEPs of 1 in 500
(this is the Operating Basis Earthquake (OBE)), 1 in
5,000, 1 in 10,000 (this is the Maximum Design
Earthquake (MDE)), and 1 in 50,000.
In accordance with ANCOLD 1998 Guidelines, following
an OBE event, the dam should remain functional with
minor damage that is considered acceptable. By the same
standard, a MDE event can result in any amount of
damage that does not prevent the dam from maintaining
its impounding capacity.
Structural arrangement of the slab and buttress section of Oberon Dam
After the upgrade works in 1996, the 232m long concrete
buttress section has a maximum height of 35.3m, a crest
width of 3m and a 1.3m high wave wall. The upstream
face slab slopes at 45 degrees with a thickness tapering
from 1.3m at the base to 0.38m at the crest. The inclined
face slab is supported by a total of 42 buttresses. The
buttresses are at 5.5m centres with a thickness tapering
from 1.14m at the base to 0.58m at the crest at the tallest
buttress. Stiffening struts, 0.45m wide x 0.6m deep, are
provided at four levels between most of the buttresses.
Figure 6 shows a vertical section drawn at one of the
tallest buttresses and a cross-section showing the
arrangement of the struts between two adjacent buttresses.
Figure 6 is extracted from an old drawing which does not
show details of the 1.77m high parapet wall added to the
dam crest in 1996.
Figure 6 Vertical cross-section of the concrete buttress
section of Oberon Dam before it was raised in 1996.
Weathered quartzite and mudstones occur on the right
bank with shale and mudstones on the left. The
foundation rock generally consists of much jointed
volcanic tuff and quartzite siltstone. Buttress foundations
vary in depth from 2m to 5m in the rock and cut-off is
generally approximately 3m into rock.
Traditional stability design approach for concrete slab and buttress dams
A buttress dam uses concrete slabs as the water seal
against the river. The concrete slabs are supported at
intervals by concrete buttresses. The upstream concrete
slab can be in the form of a series of arches, like
Meadowbank Dam in Tasman, or in the form of an
inclined reinforced concrete flat slab, like the buttress
section of Oberon Dam. The reinforced concrete flat slab
design is also called an Ambursen dam after the American
engineer who designed and constructed the first dam of
this type in 1903.
Buttress dams are essentially hollow gravity dams. The
weight of water on the inclined slab contributes to the
vertical force transmitted to the dam foundation and hence
enhances the stability of the dam. Uplift forces on a
buttress dam are relatively small as they only act on the
buttresses which usually have small footprints. Horizontal
struts are installed between buttresses to provide lateral
support in case the buttresses are relatively slender.
Since buttress dams were evolved from gravity dams,
their stability design method is similar to that for gravity
dams. For instance, the most commonly used method for
stability analysis is the linear elastic cantilever method
which treats the dam as a vertical cantilever beam and
evaluates the combined stresses on selected horizontal
sections due to bending and vertical loads. The horizontal
sections are assumed to remain plane under loading.
Note that this traditional stability design approach
considers mainly the effects of hydrostatic load acting in
the upstream-downstream direction, and does not consider
the effects of earthquake loads or any loads acting in the
cross valley direction.
Effects of earthquakes on a buttress dam – literature search
Including Oberon Dam, there are only eight buttress dams
in Australia. Few discussions have been found in the
literature on the analysis of the effects of earthquakes on a
buttress dam. Herweynen (1998) discussed the stability
study of Meadowbank Dam in Tasmania. His focus was
mainly on analysing the effects of flood loading on the
sliding stability of the dam using a probabilistic approach.
Guidelines for Design of Dams for Earthquake
(ANCOLD 1998) discuss various methods for analysing
the seismic stability of dams, but most of the methods
discussed are more applicable to embankment dams and
gravity dams than to buttress dams. For instance, the
Fenves and Chopra (1986, 1987) Method recommended
as a simplified approach for analysing earthquake load
response can only be applied to gravity dams, and for
loading applied in the upstream-downstream direction
only. The sequence of analysis for MDE and the
acceptance criteria recommended by the Guidelines are
also not applicable to buttress dams which are essentially
reinforced concrete structures. On the other hand, the
Guidelines do provide some valuable comments on the
analysis of a buttress dam. Quoting directly from the
Guidelines:
5
For arch dams, buttress dams and gravity dams
where length is less than twice the height, a three
dimensional finite element model can provide
natural frequencies and mode shapes for
determining earthquake loads.
As the mode shapes are more complex than those
for a gravity dam analysed in two dimensions, it
is more appropriate to analyse these dams in the
time domain.
Whether to do a 2D or 3D analysis will larger
depend on the type of dam and the valley
geometry. For buttress dams, especially those
with buttresses having low stiffness in the cross-
valley direction will also require a 3D analysis.
FERC (1997) Guidelines Chapter X also remarked that
the finite element method would be the only practical
method available for evaluating the dynamic response of
buttress dams.
Jonker et al. (2007) discussed the safety evaluation of
Clover Dam, a buttress dam in Victoria, using 3D finite
element analysis. They analysed the earthquake response
of a partial model of the dam, which they called a “single
buttress model”. Their study used the response spectrum
approach to analyse the effects of earthquakes in both the
upstream-downstream and the cross valley direction.
Few discussions could be found in the literature giving a
detailed account of the use of time history approach to
study the earthquake response of a buttress dam.
Adopted methodologies for the analysis of Oberon Dam
There are several available dynamic analysis
methodologies that vary with respect to accuracy,
computational effort, and theoretical basis. Two of these
methods, the response spectrum analysis and the time
history analysis, were selected for analysing Oberon Dam
model.
Response spectrum analysis
A response spectrum analysis is a linear analysis based on
a structure’s natural frequencies and a response spectrum.
Every structure has a number of natural frequencies of
vibration. Each of these frequencies corresponds to a
particular mode shape, which is the shape of the
deformation in the structure as it vibrates at a given
frequency. A finite element model can be used to run a
modal analysis to determine the many natural frequencies
and the corresponding mode shapes for a structure.
A response spectrum is the plot of the maximum response
for all possible oscillators (frequencies) to the same
specified load function or vibration. The response
spectrum can then be used to amplify the modes of
vibration to determine the maximum structure response
for each mode. The responses from multiple modes are
then combined using the square-root-of-the-sum-of-the-
squares (SRSS) method to determine a single maximum
structural response to be combined with other static load
cases.
The response spectrum method is generally, but not
always, conservative. Since it does not consider the
oscillatory nature of the ground motion, the stresses
calculated are higher than when a time history analysis is
used. The response spectrum method requires less
computational effort, and if the stresses in the structure
are acceptable using the response spectrum method, there
typically is no need for a time history analysis. If the
stresses are not acceptable, then analysis using the time
history method is performed.
Time history analysis
Unlike a response spectrum analysis, the time history
analysis, or transient analysis, is based on a time varying
load. In other words, the acceleration is defined over the
time domain rather than the frequency domain. The
response is then determined by equations of motion.
A time history analysis can be either linear or nonlinear.
Nonlinear analysis takes into account the effects of
material failure, while a linear analysis does not.
Considering material failure allows redistribution of loads
within the model as components reach their peak
capacity; however, it also requires substantially more
computing capacity due to the ever-changing nature of the
material properties and, hence, the stiffness matrix.
Since the oscillatory ground motion is considered, stresses
are typically lower than stresses from the response
spectrum method. As the accelerations increase, response
spectrum analysis results tend to become unacceptable,
and it is necessary to use the time history method to get
more accurate results.
Procedure for analysis of earthquake load effects
The Oberon Dam evaluation began with a response
spectrum analysis. Four response spectrum curves were
used in the analysis. These correspond to the four
earthquake AEPs mentioned in an earlier section.
The results of the response spectrum were combined with
the results of the static load case in both the positive and
negative directions. The results of the combinations
indicated several overstressed components. Following the
evaluation of the results, it was decided to pursue a linear
time history analysis.
A linear time history analysis was completed for three
different time history input ground motions, and again
combined with the results of the static load case.
Generation of time histories
Time histories were developed in accordance with
guidelines published by the FERC (1999). The works
included the following:
Selecting appropriate recorded natural time
histories based on the appropriate earthquake
magnitude and distance and similar site
characteristics.
Estimating an initial scaling factor for subsequent
spectral matching.
Using time-domain spectral matching of the
selected time histories to the target spectra using
RSPMATCH.
Developing final acceleration time histories for
subsequent dynamic analysis.
Selection of appropriate natural time histories
Either natural recorded time histories or synthetic time
histories can be used to represent the target spectrum.
When using natural recorded time histories, ANCOLD
(1998) and FERC (2007) suggest using at least three sets
of time histories for the analysis.
The deaggregation result presented in the Report on
Review of Seismicity (ES&S 2008) for the MDE at a
period of 0.5 seconds demonstrates that most of the
seismic hazard contribution comes from magnitude 5 to
7.5 earthquakes in a range approximately 3 to 60km from
Oberon Dam. The mean magnitude of the deaggregation
was 6.6 at a distance of 28.8 kilometer. Based on the
original seismicity report (ES&S 2005) and the update in
2008, the primary sources contributing to seismic hazard
are the Lapstone Monocline Fault (50km east of the site),
and the adjacent West Sydney Basin and Canowindra
seismotectonic zones. Seismic sources in these areas
generally display a thrust type fault mechanism.
Therefore, time histories from a thrust-type seismic
source with a magnitude of 6.0 to 7.5 at a radius of 10km
to 50km were considered to simulate the anticipated
ground motion at Oberon Dam. In addition, time histories
were selected from seismic stations installed on bedrock
to avoid amplification effects from soil layers.
Appropriate time histories were selected from the Pacific
Earthquake Engineering Research Center Strong Motion
Database (PEER 2010). The selected motions have a
comparable spectral shape and Peak Horizontal
Acceleration (PHA) with the target spectrum. The natural
time histories finally selected for analysis were:
For OBE analysis only
Morgan Hill earthquake (24 April 1984)
Coalinga earthquake (2 May 1983)
For MDE analysis only
Loma Prieta earthquake (18 October 1989)
Tabas earthquake (16 September 1978)
For both OBE and MDE analyses
San Fernando earthquake (9 February 1971)
Spectral matching
USACE (2003) explains the processes for spectral
matching. Spectral matching involves modification of an
initial time history – a natural time history or scaled
natural time history – and modifying the spectrum to
better fit the smoother target (MDE and OBE) spectrum
while preserving the non-stationary characteristics of the
time series as much as possible. The selected earthquake
time histories were each spectrally matched to the MDE
and OBE target spectra presented in Figure 7 to develop
the acceleration time histories at the bedrock outcrop.
Time-domain spectral matching with the spectral
matching code RSPMATCH (Abrahamson 1992) was
completed using SHAKE2000 as a pre-processor and
post-processor for the time histories. RSPMATCH
modifies the initial time history spectrum in the time
domain by iteratively adding or subtracting wavelets that
match the response spectrum over a group of periods.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Period (s)
0.0
0.2
0.4
0.6
0.8
1.0
Accele
ratio
n (
g) MDE (1 in 10,000 AEP)
target spectrum (horizontal)
MDE (1 in 10,000 AEP)target spectrum (vertical)
OBE (1 in 500 AEP)target spectrum (horizontal)
OBE (1 in 500 AEP)target spectrum (vertical)
Figure 7 MDE and OBE target spectra at Oberon Dam
(Extracted from ES&S (2005, 2008)
Target spectra for vertical acceleration
Also shown in Figure 7 is the vertical MDE and OBE
target spectra at bedrock. They were estimated from the
horizontal target spectra using the ratios of vertical to
horizontal response spectral amplitudes as shown in
Figure 8. The adopted ratios were based on a distance of
10 km, which gives a ratio of 1.0 for spectral ordinates
with a period less than 0.3s and a ratio of 0.67 for all
other spectral ordinates.
Figure 8 Simplified relationships between vertical and
horizontal response spectra as a function of distance R
(same as Figure 16 in USACE 1999)
7
Similar spectral matching processes described in the
preceding section for the horizontal components were
used to develop the vertical component of the time
histories. An example of matched spectral results for the
MDE vertical motion, using the Tabas Earthquake time
history, is shown in Figure 9.
(a)
(b)
Figure 9 (a) Matched vertical acceleration time history
and (b) vertical response spectra at Dayhook of the Tabas
earthquake matched with MDE vertical target spectrum
Setting up of the 3D finite element model
3D solid model and meshing
The 3D finite element model of Oberon Dam was
developed from drawings provided by State Water
Corporation.
ANSYS Mechanical, Version 13.0, was the finite element
analysis package selected for the dynamic structural
analysis. The finite element mesh, as shown in Figure 10,
is constructed from 4-node solid tetrahedron elements.
The full model contains approximately 305,000 nodes and
153,000 elements. The mesh size was adjusted
appropriately for each component and contact surface.
Both surface and volume sizing methods were utilised in
the optimisation to vary the mesh size within a component
body as needed. This variation is evident in the ground
component, where the surface below the dam utilises a
smaller mesh than the remainder of the body. The model
is divided into components categorised by function and
geometry. The six categories are slab, buttress, spillway,
strut, tower, and ground.
Modelling connectivity between structural members
(a) Modelling the connections between struts and
buttresses
The struts were constructed so that they were tied to one
buttress and pocketed 152 mm into the other with a
bitumen layer lining the pocket. The pocket was intended
to allow for movement between the struts and buttresses
for expansion and contraction. The finite element model
was constructed with the same intent: pockets on one side,
but not the other.
Figure 10 3D finite element mesh of the concrete slab and
buttress section of Oberon Dam
(b) Modelling of bonded surface and sliding contact
In a finite element analysis, contact assumptions govern
the rules of behaviour of elements at their interface with
adjacent elements. For instance, a “bonded” contact
forces the solver to maintain a fixed relationship between
the elements in question. No differential separation or
sliding is allowed at a “bonded” interface. Table 1 below
summarises the definitions for various contact
configurations available in ANSYS.
The connectivity between structural members must be
linear in a response spectrum analysis. Because of this
reason, only two contact types were applicable in the
setting up the finite element model, i.e. “bonded” and “no
separation”. The “bonded” configuration, as noted above,
prevents differential separation and/or sliding between
elements. The “no separation” configuration allows
frictionless sliding, but prevents differential separation.
Table 1 Definitions for element contact in ANSYS
Contact
type Separation Sliding
Linear
behaviour
Bonded No No Yes
No
separation No Frictionless Yes
Frictionless Yes Frictionless No
Rough Yes No No
Frictional Yes Friction No
The connection between a strut and a buttress at the
“pocket” end is a kind of “no separation” contact. The
reality is that the contact is not frictionless. Analyses of
the 3D finite element model had, therefore, been carried
out assuming either “bonded” or “no separation”
connection between a strut and a buttress at the “pocket”
end in order to assess the upper and lower bound values
of the stresses in the struts and buttresses.
Assumptions in boundary conditions
The part of the dam foundation included in the finite
element model extends beyond the dam approximately
twice the maximum height of the dam. Therefore, the
cross section of the ground was extended roughly 61m
beyond the extent of the dam in all directions. Excluding
the upper surface, the exterior faces of the rock geometry
were fixed in space for the analysis. No other rigid
boundary conditions were applied.
Interaction with the left embankment
Several buttresses are partially buried by an earth
embankment on the left end as shown on Figure 11. As
linear analysis was adopted, the soil-structure interaction
between the buttresses and the embankment could not be
modelled nonlinearly. Linear “soil-springs” had been used
to model the soil-structure interaction.
In general, soil structure interaction tends to make the
whole soil-structure system less stiff than the structure
alone. This has a tendency to shift the fundamental
frequencies to a lower range. In addition, the soil-
structure interaction involves higher material damping
and radiation damping that will reduce the seismic force
transferred to the structure. Nonlinear behaviour, such as
gap formation at the interface, releases constraints on the
structure and would also tend to reduce the stresses.
Modelling of the effects of storage
The mass of the water can increase or reduce pressure on
the slab, and therefore, it must be considered in any
seismic or other dynamic analysis. The effects of this
hydrodynamic pressure were modelled using Zanger’s
equation (Zanger 1952). A hydrodynamic pressure,
however, is not relevant to a dynamic analysis because the
direction and magnitude of the pressure vary with a
seismic event or acceleration. Therefore, Zanger’s
equation was modified to obtain a distribution of the
hydrodynamic mass acting on the slab as a function of
depth below the free surface of the water.
Modelling of the intake tower
The intake tower was included in the model for mass
purposes only. It was assumed that the failure of the
tower itself would not cause catastrophic failure of the
dam. Since the foot bridge from the tower to the walkway
was likely to transfer load from the tower to the dam, the
bridge needed to be modelled. For simplicity the bridge
was modelled as two elastic springs.
Model Validation
The model was validated with several simple static
analyses. The first check was to verify that the total
applied load was equal and opposite to the reaction at the
base. Next, the vertical reaction from the gravity-only
case was compared to the approximate weight of the
structure to confirm the two were similar. Third, the
deflection of the structure under several point loads and
hydrostatic pressure was compared to the anticipated
deflected shape. Finally, the results of the 3D finite
element static analysis were compared to a 2D static
analysis. On the basis of the above four validation
methods, the model is deemed substantially accurate for
the analysis being completed.
Key findings of the 3D FEA
Modal analysis
A modal analysis was completed on the finite element
model to determine the mode shapes and natural
frequencies for the dam. The results were used in both
the response spectrum and the linear time history
analyses.
A valid modal analysis is required to have included
enough mode shapes to reach 90 percent mass
contribution. In the 3D model of Oberon Dam, as many
as 500 mode shapes were required to reach 90 percent
contribution for vibration in all three directions. Figure 12
shows one of the fundamental mode shapes obtained from
the modal analysis.
Response spectrum analysis
Results of the analysis indicated that the strut components
were the most critical. The strut capacity is not exceeded
by the OBE case, but it is exceeded by the MDE case
assuming either “bonded” or “no-separation” contact
between the struts and buttresses at the “pocket” end. On
the basis of those results, it is clear that the dam meets the
requirements of the ANCOLD 1998 guidelines for the
OBE load case.
Figure 12 Fundamental mode shape – Frequency
11.93Hz, mass contribution 33%.
Although results of the analysis suggested failure in
several struts during the MDE, the linear analysis could
not tell if the loss of these struts would lead to a
catastrophic dam failure. Whether the dam could meet the
requirements of ANCOLD (1998) for the MDE load case
was uncertain.
Figure 11
Left end of the
buttress
section
partially
buried by an
earth
embankment
9
Linear time history analysis (MDE case only)
Due to the concern of the ability of the struts and the
buttresses to resist the MDE load, and considering that a
response spectrum analysis very often would give more
conservative results than a time history analysis, the
decision was made with State Water Corporation to
conduct the time history analysis for the MDE case in
hope of finding reduced stresses in the strut components.
Linear time history analysis was chosen over nonlinear
analysis mainly because of the significant reduction in
required computing hardware capacity and run time.
In the structural analysis of Oberon Dam, the failure of
one strut does not necessarily indicate failure of the entire
system, because the loads that act to fail a strut may be
redistributed to other structural elements adjacent to the
strut. With a linear analysis, this load redistribution is not
indicated. To simulate this, two models were executed:
the first with all struts in place, the second with all failed
struts removed. Since the act of failing a strut consumes a
significant amount of energy, the second model is
conservative because this failure energy is left in the
system to be dissipated by other components within the
model. In reality, this energy would be dissipated by the
failed struts, leaving less energy in the system. Although
conservative, the second model can be used to see where
the loads will be redistributed and how far reaching the
effects of the failure may be.
With the exception of the San Fernando time history,
analyses were carried out assuming “no separation”
contact between the struts and the buttresses. These cases
were selected because they are closer to the physical
construction and resulted in higher stresses for the strut
components. The San Fernando time history was also
analysed for the “bonded” contact condition for validation
purposes only.
(a) Analysis of the full mass model
Results of the linear time history analysis indicated that:
Highest maximum principal stress always occurs at
the strut connection to the buttress. All of the
struts are loaded in a bending fashion, with high
compression on one side and high tension on the
other. The intensity of the load is limited to a
fairly isolated area.
Specifically, three struts in the area behind the
intake tower tend to exhibit the highest stresses,
with decreasing stress values moving away from
that area.
The “no separation” contact case indicates very
high stresses on one end of the strut, while the
“bonded” case indicates higher stresses on both
ends.
Bending stresses are also plainly indicated on the
buttresses and the slabs; however, the magnitudes
of these stresses are not of concern.
(b) Analysis of the full mass model with three failed
struts removed
In the second set of analyses, the effects of strut failure
were investigated. For each earthquake time history,
three struts were removed at the beginning of the run.
The struts chosen were the only three indicating failure in
the San Fernando “no separation” run, and for each time
history, the struts removed were identical. Results of
analysis indicated that the maximum stress still occurs at
the connection between strut and buttress; however, the
magnitude of that stress has been reduced significantly.
The load distributes itself to structural elements in the
immediate vicinity of the missing or failed struts, and the
intensity of the maximum load is limited to a fairly
isolated area.
The second set of analyses implies that the loss of
individual struts will not cause catastrophic failure of a
buttress or loss of the retaining capacity of the dam.
While this does not imply that the loss of all struts will
not lead to catastrophic failure, the significant drop in
magnitude of the maximum principal stresses in the strut
components, as revealed by comparing the stress plots in
Figures 13 and 14, suggests that failure of all the struts is
not likely.
(c) Final run with 2 bays of struts removed
A final run was completed under the Loma Prieta time
history. With this run, the number of struts removed was
expanded to 20, creating two adjacent empty bays. The
stresses are similar to those determined for the case with
only three missing struts. Most importantly, the stresses
within the buttresses and the slabs have not increased and
are within acceptable levels.
Challenges of the 3D finite element analysis
From a finite element modelling standpoint, Oberon Dam
posed several technical challenges. Since the dam is a
slab-and-buttress type, the individual component
geometries are much smaller than those of an arch or
gravity dam where large concrete monoliths are common.
Due to these smaller geometries, the model element size
was forced to be small to avoid an unfavourable aspect
ratio driven by the smallest dimension of each
component. Therefore, the number of elements required
in a full-sized slab-and-buttress model is much greater
than that required for a gravity or arch model.
The model size problem is compounded by the fact that
each of these geometries must interact with one another
according to the contact definitions. In a typical arch or
gravity model, the number of contact definitions is limited
because there are relatively few contacts. That is not the
case with a slab-and-buttress dam.
With a large model size inevitable, it became impractical
to solve a non-linear analysis. Such an analysis would
require additional model components, non-linear material
properties, and non-linear contact definitions. All of these
would compound the size problem and lead to even
longer solve times.
With a large model size inevitable, it became impractical
to solve a non-linear analysis. Such an analysis would
require additional model components, non-linear material
properties, and non-linear contact definitions. All of these
would compound the size problem and lead to even
longer solve times.
Figure 13 Maximum principal stresses for strut
component (full mass model)
Figure 14 Maximum principal stresses for strut
component (3 struts removed)
For time constraints and practicality, a linear analysis was
chosen. Though not as sensitive to model size, a linear
analysis has its own challenges. For instance, constrained
to linear contact definitions, it was impossible to correctly
model the slab-to-buttress interaction. At this location,
friction would dictate the sliding between the two
surfaces; and lift-off would be prevented by self weight
and hydraulic pressure alone. Both of these are non-linear
behaviours and therefore not allowed in a linear model.
Another challenge was energy dissipation. The linear
analysis suggested that several strut components would
see load beyond their capacity, thus ending in failure. As
failure is a non-linear behaviour, it’s not possible to
remove strut components from the model mid-way
through the analysis. They can however be removed prior
to the analysis, but the energy dissipation associated with
the failure would not be indicated in the results. Instead,
the full energy would have to be dissipated by the
remaining components.
As with any finite element modelling, modelling Oberon
Dam was a careful balance of accuracy and practicality.
While one decision may have resulted in better results, the
same decision may have simultaneously increased the run
time ten-fold. The balance is in how much the additional
accuracy is worth in project schedule and cost.
COMMENTS AND CONCLUSIONS
State Water Corporation has an on-going program of
analysing and monitoring the risks of its portfolio of
dams. In order to better understand the risk of Oberon
Dam, State Water Corporate engaged Black & Veatch to
carry out 3D FEA of the concrete buttress section of the
dam to study its response under earthquake loads.
Comments and conclusions of the study are summarised
as follows:
A concrete buttress dam is treated as a hollow
gravity dam in traditional dam stability analysis
which considers loading mainly in the
upstream/downstream direction. In addition, the
design of traditional concrete slab and buttress
dams before the 1960s did not normally take into
account the effects of earthquakes. It is, therefore,
essential to consider the load effects of earthquake
in a safety review of a buttress dam, and in
particular to consider the effects of earthquake
striking in the cross-valley direction.
Current ANCOLD guidelines cater mainly for
gravity dams and embankment dams, and provide
little guidance on analysis of the seismic load
response of concrete slab and buttress dams. Few
reports are available from the literature discussing
the analysis of a concrete slab and buttress dam for
the effects of earthquake loads.
For a concrete slab and buttress dam, 3D structural
analysis appears to be the best method for properly
assessing the effects of various loadings, in
particular earthquake loads in both upstream-
downstream and cross-valley directions.
The 3D structural analysis of a buttress dam for
earthquake loads can employ the relatively simple
but more conservative response spectrum
approach, or the more sophisticated time history
approach. The latter approach is more demanding
on computer hardware speed and data storage
capacity requirements and needs much longer
computer run-time compared to the response
spectrum approach.
Although a non-linear-analysis can more
accurately model yielding of a structure, a linear
time history analysis was selected in lieu of a non-
linear analysis largely due to practicality. As
evident by the large file sizes and long run times
for the linear runs, a full non-linear analysis would
have been impossible to complete on a reasonable
timeline under a reasonable budget. A partial
model could have been pursued, but the loss in
accuracy due to boundary condition assumptions
may have negated any gains made by choosing
non-linear.
The 3D structural analysis of the concrete buttress
section of Oberon Dam indicated that damages to
the dam by the OBE would be unlikely. The dam
structure would suffer from damages during the
MDE, mainly in the struts connecting adjacent
buttresses. However, the damages would unlikely
result in collapse and breach of the dam.
11
ACKNOWLEGEMENTS
The Authors would like to acknowledge the State Water
Corporation for their permission to publish this paper.
REFERENCES
Abrahamson, N. A. 1992, “Non-Stationary Spectral
Matching,” Seismological Research Letters, Volume 63,
No. 1, 1992, p. 30.
Australian National Committee on Large Dams
(ANCOLD) 1998, Guidelines for Design of Dams for
Earthquake, August 1998.
Environmental Systems & Services (ES&S 2005, 2008),
Review of Seismicity, prepared for State Water
Corporation, June 2005, updated in 2008.
Federal Energy Regulatory Commission (FERC) 1997,
Engineering Guidelines for the Evaluation of
Hydropower Projects, Chapter X, Other Dams, October
1997.
Federal Energy Regulatory Commission (FERC) 1999,
Engineering Guidelines for the Evaluation of
Hydropower Projects, Chapter 11, Arch Dams, October
1999.
Federal Energy Regulatory Commission (FERC) 2007,
Engineering Guidelines for the Evaluation of
Hydropower Projects, Chapter 13, Evaluation of
Earthquake Ground Motions (Draft Version 6.5),
February 2007.
Fenves, G. and Chopra, A.K. (1986), Simplified
earthquake analysis for earthquake resistant design of
concrete gravity dams, Report No. UCB/EERC-85/10,
Earthquake Engineering Research Centre, University of
California, Berkerley, June 1986.
Fenves, G. and Chopra, A.K. (1987), Simplified
earthquake analysis of concrete gravity dams, Journal of
Structural Engineering, ASCE, Vol. 113, No. 8, August
1987.
GHD 2009, Report for Quantitative Risk Assessment for
Oberon Dam, November 2009.
Herweynen, R.I. 1998, Safety of Meadowbank Dam
Against Sliding Parameter Uncertainty, Proceedings,
ANCOLD-NZSOLD 1998 Conference on Dams,
September 1998, Sydney, Australia.
Jonker, M., Lopez, F. and Bosler, J. 2007, Safety
evaluation of a slab and buttress dam, Proceedings,
NZSOLD-ANCOLD 2007 Conference on Dams, 17 – 21
November 2007, Queenstown, New Zealand.
Pacific Earthquake Engineering Research (PEER) Center
strong motion database, October 2010
http://peer.berkeley.edu/smcat/sites.html, (accessed on
2/14/2011).
US Army Corps of Engineers 1999, Engineer Manual:
Response Spectra and Seismic Analysis for Concrete
Hydraulic Structures (EM 1110-2-6050), June 30, 1999.
US Army Corps of Engineers 2003, Engineer Manual:
Engineering and Design – Time-History Dynamic
Analysis of Concrete Hydraulic Structures (EM 1110-2-
6051), December 22, 2003.
Zanger, C.N. (1952), Hydrodynamic pressures on dams
due to horizontal earthquake effects, Engineering
Monograph No. 11, Bureau of Reclamation, Denver,
Colorado, May 1952.