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INELASTIC DYNAMIC ANALYSIS FOR A CONCRETE FRAMED INTAKE
TOWER SUBJECT TO EARTHQUAKE LOADINGS 1(*)
Nihal VITHARANAPrincipal Engineer, BSc(Eng)Hons, PhD(Struct.), MBA, PG-Dip(Geotech.)
GHD Pty Ltd, Perth
Priyan MENDIS
Associate Professor, BSc(Eng)Hons, PhD (Struct.), MIE(Aust)
University of Melbourne
Jayanta SINHA
Project Engineer, BSc(Eng), MTech, PhD (Geotech.), MIE(Aust)
NSW Department of Land and Water Conservation
AUSTRALIA
1. INTRODUCTION
Burrendong Dam is located on the upper reaches of the Macquarie River
approximately 450km west of Sydney, New South Wales, Australia. TheMacquarie River rises in the Great Dividing Range west of Sydney.
The dam was constructed in 1967. The dam has a water conservation
storage of 1,188 GL and a flood mitigation storage of 490 GL controlled by seven
17m wide x 6m high spillway radial gates. The main embankment is 76m high
and has a crest length of 1,116m. It is a zoned earth and rockfill type dam with a
central impervious core and shoulders of different materials.
The intake works comprise of a reinforced concrete tower connected to a
3.0m diameter steel penstock installed in a 8.2m diameter tunnel. The system is
a bottom-outlet (single-level) offtake. Emergency closure is provided by a fixed
wheel gate in the intake tower.
The intake tower consists of 10-vertical reinforced concrete columns
forming an internal diameter of 9m and an external diameter of 14m (Fig. 1a).
These columns are inter-connected by circumferential ring beams acting as
bracing members. The tower is 43m high from its foundation to the maintenance
floor level. A cylindrical concrete tower of 14m height exists above the
(*)Analyse de la dynamique inlastique dune prise deau en structures de btonassembls sujet des tremblements de terre dus aux chargements
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maintenance floor level up to the hoist house floor level. Access to the tower is
by an access bridge. The full-supply level is 37m above the tower foundation.
2. BACKGROUND TO THE CURRENT STUDY
Department of Land and Water Conservation has undertaken a program for
assessing the seismic resistance ability of dams and associated structures. The
ANCOLD Guidelines for Design of Dams for Earthquake [1] provides
recommendations for all types of existing and new dams. Based on a screening
level of analysis on a portfolio of intake structures, it was decided to carry out a
detailed seismic assessment of the Burrendong intake tower. An inelastic
dynamic analysis was recommended by the consultant, GHD Pty Ltd, to capture
the energy dissipation due to the structures inelastic hysteresis behaviour
resulting in reduced inertia forces.
As the Burrendong Tower is a concrete framed structure, its behaviour isquite different from that of a cylindrical tower [2,3]. In particular, under extreme
loadings, plastic hinges and yielding occur in different members at different times
resulting in energy dissipation and reduced inertia loads. This beneficial effect is
being recognised in some of the modern building standards, based on pioneering
work by Park and Paulay [4]. This approach was adopted in the current study.
3. ASSESSMENT CRITERIA
In the case of seismic loadings for intake towers [1], there is no specified
annual probability of exceedence and this is to be determined by each dam
owner considering the level of damage or consequence which is acceptable. In
building design practice [8], the ultimate limit state earthquake loading is defined
as the event with an Annual Exceedence Probability (AEP) of 1:452 years.
An important facility at the dam is to release water in a controlled manner.
If there has been an earthquake and the dam is damaged to the extent that the
dam is not serviceable then it may be necessary to lower the storage so that
remedial works can be undertaken. The appurtenant structures such as intake
tower associated with the dams operation should maintain their normal operating
condition after an Operating Basis Earthquake (OBE). For a more extreme
earthquake up to the Maximum Design Earthquake (MDE), these structures
should not experience any damage to the extent where they could allow suddenor uncontrolled loss of water from the storage.
A discussion of the selection of appropriate AEPs is beyond the scope of
this paper. It was agreed to adopt an AEP of 1:500 for the Operating Basis
Earthquake and an AEP of 1:10,000 for the Maximum Design Earthquake for the
seismic assessment of the intake tower. The performance criteria adopted are:
OBE: Under combined static and earthquake loads to induce maximum concrete
and steel stresses to allowable values to avoid permanent deformations (ie, steel
reinforcements not yielded) and the tower to remain stable.
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MDE: Steel reinforcement can yield, concrete compression zone to be confined
by well-detailed hoop reinforcement at high strain levels, and longitudinal bars to
be prevented from buckling by hoop reinforcement.
4. INELASTIC DYNAMIC RESPONSE OF STRUCTURES
The important feature with inelastic behaviour is that the lateral inertia loads
generated in the structure by the earthquake are much less than those given by
an elastic dynamic analysis. This reduction has been attributed mainly to the
ability of ductile structures to dissipate energy by postelastic deformations. To
avoid collapse during severe earthquakes such as MDE, members must be
ductile enough to absorb and dissipate energy by postelastic deformations. This
philosophy is being introduced in modern concrete design standards and some
details of these aspects can be found in [4]. The load reduction factor R is
related to the displacement ductility factor of the structure :
y
u
loaddesignduced
loadresponseElasticR
===
Re(1)
where u is the ultimate lateral deflection at the end of the postelastic range
and y is the lateral deflection when yielding is first reached or the beginning of
the inelastic behaviour. In the case of a reinforced concrete member, u may
correspond to the crushing strain of concrete in compression (or a specified lower
value) and y to the yielding of reinforcing steel. Eq. 1 indicates that the
reduction in load is inversely proportional to the displacement ductility factor of
the inelastic system and this was shown to be valid for structures with natural
periods more than 0.40 secs. In other words, if a structure is designed for a
reduced design load compared with the values given by an elastic analysis, the
structure should be provided with a displacement ductility capacity greater than or
equal to the load reduction factor R.
5. INELASTIC ANALYSIS APPROACH
5.1 STRUCTURAL MODEL
The structure was modelled as a 3-dimensional moment resisting frame
consisting primarily of vertical columns and ring (circumferential) beams up to the
maintenance floor level at 43m (Fig. 1). Cylindrical wall elements were used to
model the upper portion above this level. A plan view showing the location of
10 vertical columns is also shown with typical section details.
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The 3-dimensional non-linear analysis was performed using Program
RUAUMOKO [10] which is one of the most popular programs for earthquake
analysis. This is capable of carrying out inelastic time-history analysis of framed
structures. For the current study, several purpose-written programs and
spreadsheets were used to pre and post-process data.
The stiffness of each member was modified at each time interval depending
on displacement,x, and the direction of change inx(loading or unloading). The
load-displacement relationship of structural elements is represented by their
hysteresis loops which could be bilinear (elastic-perfectly plastic) or a much more
complex one.
5.2 CONCRETE AND STEEL BEHAVIOURS
In particular, the inelastic behaviour under MDE requires a detailed
estimate of the section capacity considering the stress-strain behaviour of
longitudinal and hoop steel, confined (inner) concrete and unconfined (cover)concrete. In routine design of concrete members subject to gravity loads,
concrete is assumed to be unconfined (ie, uniaxial compression) and maximum
compressive strength is taken as the unconfined compressive strength [5] with
corresponding strain of 0.003. Under seismic loadings, the other important
parameter for ductility calculation is the ultimate compressive strain. It has been
shown that even unconfined concrete can sustain strains as high as 0.008 before
spalling [6].
When adequate transverse steel (ie, hoop steel) is provided, both
compressive strength and ultimate compressive strains are enhanced due to the
passive confinement provided by transverse steel to the core concrete.Therefore, structural elements subjected to high seismic loads should be
provided with well-detailed transverse steel to achieve sustainable ductility under
cyclic loading. They also prevent the buckling of longitudinal bars. Fig. 2 shows
the stress-strain relationship for both confined and unconfined (cover) concrete.
In the current analysis, the model proposed by Mander [7], based on strain
energy principles, was used.
Fig 2
Confined and unconfined model for concrete in compression
Model forces-contraintes pour bton coffr et non coffr sous compression
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A strain-hardening model [4] was used to represents the actual behaviour
of normal strength steel. The yield strength fy of reinforcing steel used in
Burrendong Tower is 230 MPa.
5.3 DEVELOPMENT OF SECTION RESPONSES
With the above knowledge of individual stress-strength relationships of
unconfined cover concrete, confined core concrete and steel, the section
responses can be determined for a given concrete element. The concrete
section was divided into a number of elements. Then the concrete and steel
stresses were calculated for a given strain, direction of loading (loading or
unloading). This enabled hysteresis loops to be developed for a given section.
In the current study, the maximum allowable concrete strain was limited to
0.004 for both unconfined (cover) and confined (core) concrete. This is a very
conservative approach as concrete softening would only commence at this strain
level [6].
The cross sectional details of the critical members are given in Fig. 1. The
concrete compressive strength fc = 25 MPa, Modulus of elasticity of concrete
Ec = 25,000 MPa, Yield strength of steel fy = 230 MPa, Modulus of elasticity of
steel = 200,000 MPa.
6. LOADING CONDITIONS
6.1. STRUCTURAL LOADS
As the structure is submerged in water, the buoyant weight of structuralmembers and trash screens were used for calculating the static loadings. For
dynamic analysis, actual masses were used.
6.2. HYDRODYNAMIC MASS
Hydrodynamic pressures were represented by an equivalent hydrodynamic
mass. For enclosed structures such as cylindrical/rectangular towers, it is
possible to calculate the hydrodynamic mass based on Chopras guidelines [9].
For a framed tower, the conventional practice, although conservative, would be to
assume the frame tower to be an enclosed tower circumscribed by the trash
screen slots and then use Chopras charts for inside and surrounding water,
Fig. 3. The circumferential distribution of the hydro mass was assumed to be
sinusoidal with the maximum mass on columns oriented in the earthquake
direction. Analysis results presented in this paper are for the hydro mass with the
assumption of an enclosed cylindrical tower (see Section 7.4 for a comparison
with a refined hydrodynamic mass).
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6.3. SEISMIC LOADING
A site-specific seismic assessment was undertaken by an experienced
seismologist for 100, 500 (OBE), 1,000 and 10,000 (MDE) return periods. For
each return period, three accelerograms were specified to cover a range of
seismic parameters with the recommendation to select the critical one based on
the structural analysis. The analysis results from only the critical accelerogram
are reported in this paper.
Initial analyses were carried out with concurrent horizontal and vertical
accelerograms and the results showed that the difference from the horizontal
acceleration alone is insignificant for practical purposes. This is due to the
difference in natural periods for flexural and axial responses resulting in a wide
separation of vertical and lateral response peaks.
7. ANALYSIS RESULTS
The natural periods of the structure for first five nodes were calculated and
are 1.70, 0.95, 0.50, 0.47 and 0.45 secs. For the calculation of periods, elastic
member properties were used in line with the conventional practice. The modal
shapes did not show any unfavourable torsional deformations of the structure.
7.1 ACCELERATIONS AND DISPLACEMENTS
7.1.1. Operating Basis Earthquake
The time-history of the ground accelerations associated with the critical
accelerogram is shown in Fig. 4 with its Single-Degree-Of-Freedom (SDOF)
acceleration and displacement spectra. The peak ground acceleration is .087g.
As can be seen from the displacement spectra, the fundamental period (1.70
secs) is not in a peak region of the spectral displacement.
The time-history of the tower top displacement is shown in Fig. 4d with the
maximum value of 50mm occurring at 12.5 secs. The corresponding
displacement at the bridge level is 30mm. The analysis showed no yielding of
the structural members and the tower and its foundation is stable. Therefore, the
Fig. 3
Distribution of hydrodynamic mass
Distribution des masses hydrodynamiques
0.0
0.2
0.4
0.6
0.8
1.0
0 50,000 100,000 150,000
Hydrodynamic mass (kg/m)
Heightratio
(Z/H)
Surrounding water (Eau
priphrique)
Inside water (Eau
intrieure)
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tower would return to its original static position after the earthquake (ie, no
permanent deformation).
7.1.2. Maximum Design Earthquake
The time-history of the ground acceleration associated with the critical
accelerogram is shown in Fig. 5 with the (SDOF) acceleration and displacement
spectra. The peak ground acceleration is 0.18g. The time-history of the tower
top displacement from the inelastic dynamic analysis is shown in Fig. 5d with a
maximum displacement of 190mmm at 18.5 secs.
In order to highlight the significance of the inelastic behaviour on the
predictions, the tower was analysed as an elastic structure with the same
earthquake. The maximum tower top displacement is 300mm which is a value
much higher than that given by the inelastic analysis. This can be simply
explained by looking at the displacement spectrum in Fig. 5a which shows a peak
at the structure period (=1.70 secs) followed by a trough. The increase of periodduring the inelastic cycles would reduce the displacement.
7.2. SECTION CAPACITIES AND DUCTLITIES
The moment-axial force interaction diagrams for the base column bending
about its major principal axis is shown in Fig. 6a. These values were calculated
at a maximum concrete strain equal to 0.004. (Section 5.3).
In order to understand the ductile behaviour of the structural members with
different axial loads, Fig. 6b shows two curvature ductility ratios: (1) Allowable
curvature ratio = curvature at the allowable concrete strain of 0.004 divided by
the yield curvature and (2) Ultimate curvature ratio = ultimate failure curvature thesection can sustain divided by the yield curvature. These were calculated using
the Manders model for confined concrete columns (Sections 5.2 and 5.3).
For example, the maximum curvature demand (equal to .0021) was
obtained at 18.3 secs for an axial load of 4,000 kN for Column 1 in the bottom
most level in the direction of the earthquake. The allowable curvature is equal to
0.0095 and the section is therefore satisfactory.
In order to show the improvement in the ductility with the existence of
transverse steel (ratio = 0.003 for the columns), Fig. 6c shows the moment-
curvature relationships with and without considering the confinement by the
transverse steel for an axial compressive force of 10,000 kN. As can be seen,
the transverse steel has increased the ultimate curvature (or strain) of the
columns significantly with limited degradation of the peak ultimate moment. This
highlights the need for considering the confinement from the transverse steel in
predicting the behaviour of reinforced concrete structures subject to severe
earthquakes.
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7.3. MEMBER FORCES FROM ANALYSIS
Fig. 7 shows the critical axial force and flexural moment values on columns
in the earthquake direction (note that these values would not occur at the same
time). Column 1 at the base has a maximum axial compressive force of 8,000
kN from the inelastic analysis. The corresponding axial force values from the
elastic analysis are 14,000 kN (compressive) and 8,000 kN (tensile). If an
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elastic analysis was carried out, it would have erroneously shown that the tower
is unsafe.
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7.4 SIGNIFICANCE OF HYDRODYNAMIC MASS
Section 6.2 described the conventional assumptions behind the evaluation
of the hydrodynamic mass. Hydrodynamic mass was also calculated for each
frame member considering the orientation of each member. A significant
difference of the mass was the result (60% reduction from the above cylinder
assumption) with the columns in the earthquake direction carry less
hydrodynamic mass due to their longitudinal orientation. The maximum
displacement at the top of the tower with the MDE earthquake is only 115mm
compared with 190mm from the inelastic analysis. Therefore, the conventional
assumptions would be conservative in the case of concrete framed towers.
7.5. NEED FOR TIME-HISTORY ANALYSIS
As a part of this study, three earthquake records were studied as
recommended by the seismologist. The critical one was found to be the one with
a peak ground acceleration (pga) =0.18g (note all the above results arepresented for this accelerogram). One of the other earthquakes recommended
has a pga of 0.45g. This gave a maximum tower top deflection of 60mm only
compared with 190m. Member forces were also reduced in a similar proportion.
This is due to the fact that 0.45g is a large pulse only. This comparison
highlighted: (1) the need to move away from the myth that pga alone is always
critical, (2) generic accelerograms should not be used and (3) several
earthquakes should be considered to identify the critical earthquake due to
uncertainty in earthquake data, typically for events exceeding AEPs of 1:1000.
8. CLOSURE
This study showed that inelastic time-history analysis would help
understanding the behaviour of intake towers subject to extreme earthquakes.
The energy dissipation due to the ductile hysteresis behaviour reduces the inertia
forces significantly. To estimate member responses accurately, a confined
concrete model such as that developed in this study should be used.
ACKNOWLEDGEMENTS
The Authors would like to acknowledge the NSW Department of Land and
Water Conservation for their permission to publish the paper. Thanks are alsodue to Mr Gideon Kusuma for carrying out the dynamic analyses and Ms Glennys
Hebenton for formatting the text and figures.
REFERENCES
[1] Australian National Committee on Large Dams, ANCOLD, (1998):
Guidelines for Design of Dams for Earthquakes.
[2] Chopra, A.K. and Liaw, C.Y. (1974): Earthquake Resistant Design of
Intake-Outlet Towers, Journal of Structural Division, ASCE, Vol. 101, No.
ST7, pp.1349-1366.
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[3] American Concrete Institute, ACI 307-88 (1988): Standard Practice for the
Design and Construction of Cast-in-Place Reinforced Concrete Chimneys.
[4] Park, R. and Paulay, T. (1974): Reinforced Concrete Structures, John
Wiley & Sons, pp. 769.
[5] AS3600 (1994): Concrete Structures, Standards Association of Australia.[6] Mander, J.B., Priestley, M.J.N., and Park, R. (1988): Observed Stress-
Strain Behaviour of Confined Concrete, Journal of Structural Engineering,
ASCE, Vol. 114, No. 8, Aug 1988, pp. 1827-1849.
[7] Mander, J.B., Priestley, M.J.N., and Park, R. (1988): Theoretical Stress-
Strain Model for Confined Concrete, Journal of Structural Engineering,
ASCE, Vol. 114, No. 8, Aug 1988, pp. 1804-1826.
[8] AS 1170.4 (1993): Minimum Design Loads on Structures-Earthquake
Loads, Standards Association of Australia.
[9] Goyal, A. and Chopra, A.K. (1989): Simplified Evaluation of Hydrodynamic
Mass for Intake Towers, Journal of Engineering Mechanics, Vol. 115, No.
7, July 1989, pp. 1393-1412.
[10] RUAUMOKO (2001): Computer Program to Derive Time-History
Responses of Non-Linear 3-D Framed Structures, University of
Canterbury, New Zealand.