Burr End Ong

7/27/2019 Burr End Ong

1/12

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


2/12

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.


3/12

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.


4/12


5/12

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


6/12

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).


7/12

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)


8/12

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.


9/12

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


10/12

elastic analysis was carried out, it would have erroneously shown that the tower

is unsafe.


11/12

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.


12/12

[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.

Burr End Ong

Documents

Transcript of Burr End Ong