The design of cooling towers in extremely severe earthquake conditions

The design of cooling towers in extremely severe earthquake conditions Th Castiau and R Gaurois* Abstract - This p a p e r summarizes the experience gained in the design of the Ohaaki cooling tower in New Zealand. The design was governed by the strong seismicity of the site, and unusually complex step-by-step calculations including large displacements, uplift and sliding of the foundations were performed. The analysis showed the low-energy dissipation in the plastic range offered by the diagonal supports, despite some modification of the initial design, such as the use of mild steel reinforcement in the supports. A comparison between the actual design and alternative designs for the supporting structure is also given.

As New Zealand is exposed to very strong earthquakes, the cooling towers of a thermal p o w e r plant have to be designed to withstand severe seismic events. New Zealand Standard 4203 contains advanced design methods to provide adequate protection against such events. This standard is based on the ductile capability of the structure, giving rise to large deformations. Usual buildings can be designed by simple rules given in the standard, but special structures such as a cooling tower need a specific study to prove their ductile capability. This means the use of an analysis including material (inelastic) and geometric (large displacements) non-linearities and a dynamic time history analysis. Both involve high computational costs and require a design/analysis/redesign iterative process as the components of the structure need to be fully detailed before the input parameters can be specified. The input parameters for the cooling tower were estimated initially using a high wind loading so that the primary design would not be greatly altered. The design basis, a minor earthquake under which the structure has to remain fully elastic, was carried out with an elastic response analysis and served as a guide to choosing the input parameters for the non-linear analysis. The dynamic analysis was performed in three steps. The first step was carried out in the elastic domain for the minor design earthquake for comparison with the classical response analysis and to find the eigenfrequency spectra of the cooling tower. The second step was carried out for a high seismic attack taking into account material non-linearities. The final step contained, in addition to the second step, geometric non-linearities.

*Hamon-Sobelco SA, rue Capouillet, 50-58, 1060 Brussels, Belgium CONSTRUCTION & BUILDING MATERIALS VoI. 6 No. 4 1992

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Descriptionof the tower Located near Reporoa in the Central North Island, New Zealand, the Ohaaki t o w e r is 105 m high, with a base diameter of 71.5 m. The shell is supported on 600 mm 2 precast concrete columns which in turn rest on a ring beam 4 m wide by 1.3 m deep. The main dimensions of the t o w e r are shown in Fig 1. The ring beam is placed over a backfilled trench with a minimum base dimension of 6.5 m and extends down to the bedrock some 3 to 8 m below the ring beam. The backfill materials are mainly reconstituted, compacted inplace site material. The diagonals are reinforced with mild steel grade bars (12 ,~ 24 ram) in order to increase ductility. Full shear resistance is obtained by unusually strong stirrups to meet special NZ requirements for capacity design (Fig 2). The material quantities for the Ohaaki tower are listed in Table 1.

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Table 1 Material quantities

Shell Diagonals Pedestals Ring beam

Concrete (m3)

Steel ratio (in t/m3)

3265 155 95 1170

0.140 0.335 0.135 0.110

0950 - 0618/92/040239 - 07 (~ 1992 Butterworth-Heinemann Ltd

239

The design of cooling towers in extremely severe earthquake conditions

Philosophy of the New Zealand standard Every building should be designed and constructed to withstand a total horizontal seismic force (V) in each direction under consideration in accordance with the following formula V=

C.I.S.M.R. Wt

where C / S M R Wt

seismic zone class of buildings (ambulance centres, post offices, etc) ductility of the structure type of material risk factor total reduced gravity load

Apart from S, all the factors were given in the job specifications, ie C = / = M = R=

0.15 1.3 1.0 (reinforced concrete) 1.0

Since only unidirectional horizontal loads are being considered a further concurrency factor of 1.1 is to be used. As the ductile capabilities of the cooling tower were unknown, the factor S could not be specified. As a consequence, a special study based on capacity design principles had to be performed. In the capacity design of earthquake-resistant structures, the elements of the structure should be proportioned so that a rational yielding hierarchy of the primary structural system provides an appropriate level of energy dissipation under severe deformation. The hierarchy is required because the structure should be designed to fail in a controlled manner under overload conditions. A severe deformation is defined as a value of the ductile capability factor p. = A y / A u > 4. Ay is the deformation of the structure due to a loading originating yielding and Au is the total deformation in the elastic and plastic domain. The structure does not have to withstand a loading corresponding to a value of S greater than 5. The chosen energy dissipation elements (primary elements) have to be suitably designed and detailed for ductile behaviour and all other structural elements (secondary elements) should be provided with sufficient reserve strength to ensure that the energy dissipation system is sustained. Thus for the capacity design, the cooling tower was divided into two parts •

the primary elements represented by the diagonals supporting the shell and designed for ductility demands, the secondary elements represented by the ring beam foundation and the shell designed to remain elastic under severe deformation.

•

As a consequence, the former philosophy calls for a time history analysis including inelastic material behaviour, geometric non-linearities (large displacements), and uplifting and sliding capabilities of the foundation. The maximum seismic horizontal attack, taking S = 5, is 0.15g × 1.3 × 1.0 × 1.0 x 1.1 x 5 = 1.07g (peak spectral acceleration)

Z

x

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y

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The 'special study' The 'special study' specification calls for a time history (stepby-step analysis), including a realistic model of the tower, and a realistic ground acceleration history. The study was carried out by Electrowatt Engineering Services, ZLirich, using the ANSYS general purpose finite element program. It took approximately 150 h of computer time. The first analysis, performed in a fully linear elastic run with an excitation of 30% of the design earthquake, was used to check the validity of the tower model. Since the predicted displacements were comparable with the results from typical modal response analysis, the model was then modified to include both material and geometric non-linearities in the columns and uplift of the foundation whenever required, and a full non-linear dynamic analysis was performed. Finally, the non-linear dynamic analysis was carried out taking into account the material non-linearities included in the second run and geometric non-linearities (large displacements).

The maximum seismic vertical attack is 0.15g x 1.3 × 1.0 × 1.0 × 5 = 0.49g 2 (A concurrency factor of 1.1 is not needed for the vertical attack.) 240

Model L i n e a r m o d e l (see Fig 3) A half model of the tower was developed, for symmetrical reasons (and because ground motion is supposed to apply to the whole foundation simultaneously).

CONSTRUCTION & BUILDING MATERIALS Vol. 6 No. 4 1992

Th Castiau and R Gaurois

Ill

Gap

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Elastic- plastic spar (steel) I

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Ideal strength

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2000 Columns

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4o00

Foundations (7.0 x 4.0 m 2 strip)

LL

Vertical stiffness kv = 6.1 x 106 kN/m Horizontal stiffness kH = 4.4 × 106 kN/m Rocking stiffness about tangential axis k s = 1.89 x 10, kN m/rad Radiation d a m p i n g ~R = 0 Coefficient of friction (0 = 40 °) H = 0.84

5000

8000 8400

E = 2.78 x 107 kN/m 2 p = 2.4 t/m 3 v = 0.167

Material damping (Rayleigh damping)

Ductility limit For the w h o l e structure ~h = 5%

Fig 5

Column force-strain curve

The shell is represented by 13 rings of q u a d r a n g u l a r (or d e g e n e r a t e d triangular) flat plate elements. Along the circumference, one e l e m e n t covers a m a x i m u m angle of 15°. The ring beam, pedestals and columns are the usual beam elements, w h i l e the soil stiffness is m o d e l l e d by distributed springs along the ring beam. The material and spring characteristics are listed below. Shell and ring beam

Young's modulus

E = 2.57 x 107 kN/m 2

CONSTRUCTION & BUILDING MATERIALS Vol. 6 No. 4 1992

It should be noted that to take the stiffness reduction due to the cracking of concrete into account, the cross m o m e n t of inertia of the column elements is reduced to 75% of its geometric value. Non-linear model The s e c o n d a r y 'elements' (shell, ring beam) remain unaltered, but the c o l u m n model now includes tension cut-off and plastic hinges in the concrete, and elastic plastic b e h a v i o u r of the reinforcement (Fig 4). The steel is represented by a spar element, having the s a m e a r e a (12 .(~ 24 mm, say 54.3 cm2). In tension, a c o m p o site action of the steel and the cracked concrete is assumed,

241

The design of cooling towers in extremely severe earthquake conditions

Rod (steel)

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Design spectrum for 5% damping

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Time histories C O N S T R U C T I O N & BUILDING M A T E R I A L S Vol. 6 No. 4 1992

Th Castiau and R Gaurois Table 3

Extreme values of displacements and forces Non-linear

Extreme values Foundation radial displacement Shell radial top displacement Shell radial bottom displacement Shell middle meridional tension Shell middle meridional compression Shell middle radial tension Shell middle radial compression Tension in columns Compression in columns Plastic deformation Normal force in foundation ring beam Bending moment in foundation ring beam Soil reaction Uplift Sliding

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Material

0.3 53.4 4.8 617 989 46 125 2672 4873 1484 1154 5198 -

27.7 82.7 39.6 529 933 77 164 1717 5395 0.20 x 10 4 6034 8534 5253 14 27

Material and geometric 23.7 79.0 35.2 526 934 82 160 1720 5463 0.52 x 10 4 5816 8593 5268 14 24

Gap stiffness kG = 1.50 x 106), Beam stiffness kB 1.55 x 107) Rod stiffness kR A x i a l stiffness of system Actual stiffness a c c o r d i n g to Fig 5 #

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l e a d i n g to a t e n s i l e stiffness of n e a r l y 2 0 % of the c o m p r e s sive stiffness (Fig 5). Y o u n g ' s m o d u l u s of the s p a r is therefore a d j u s t e d to c o r r e s p o n d with the l o a d - s t r a i n d i a g r a m (say, Espar = 3.91 x 108 kN/m2). It should be noted that the main r e i n f o r c e m e n t is mild steel, with a c h a r a c t e r i s t i c y i e l d strength Fy = 275 MPa. H o w e v e r , to a v o i d o v e r e s t i m a t i n g the ductility, a m o r e realistic s t r e n g t h of ,~Fy = 1.15 x 275 = 316 MPa is used. (The p r o b a b l e strength is c o m p a r e d with the ideal strength in Fig

6.) The c o n c r e t e is m o d e l l e d as follows: at the top and bottom of the column, a plastic h i n g e is used to limit the b e n d i n g m o m e n t transmitted to the shell and to the ring beam. The m a x i m u m m o m e n t is set at 750 kN m for the t h r e e rotations. The c r o s s m o m e n t of inertia of the elastic b e a m e l e m e n t s CONSTRUCTION & BUILDING MATERIALS Vol. 6 No. 4 1992

1.37 x 108 3.29 x 105 1.70 x 10~ 1.63 x 10e

The effects of uplift and slip of the f o u n d a t i o n a r e m o d e l l e d by g a p e l e m e n t s which are put b e t w e e n the nodes of the ring b e a m and the t h r e e translational soil springs. A spring stiffness has to be d e f i n e d for the g a p e l e m e n t s which is the s a m e in the vertical and horizontal direction. T o g e t h e r with the soil s p r i n g s they form a series of two springs. In o r d e r to a v o i d n u m e r i c a l p r o b l e m s the g a p stiffness was m a d e small and the soil s p r i n g stiffness l a r g e so that the p r o p e r foundation stiffness is a c h i e v e d for both stiffnesses in series. The stiffnesses g i v e n for a foundation strip of 3.5 m (area 3.5 x 4 m 2) are as f o l l o w s (in kN/m) Gap

5

Fig 10

(kN} (kN m) (kN) (ram) (mm)

b e t w e e n these hinges is reduced to 60% of its uncracked value. Finally, a g a p e l e m e n t is placed at the top of the column; it disconnects the c o l u m n from the shell w h e n tension occurs. M o m e n t s and s h e a r s remain fully transmitted. The resulting a x i a l stiffness of the c o m b i n e d b e a m and g a p e l e m e n t s is s e l e c t e d to c o r r e s p o n d to Fig 5. The resulting stiffness in c o m p r e s s i o n is (kN/m)

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1~2

3,4

(mm) (mm) (mm) (kN) (kN) (kN) (kN) (kN) (kN)

Soil spring

Resulting stiffness

Horizontal 3.05 x 10e

7.0 x 107

2.12 x 10~

(2.20 x 10e)

Vertical 3.05 x 106

3.5 x 107

2.8 x 106

(3.05 x 106)

The stiffnesses achieved are a p p r o x i m a t e l y 4 to 8 % smaller than the specified ones, indicated in brackets. The behaviour of the model columns for two load cycles is shown in Fig 7. For the ring beam the mass is lumped at the nodes (ie zero density for the beam elements) to model the soil-ring beam interaction more realistically as c o m p a r e d with the linear model where a consistent mass matrix was used. The bending stiffness is reduced to 65%. Earthquake excitation The basis for the earthquake motion is the design spectrum defined by the code NZS 4203. For the non-linear calculations carried out here, the motion has to be specified in terms of a time history. In o r d e r to obtain a meaningful acceleration time history, the standard USNRC Reg. Guide 1.60 spectrum, which is used worldwide, is scaled to the m a x i m u m acceleration of 1.07g of

243

The design of cooling towers in extremely severe earthquake conditions

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Radial deflection of the shell on various support geometries (modal analysis with RMS superposition) Table 4

Results of modal response analysis

1 First axial frequency(Hz) First bendingfrequency(Hz) Top deflection (cm) Vertical shear force (MN) Horizontalshear force (MN)

2

3

761 717 766 268 2.52 2.64 582 6.76 6.23 11.73 1240 1168 4954 5273 54.65

4

5

7.25 2.38 6.75 12.32 63.35

7.96 2.71 6.13 11.54 60.06

the NSZ spectrum at the frequency of the first mode of the first harmonic (2.75 Hz). The acceleration at 33 Hz is adjusted to the ground acceleration of 0.46g. Between this point and the control frequency of 9 Hz the accelerations are linearly interpolated on the log scale. The resulting spectrum is given in Table 2. The damping value is 5%. The spectrum is plotted in Fig 8. Two artificial time histories are generated such that their spectrum matches the design spectrum within a range of + 10%. After a check in a linear run, a unique time history was finally selected for the non-linear analysis (Fig 9).

Analytical procedure The ANSYS general purpose program was used for the analysis. The linear and non-linear transient dynamic options are used. The degrees of freedom of the linear elastic shell are not reduced in view of the geometric non-linear analysis. The integration time step of the step-by-step procedure is 0.01 s leading to a total of 3000 time steps in the linear elastic analysis. In the non-linear analysis, a smaller time step, ie 0.005 s, was used during the time interval where the largest response occurs; this was done to improve convergence. The integration procedure reformulates the stiffness matrix for each time step in the non-linear run. No iterations were carried out. The dynamic system is damped by a Rayleigh-type damping, ie stiffness and mass proportional damping

Damping D = ~z/(2*e)) + 13,~o/2 244

A damping of 5% at the reference frequencies of 1 Hz and 5 Hz is chosen leading to ~ = 0.542 and 13 = 0.00265. The damping around the fundamental frequency is about 4% (minimum). To perform a seismic analysis with ANSYS a large mass equal to 10 000 times the total mass of the structure is placed in the centre of the tower at the foundation level. All soil springs are connected to this mass. The time history is applied to this mass as a force leading to the corresponding acceleration. The large mass is held in place by a set of very soft springs. Extreme values for the displacements and forces are given in Table 3.

Results The main reinforcement of a few columns yielded slightly but there was no noticeable plastic hinge formation at the top and bottom. This means that the value of the capacity factor p is close to 1 and therefore those primary elements did not dissipate any energy as expected. In fact, the cooling tower structure has shown a quasi-elastic response under the overloaded seismic attack. As a consequence, the amount of steel in the secondary elements (foundation ring beam and shell), which had to remain elastic, had to be increased substantially in comparison with the quantities needed to sustain the basic design earthquake. We concluded that the columns, representing only 3% of the total mass of the structure, are not adequate as primary elements because other parts of the structure are becoming plastic before they do. Moreover, the columns could suffer a brittle failure under high compression loads before they enter the plasticity domain in tension. Finally, we think that the classical elastic design method, taking into account the uplifting of the foundations, remains adequate for the design of a cooling tower. As it was designed for New Zealand conditions, the structural factor S f o r the cooling tower should be taken to be equal to 5. The top of the shell moved about 80 mm, say only 55% more than the predicted elastic response. The expected ductility CONSTRUCTION & BUILDING MATERIALS Vol. 6 No. 4 1992

Th Castiau and R Gaurois

mechanism was overshadowed by the large lift-off and sliding of the ring beam, nearly 15 and 24 mm respectively, spread over a 140° sector during the strongest ground acceleration. Because of lift-off and sliding, the cooling tower did not recover its original position and shape. The ring beam remains ovalized, and strains and stresses were caught in the structure. It is also important to note that the results of the material nonlinear run and of the geometric and material non-linear run do not differ much. This means that large displacement effects are of minor importance for the size of the tower, soil conditions and earthquake considered here. The allowable compression stresses in both the soil and columns were not exceeded. The analysis has confirmed that the assumed member sizes were adequately designed.

Conclusions Due to the large uplift effect, the inelastic demand on the diagonals remained small. This can also be checked a posteriori by a statical calculation of the tower taking uplifting of the foundation into account. We have performed such a check under dead load and earthquake equivalent forces corresponding to the first mode responses of a linear spectrum analysis. Though this calculation does not stand up to rigorous discussion, it already gives surprisingly accurate stress and displacement predictions, with a lifted zone of nearly 160° and maximum tensile forces in the column equal to the yield strength of the reinforcement ( ± 1800 kN). So it was predictable that no significant ductility mechanism could develop in the supporting structure, which represents, as stated, 3.3% of the total material quantity. Clearly this result is restricted to towers with direct foundations: a pile foundation with a large friction resistance against uplift would significantly influence inelastic demand in the base. One may also consider whether another type of support would modify the dynamic behaviour of the tower. To give a preliminary response, five different supports are compared (Fig 10) in a linear calculation. 1 2

The actual diagonals chosen for Ohaaki. An alternative using considerably weaker circular diagonals with the same geometry.

CONSTRUCTION & BUILDING MATERIALS Vol. 6 No. 4 1992

3 4 5

Diagonal supports of the same section (0.6 x 0.6 m2), but with equal division of the lintel beam. The same but with circular diagonals of 50 cm diameter. Meridional supports like those for the latest EdFtowers.

All these towers rest on the same foundations. The last one, on meridional supports, is slightly heavier than the previous ones (thicker lower edge). The radial deflection is shown in Fig 11. Table 4 summarizes the principal results of the modal response analysis. It is obvious from Table 4 that even if the less steeply inclined diagonals and the meridional supports give very similar frequencies, the earthquake SRSS response is nearly 10 to 20% greater than with the original support. So, even before starting a ductility study of the other supports, we are obliged to admit that they are less competitive with respect to smaller and more probable earthquakes: it is not desirable that they yield plastically. The solution consisting of selecting 'soft' supports to improve ductility for major earthquakes is also impractical. Obviously, we cannot give general rules from a single example, since the soil stiffness and the influence of a pile foundation would probably modify the analysis significantly. But we can suggest preliminary conclusions about the difficulty of providing adequate ductility to this kind of structure. Clearly, ductility factors, as introduced in several recent regulations to take post-elastic behaviour into account, need to be carefully selected when assessing cooling tower responses to earthquakes. A conservative approach seems necessary, until other analyses are performed.

Acknowledgements The authors thank Dr J Wolf and Mr B~cher of Electrowatt Engineering for their work on the Ohaaki project. This paper was first published in Engineering Structures, 13, January, 1991, 13-20.

References A comprehensive description of the new regulation philosophy can be found in the various NZ standards: NZS 4203. General structural design and design Ioadings for buildings, 1976 NZS 3103. The design of concrete structures (code of practice plus commentary), 1983

245