ELASTO-PLASTIC RESPONSE OF REINFORCED CONCRETE COOLING TOWER UNDER SEVERE EARTHQUAKE MOTIONS Shiro KATO2) and Rachana HIN1) 1)

Graduate Student, Dept. of Arch and Civil Eng, Toyohashi Univ. of Technology, JAPAN

2)

Dr. Eng, Professor, Dept. of Arch and Civil Eng, Toyohashi Univ. of Technology, JAPAN E-mail: [email protected], [email protected] ABSTRACT

Although many researches have been conducted on a RC cooling tower, the earthquake response considering the effects due to material nonlinearity have not jet been broadly discussed. On the other hand, construction of cooling towers has significantly increased in countries of high seismicity. In such a case, seismic analysis on RC cooling tower is absolutely necessary. This study reports in detail the elasto-plastic nonlinear behavior of a reinforced concrete cooling tower, under cyclic loads of earthquake motion. The tower is supported at a lower lintel by columns. Based on Lattice Model for the constitutive equations for concrete, the analysis considers the effects of cracks and tension stiffening due to tension, and crash due to uni- and bi-axial compressions of concrete as well as yielding of reinforcement. The analysis is based on isoparametric shell elements modeled with 9-note Heterosis elements for shell panels and fiber elements for the circular stiffening rings at top and lower cornices, columns and footing ring. From the result of the analysis, the elasto-plastic behavior of a cooling tower under earthquake motions together with self weight is made clear and the collapse mechanism of such a structure is clearly discussed. Based on these analyses, the suggestion for designing a RC cooling tower against severe earthquake motion is drawn. KEYWORDS Reinforced Concrete Cooling Tower, Earthquake Response, Ring-Typed Lattice Model, Dynamic Analysis, Collapse Acceleration 1. INTRODUCTION Recently, reinforced concrete (abbreviated hereafter as RC) cooling towers have being built in some countries of high seismicity like Turkey, China and India to cool down the hot drain water from power plants. Many of those cooling towers, especially in these years, are becoming in large scale of over 200m tall[1]. Such cooling towers have been designed subjected to wind loads or a medium level earthquake within their service life. During and after 1975, many cooling towers of approximately 100m tall have been built[2]. As those cooling towers are under aged deterioration, there are many studies focused on retrofitting[3] but most of them are based on small size cooling tower or under monotonic loading. Hence, the stiffness degrading caused by cracks in concrete shell panel or the collapse mechanism under cyclic loading like wind load or earthquake has not jet been broadly discussed. As an extension from previous papers which focused on non-linear deformation and elastoplastic behavior under cyclic loading process of wind loads[4, 5], this paper focused mainly on rather a large scale cooling tower of approximately 160m tall under earthquake motion, and studied in detail the non-liner deformation and the elasto-plastic response under earthquake motion. In this paper, the numerical analysis is based on Finite Element Method with laminated layers, while the concrete constitutive equation is based on the concept of Ring-Typed Lattice Model[6]. As shown in the study[7], this Lattice Model can express the behavior of concrete under cyclic bi-axial stresses for shells.

2. ANALYSIS MODEL 2.1 Geometrical Shape and Material Properties A cooling tower for the present analysis, shown in Fig.1, is almost same in size as the cooling tower built in Gundremmingen. From the top, there are circular stiffening rings (abbreviated as top ring), shell, lower cornice, column and footing ring. The tower is 159.16m tall, the throat is 119.15m in height, and it has a radius of 44.6m at the top, 38.1m at throat, and 64.4m at bottom. The shape of the cooling tower is defined as follows. r = r0 + a

(H − z) 1+ T

2

Eq.(1)

b2

Top ring

B

16.0

(b) Normalized Shell Thickness z

y

22.0 70cm

34.2 55.2

(c) Column Cross Section z 50cm

A

y

Lower Cornice Footing ring

Column 128.8m

125cm (d) Top Ring Cross Section

(a) Analysis Object

z

y

200cm

z

400cm

Reinforcement

70cm

159.15m

Throat

17.5 20.5

2.0

Shell thickness [cm]

0.5

89.1m

0.5

where, r0 = 29.563m, a = 8.537m, b = 27.589m and H T = 119.15m

y

500cm (f) Footing Ring Cross Section

Note

70cm (e) Lower Cornice Cross Section

Fig.1 Structure

:Steel bar

Table.1 Material Properties

Concrete Reinforced fc [MPa] ft [MPa] Ec [GPa] σy [MPa] Es [GPa] 50cm × 125cm 33.8 Top Ring 3.38 30.2 235 206 Shell 33.8 3.38 30.2 235 206 Lower Cornies 400cm × 70cm 33.8 3.38 30.2 235 206 Dimension

70cm × 70cm

Column

33.8

3.38

30.2

235

Reinforcing Ratio 0.5% 0.3%* 0.3%

206

0.5%

Footing Ring 200cm × 500cm 33.8 3.38 30.2 235 206 0.4% * note: the ratio is common respectively to outer and inner steel layers, and total ratio of 0.6% in a section is placed, being same in the two orthogonal directions. Table.1 shows the material properties used, while the thickness of the shell is being categorized into 6 types as shown in Fig.1. 2.2 Loading Conditions 2.2.1 Self Weight There are two types of loads, one is a static load and other is an earthquake motion. For the static load, the study assumed only the self weight of the structure which can be calculated with the density of ρ = 23.5kN/m3.

1000

314

SA [cm/sec2]

Acceleration [cm/sec2]

2.2.2 Earthquake Loading The earthquake motion applied to the base of the cooling tower is the record of Elcentro-NS with an acceleration response spectrum for PFA=341cm/s2 as shown in Fig.2b. The dynamic earthquake motion was applied to the structure after quasi-static analysis for static loading (Fig.2c). The quasi-static analysis raises the static load gradually upto self weight in one second using a critical damping of 100% for natural period of T = 0.6sec., and then the load is kept constant at self weight until two second. After the quasi-static analysis, the earthquake response analysis was applied using stiffness proportional damping with a damping factor of h = 5% for natural period of T = 0.6sec.

157 0 -157

h=2% h=5% h=10% h=100%

800 600 400 200

-314 0

1

2

3

4

5

6

7

8

9

0

10

Time [sec]

1.0

1

2

Earthquake Response

2.0

3

4

Period [sec] (b) Response Spectrum Amax =341cm/s2

(a) Elcentro-NS Amax =341cm/s2 Self weight

0

(c) Loading History

12.0

Fig.2 Applied Earthquake Motion

Time [sec]

2.3 Numerical Analysis Method For the numerical analyis method, the Finite Element Method with laminated elements is applied. As a constitutive equation for concrete, Ring-Type Lattice Model were used for material properties shown in Table.2 (Reference [7] for details about Lattice Model). According to the previous study[8], the shell elements are modeled with 9-note Heterosis element, while the circular stiffening rings at the top and lower cornices, columns and footing ring are modeled with fiber elements. Furthermore, each shell element has also been divided into 8 layers through the thickness, while the reinforcing bars were replaced with reinforced sheets and were put into double layers in both the hoop and meridian directions. In the analysis, bi-linear type loading histteresis was applied to reinforcing bars for stress-strain relation. For the numerical integration, 3 × 3 Gauss integration rule was applied to the in-plane rigidity while 2 × 2 Gauss integration rule was applied to the out-plane rigidity. For the dynamic analysis, the Newmark- β Method was used, where β = 0.3025 and γ = 0.6, were applied. L t h

i d

g

c

j L

Vertical Brace V

Horizontal Brace H

b a k f

Brace B2

e

l

Brace B1 Rigid Body

Hub Strut

(b) Ring Element

(a) Rigid Body and Ring Element Fig.3 Ring-Typed Lattice Model

Table.2 Material Properties in Lattice Model Ec [MPa] 30130.36 E [MPa] 40334.44 Element Type Hub strut Horizontal Ring Vertical Brace

ν 0.16667 E r [MPa] 8066.92 σc[MPa] -0.632 -6.324 -0.000 -6.324

σt MPa] 0. 563 0.499 0.676 0.128

fc [MPa] -33.8 H E r [MPa] 7151.79

εc

-0.003 -0.003 -0.001

ft [MPa] 3.38 BV Er [MPa] 7321.07 R ε cr -0.010 0.2 -0.010 0.2 -0.002 0.2 -0.003 0.2

ε0 -0.002 φ [deg] 60.0

α

β

0.1 0.5 0.0 2.0

2.0 2.0 0.0 2.0

Λ 0.4 0.0 0.4 0.8

3. RESULTS 3.1 Non-linear behavior under self weight 3.1.1 Response of Shell

Height [m]

Loading Factor λs [-]

Initial form

(a) Deformation mode

A

x Nm

Nh

Nh

notes

Nm

Height [m]

B

z

8 Reinforcement yielded wB wA

6 4 2 0

Self weight

-8

160 140 120 100 80 60 40 20 0 -800

-7

-6

-5

-4 -3 -2 -1 0 Vertical Displacement [cm] (b) Load-Displacement

Nm -600

Nh -400

-200 0 Axial Force [kN/m]

(c) Internal Forces (for Self Weight) 160 140 120 100 80 60 Nm Nh 40 20 0 -6000 -5000 -4000 -3000 -2000 -1000 0 Axial Force [kN/m] (d) Internal Forces (for Ultimate Loading)

Fig.4 Cooling Tower under Self weight Fig.4a represents the deformation mode of the cooling tower under static loading. Fig.4b represents the Load-Displacement relations of point A at lower cornice and point B at top ring. Fig.4c and 4d represent the internal forces along the height of cooling tower, respectively, for self weight loading ( λs = 1.0) and for ultimate loading ( λs = 7.9). According to the deformation mode of the cooling tower (Fig.4a), columns significantly deform compared to the shell. The load-displacement relationships are obviously shown in Fig.4b, while the dispalcement ratio at lower cornice is 0.18% (=2.2/1200), being large compared to that at top ring is 0.05% (=7.9/15915). The characteristics of the deformation are also shown almost linear for any loading level but gradually becomes non-linear afterward until the loading reached ultimate at λs = 7.9 (time to self weight). The axial forces for self weight loading (Fig.4c) show virtually proportinal in distribution to but different in intensity from the axial forces for ultimate loading (Fig.4d).

3.1.2 Rsponses of Column and Ring C4

0.5

C3 C2 C1 C1: Footing Ring C2: Column C3: Lower Cornice C4: Top Ring

Mz z

y

My

Qz Q y N x

N, M x

Qz , M z

Qy , M y

notes

-1.5 0

Lower cornice 0

1

2

3

2

3

4 5 6 7 8 Load Factor λs [-] (a) Axial Force N

Lower cornice 0

1

2

3

4 5 6 7 8 Load Factor λs [-] (b) Twisting Moment M x

-20.0 -40.0 -60.0

Lower cornice

-80.0 0

4 5 6 7 8 Load Factor λs [-]

(c) Shear Force Qy M [×10 kN･m]

0.0 -1000.0

1

4 5 6 7 8 Load Factor λs [-] (d) Bending Moment M y

-2000.0

Lower cornice

-3000.0 0

1

2

3

2

3

3.0 2.0

Lower cornice

2

Q [kN]

1

0.0

M [×102 kN･m]

Q [kN]

-1.0

100.0 0.0 -100.0 -200.0 -300.0 -400.0 -500.0

C2 C3 C4

0.0 -20.0 -40.0 -60.0 -80.0 -100.0

-0.5

-2.0

M[kN･m]

x

0.0

N [×104 kN]

z

1.0 0.0

4 5 6 7 8 Load Factor λs [-]

0

1

2

3

4 5 6 7 8 Load Factor λs [-]

(f) Bending Moment M z

(e) Shear Force Qz

Ultimate strength Load intensity for column yielded

0

1

2

3

4

5

6

(g) Failure progress

Fig.5 Cooling Tower under Self weight

7 8 Load Factor λs [-]

Fig.5a and 5b show respectively load factor-axial force and load factor-twisting moment relations for the columns, lower cornice and top ring. The figures show that either the axial forces or the twisting moments of the above members remain linear for the whole loading process. Differrent from the axial force of the top ring which is tensile force (+), the axial forces of column at lower cornice are compressive forces (-). Focusing on twisting moments, we can say that the lower cornice gets twisted according to discontinuous deformation between columns and shells. Fig.5c to Fig.5f show, for different load levels, shear forces in the Y-axis direction, bending moments around Y-axis, shear forces in the Z-axis direction, and bending moments around Zaxis, respectively for top ring, lower cornice and columns. With respect to the shear force of lower cornice in the Z-axis direction, the stress is relatively large at ultimate load level, and this shear is due to the concentrated forces from columns. Since the sectional area of the lower cornice is now assumed as 400cm by 70cm, the shear stress is considered under allowable stress. However, the axial force becomes so large at the ultimate level for the columns with a section of 70cm by 70 cm. Accordingly, the ultimate state is judged to be determined by the ultimate strength of column compression. At the load level of λ = 6.9, the columns start yielding of concrete, and the cooling tower reaches its ultimate strength at the load with load factor of λul = 7.9, in other words, the tower can resist about eight times the self weight.

Height [m]

Displacement [cm]

3.2 Earthquake Response 3.2.1 Elasto-Plastic Behavior

(a) Deformation mode

A

x Nm

Nh Nh

notes

Nm

Height [m]

B

z

3 2 1 0 -1 -2 -3

Point B

Point A 0

2

4

6

8

10 12 Time t [sec]

(b) Displacement 160 140 120 100 80 60 Nm Nh 40 20 0 -800 -700 -600 -500 -400 -300 -200 -100 0 100 Axial Force [kN/m] (c) Internal Force (at t = 2.0sec.) 160 140 120 100 80 60 Nm Nh 40 20 0 -1200 -1000 -800 -600 -400 -200 0 200 Axial Force [kN/m] (d) Internal Force (at t = 6.6sec.)

Fig.6 Cooling Tower under Amax = 300cm/s2

Fig.6a represents the deformation mode of the cooling tower subjected to earthquake motions of ground peak acceleration of Amax = 300cm/s2. Fig.6b represents the time histories of horizomtal displacements at point A of lower cornice and point B of top ring. Fig.6c and 6d represent the internal forces along the height of cooling tower respectively at t = 2.0s for self weight loading and at t = 7.1s during earthquake motions for the instance where the displacement grows the largest. The time histories of two displacements of point A and point B, being almost the same, gives us an understanding that the upper part of the cooling tower (from lower cornice to top ring) sways horizontally like a rigid body bonded to the columns. The internal forces of the cooling tower by quasi-static analysis under self weight (Fig.6c) and the internal forces under the ground acceleration of Amax = 300cm/sec2 at the instance for peak (Fig.6d) show almost the same characteristic but slightly different in intensity. The internal forces for this intensity is not so large for the cooling tower and the behavior still presents linear behavior. In other word, the cooling tower remaines safe with no damaged under the ground acceleration of Amax = 300cm/s2.

Acceleration [cm/s2] 0

40 30 20 10 0 -10 -20 -30

2

8 10 12 Time t [sec] (a) Displacement Response

0

2

4

8 10 12 Time t [sec] (b) Velocity Response

z

4

6

6

y x

x

notes

Acceleration [cm/s2.s]

3 2 1 0 -1 -2 -3

Acceleration [cm/s2]

Velocity [cm/s]

Displacement [cm]

3.2.2 Response Characteristic 500 400 300 200 100 0 -100 -200 -300 -400

0

2

4

6

8 10 12 Time t [sec] (c) Acceleration Response

30 25 20 15 10 5 0

0 2 4 6 8 10 12 14 16 18 20 Frequency f [Hz] (d) FFT Spectrum for Acceleration Response 500 400 300 200 100 0 -100 -200 -300 -400

0 1 2 3 4 5 6 7 8 9 10 11 12 Time t [sec] (e) FFT, f = 10.0Hz for (c)

Fig.7 Earthquake Response at throat ( Amax = 300cm/s2) Fig.7a to 7e show, at the throat level, the responses of displacement, velocity, absolute acceleration, Fourier spectrum for absolute acceleration response, and absolute acceleration response filtered by using a low-pass filter of f = 10.0Hz. The intensity of PGA is

2 Amax = 300cm/s . Compared with the displacement response at lower cornice and at top ring (Fig.6b) the displacement response at throat (Fig.7a) also shows the same characteristic as described in 3.2.1. For the absolute acceleration response (Fig.7c), the time history of acceleration directly obtained from numerical integration includes so high frequencies due to a discontinuity, and this irregularity in acceleration can be eliminated succesfully by using the FFT with low-passe filter of f = 10.0Hz (Fig.7e). This kind of filter is judged permissible, since the dominant response is around 2.0Hz for velocity and displacement.

Displacement [cm]

10 5 0 -5 -10 -15 0

2

4

8 10 12 Time t [sec] (a) Lower Cornice at point a

(c)

z

y x

(b)

x

(a) notes

10 5 0 -5

-10

6

Displacement [cm]

Displacement [cm]

3.2.3 Collapse Acceleration

0

2

4

8 10 12 Time t [sec] (b) Throat at point b

10 5 0 -5 -10 -15

6

850gal 900gal 0

2

2

300 900cm/s . Ground Acceleration

4

6

8

10

12

Time t [sec] (c) Top Ring at poin c

Fig.8 Collapse Acceleration Fig.8 shows the relationships between ground acceleration Amax (cm/s2) varied from 300 to 900cm/s2. and the time history displacements, respectively at lower cornice (Fig.8a), at throat (Fig.8b) and at top ring (Fig.8c). Macroscopically, the displacement at lower cornice features a large deformation compared to those at throat and at top ring. As for the displacement at lower cornice and at throat, the figures show that the deformation grow larger simultaneously to the applied ground acceleration. Furthermore, the time histories of displacements at cornice revel and at throat look almost same for low PGA with a tendency that the natural period of oscillation is almost same. Even if the intensity of PGA grows over 850cm/s2, the displacements at thoat remain rather moderate, on the other hand, the displacement at top ring grows very large if the applied PGA becomes beyond 900cm/s2. From this observation, we could assume that the elements at lower cornice and at throat are still in good condition. However, for the displacement at top ring (Fig.8c), the response stays stable for PGA less than 850cm/s2 and became unstable for PGA over 850cm/s2. Fig.8c shows that the displacement under Amax = 900 cm/s2 became unstable from t = 7.5s acompanied with growing of residual displacement. This behavior shows that the cooling tower reaches its maximum bearing capacity at the collapse acceleration of Amax = 850cm/s2. Here the details of reinforcement and concrete under ground peak acceleration of Amax = 900 cm/s2 is not shown, but analysis shows that, crack occurred in column at t =3.3sec, reinforcing bars of column yielded at t =7.4s and crack occurred in shell panels at t =8.2s.

3.2.4 Pre- and Post- Collapse Acceration 5.93cm z (2)

(3)

(1)

21.32cm

(3)

y

x

(3)

(2)

(1)

(2)

(1)

x Deformed Original

notes

3.79cm

16.78cm

(a) at-collapse ( Amax = 850cm/s ) 2

(b) Post-collapse ( Amax = 900cm/s2)

Fig.9 Deformation (5000%) Fig.9a and 9b show respectively the deformation of lower cornice, throat and top ring at precollapse and at post-collapse acceleration. The numbers of (1), (2) and (3) show respectively the position of the lower cornice, throat and top ring. As described in the previous section, before collapse acceleration, the cooling tower deforms in stable due to effective restoring forces. At collapse acceleration of Amax = 850cm/s2, the maximum deformation is detected a displacement of δ = 5.93cm(Fig.9a) at lower cornice. But at post-collapse acceleration of Amax = 900cm/s2, the deformation notably grows up with the maximum displacement δ max = 21.32cm at lower cornice and δ max = 16.78cm at top ring. The figure also shows that the lower cornice, shell and top ring deform in the second and third Fourier modes in the circumferential direction, which means the appearance of bending moments in the lower cornice, shell and top ring. As stated in the upper chapter, at the collapse acceleration, the column reaches its ultimate state, and the residual deformation becomes greater and is acompanied with the second and third Fourier modes deformation. This kind of deformation characteristics becomes dominant at and after the collapse acceleration. 4. CONCLUSION

The elasto-plastic earthquake response of a cooling tower under dynamic analysis was performed using Elcentro-NS observed record as input earthquake motion. Based on the results shown in the present study, following conclusions were drawn. In the study for a analytical method, Ring-Typed Lattice Model as constitutive equation for concrete and Newmark- β method for the solution of the dynamic analysis were applied. ① Under a vertical loading proportional to the selfweight, the cooling tower reaches its ultimate strength at loading factor λul = 7.9 times its self weight. And the cooling tower reached its ultimate strength while the column reached its compresive strength. ② The cooling tower studied in the present study can stand with the ground acceleration of up to Amax = 850cm/s2 (Elcentro-NS). ③ Different from the static collapse under a vertical load proportional to the selfweight, the dynamic analysis shows that the structure reached the collapse of the columns due to cracking and yielding, accompanied with cracking and yielding at the lower cornice and shell. ④ Under the earthquake response, the noises formed in the acceleration response can be eliminated succsessively by using a low-pass filter. In this study the lower-pass filter of f = 10.0Hz, was applied to eliminate the noises.

REFERENCES

[1] Udo Wittek : A first step to a documentation of the structural heritage of RC Cooling Towers, NATURAL DRAUGHT COOLING TOWERS, Proceedings of the 5th International Symposium on Natural Draught Cooling Towers, Istanbul, Turkey, pp.31-34, 2004 [2] R Engelfried : Surface protection measures for cooling tower shells for REA operations: Concept and process surveillance for retrofitting and new constructions, Proceedings of the 4th International Symposium on Natural Draught Cooling Towers, Kaiserslautern, Germany, pp.199-206, 1996 [3] P. B. Bosmann, I. G. Strickland and R. P. Prukl : Strengthening of natural draught cooling tower shells with stiffening rings, Proceedings of the 4th International Symposium on Natural Draught Cooling Towers, Kaiserslautern, Germany, pp.293-301, 1996 [4] T. Hara, S. Kato and M. Ohya : Ring Stiffened Cooling Tower Behavior subjected to Cyclic Wind Loading, Proceedings of IASS Symposium 2002, Istanbul, pp.407-416, 2002 [5] M.Ohya, S.Kato, S.Shimaoka, T.Hara: Finite element analysis of reinforced concrete cooling tower under cyclic loading, National Draught Cooling Towers, Mungan & Wittek(eds) 2004 Taylor & Francis Group, London, pp.227-235 [6] S. Kato, M. Ohya and T. Hara : Finite Element Analysis of Reinforced Concrete Shells under Cyclic Loading, Journal of IASS, Vol. 43, n.1, pp.23-40, 2002 [7] M Ohya, S Kato, S Shimaoka, T Hara : Finite Element Analysis of reinforced concrete cooling tower under cyclic load; Natural Draught Cooling Towers Mungan & Wittek, London, pp.227-235, 2004 [8] T. Hara, S. Kato and H. Nakamura : Ultimate strength of RC cooling tower shells subjected to wind load”, Engineering Structures Vol.16, No.3, pp.171-180, 1994