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 However, many buttress dams were designed over 60 years ago using outdated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,

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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:

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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)

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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.

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