NPP planning based on analysis of ground vibration caused by collapse of large-scale cooling towers

Nuclear Engineering and Design 295 (2015) 27–39

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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

NPP planning based on analysis of ground vibration caused by collapse of large-scale cooling towers Feng Lin a , Hongkui Ji a , Xianglin Gu a,∗ , Yi Li a , Mingreng Wang b , Tao Lin b a b

Department of Structural Engineering, Tongji University, No. 1239 Siping Road, Shanghai 200092, China East China Electric Power Design Institute Co., Ltd, No. 409 Wuning Road, Shanghai 200063, China

h i g h l i g h t s • New recommendations for NPP planning were addressed taking into account collapse-induced ground vibration. • Critical factors influencing the collapse-induced ground vibration were investigated. • Comprehensive approach was presented to describe the initiation and propagation of collapse-induced disaster.

a r t i c l e

i n f o

Article history: Received 13 March 2015 Received in revised form 11 August 2015 Accepted 15 August 2015 Available online 18 October 2015

a b s t r a c t Ground vibration induced by collapse of large-scale cooling towers can detrimentally influence the safe operation of adjacent nuclear-related facilities. To prevent and mitigate these hazards, new planning methods for nuclear power plants (NPPs) were studied considering the influence of these hazards. First, a “cooling tower-soil” model was developed, verified, and used as a numerical means to investigate ground vibration. Afterwards, five critical factors influencing collapse-induced ground vibration were analyzed in-depth. These influencing factors included the height and weight of the towers, accidental loads, soil properties, overlying soil, and isolation trench. Finally, recommendations relating to the control and mitigation of collapse-induced ground vibration in NPP planning were proposed, which addressed five issues, i.e., appropriate spacing between a cooling tower and the nuclear island, control of collapse modes, sitting of a cooling tower and the nuclear island, application of vibration reduction techniques, and the influence of tower collapse on surroundings. © 2015 Elsevier B.V. All rights reserved.

1. Introduction China has been planning to build new nuclear power plants (NPPs) inland to meet the fast-growing domestic energy demand. Consequently, larger-scale cooling towers are to be constructed to meet NPP technological requirements. These towers have been designed to stand more than 200 m high, probably the highest planned ones worldwide (Busch et al., 2002), with typical spacing of about 300 m to the adjacent nuclear island. This is partly due to strict regulations on land utilization in China. For the sake of safety, it is reasonable to think about that these huge towers may collapse under accidental loads, e.g., earthquakes or strong winds. As a result, the structural collapse may cause ground vibration which may detrimentally affect the safe operation of the nuclear-related facilities in the nuclear island. The situation may be even worse in

∗ Corresponding author. Tel.: +86 21 65982928. E-mail address: [email protected] (X. Gu). http://dx.doi.org/10.1016/j.nucengdes.2015.08.025 0029-5493/© 2015 Elsevier B.V. All rights reserved.

the event of an earthquake. This is because the seismic performance of cooling towers is usually not as strong as those structures in the nuclear island (GB 50267-97, 1998; VGB Guideline, 2005). Consequently, cooling towers may collapse before the nuclear-related structures under strong earthquakes, and collapse-induced ground vibration may enhance the earthquake-induced ground motion. Unfortunately, the current concepts of NPP planning have not included this vibration-related potential risk (HAD102/01, 1989; IAEA safety guide, 2003). One possible reason for this is that previous cooling towers were not built so high and were placed relatively far away from nuclear islands. However, critical rethinking about previous knowledge on disasters should be made, as revealed by the nuclear accident at Fukushima, Japan in 2011. That is, it seems necessary to reevaluate the known disasters, to find new potential threats, and to take into account secondary and combined disasters (Rainer, 2013). The ground vibration generated by certain vibratory sources, e.g., collapse-induced impacts, transportation, blast and impact, were studied in depth (Lin et al., 2013, 2014a,b; Milutin, 2010; Adam and Estorff, 2005; Khandelwal and Singh, 2007; Kwang

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F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

Fig. 1. The FEM model of the cooling tower.

and Tu, 2006). However, information on the critical influencing factors related to collapse-induced ground vibration is rather limited in literature. Furthermore, an integrated and clear understanding on NPP planning concerning these issues is not available. In this regard, this study offers a new contribution to NPP planning considering critical factors on ground vibration due to the collapse of large-scale cooling towers. A “cooling tower-soil” numerical model is presented in Section 2 of this study and verified in several aspects to predict collapseinduced ground vibration. By means of the model, the factors that affected the ground vibration are parametrically analyzed and presented in Section 3. Section 4 uses the obtained results to make recommendations for the NPP planning. 2. Numerical model and model verification 2.1. Numerical model A finite element method (FEM) based model was developed to predict ground vibration caused by the collapse of cooling towers. The model consists of a cooling tower model and a soil model. The information about the dimensions, reinforcements and material properties of the towers and soils are given in Section 3.1 where study plan for influencing factors is presented. Four types of accidental loads are considered, i.e., strong earthquakes, strong winds, aircraft impacts, and failure of all the columns simultaneously. The last load type rarely happens but was chosen to determine the upper limit of ground vibration, because it generally excites the most intensive vibration among those excited by the four types of accidental loads (Lin et al., 2013). The commercial finite element program ANSYS/LS-DYNA was used to perform the numerical analysis. The considered cooling towers were constructed with reinforced concrete and consisted mainly of a shell body and supporting columns. As illustrated in Fig. 1, the hyperbolic shell body was discretized into a certain number of vertical “levels” and of meridional “strips” (150 or 161 levels depending on tower geometries and 728 strips). The maximum mesh size on the shell surface of the generated “patch” was about 0.8 m × 1.5 m and each “patch” was modeled using four-node shell elements (SHELL163) with both bending and membrane capabilities. The continuously varied shell thickness was properly modeled by changing the thickness of the shell elements at each “level”. All the shell elements were divided into 15 “layers” along the direction of thickness. Each layer could be assigned to a specific material, i.e., concrete, meridional steel reinforcements or circumferential steel reinforcements, in accordance with their actual positions. The common used material model

with the keyword *MAT CONCRETE EC2 was used for the concrete and steel reinforcements with their corresponding material equations proposed in Eurocode 2 Part 2.1 (2004). Tension softening and strain rate effect of concrete were also considered (Lin et al., 2014a). For the modeling of the columns, two strategies related to different load types were applied for the purpose of improving the computational efficiency. The first strategy was for the cases where the columns might fail during collapse. The hexahedral elements (SOLID164) and beam elements (BEAM161) were used for the concrete and reinforcing steel bars, respectively, without considering the slip behavior between them. The Holmquist–Johnson–Cook (HJC) constitutive model for concrete (Holmquist et al., 1993) was used for modeling the concrete in the columns. This material model can describe the complex behavior of concrete subjected to large strains and high pressures, as in situations relating to earthquakes and impacts. A plastic kinematic model (*MAT PLASTIC KINEMATIC) was applied for modeling the reinforcing steel bars in the columns with consideration of strain rate effects. By doing this, the possible failure process of columns could be accurately simulated; however, this process was inevitably accompanied by tremendous numerical efforts. To partly overcome this shortcoming, a second strategy was applied, which was for cases where columns did not fail, e.g., the cooling towers under winds or aircraft impacts (Li et al., 2013). In this strategy each column was simulated as one beam element. As a result, the ultimate loading capacities of the columns were overestimated; however, the results were still reasonable and the computational cost was significantly reduced. The FEM-based model of the soil is illustrated in Fig. 2, with consideration of element type, material model, model dimension, mesh size, and model boundaries. Eight-node isoparametric elements (SOLID164) were also used for the soil model. The mechanical

Fig. 2. The FEM model of the soil.

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

behaviors of different soils were assumed to be ideal elasto-plastic and could be described using the Drucker–Prager model (Drucker and Prager, 1952). Gu and Lee (2002) applied this model and successfully predicted the ground response in a similar scenario concerning soil dynamic behavior. The dimension of the soil model was 1000 m × 1000 m in plane and 35 m in depth, which was adequately accurate according to the theory of surface wave propagation and the study results presented by Lou et al. (2003). A reasonable mesh size was critical both for appropriate accuracy and numerical efficiency. Generally, based on the wave propagation theory, the maximum mesh size, le , used in a FEM-based dynamic analysis should fit Eq. (1) (Kausel and Manolis, 2000): le ≤

1

12

∼

1 6



· − − −T =

1

12

∼

1 6

 v ·

fT

(1)

where T is the wavelength corresponding to the dominant wave frequency, fT ; v denotes the propagation velocity of the wave under consideration. For the impact-excited ground vibration, Rayleigh wave (R-wave) is the predominant component of the surface waves (Bolt, 1988). In principle, the dominant wave frequency, fT , could be obtained from the Fourier acceleration amplitude spectra of the vibration points after the numerical computations in Section 3 were completed. The propagation velocity of the R-wave could be derived according to the soil properties. Based on this, the mesh size of 5 m × 5 m × 5 m was verified by trial computations and eventually adopted. Besides, the commonly used non-reflecting boundaries were set in the undersurface and in the four vertical side surfaces of the soil model. By doing this, the waves could transmit through these boundaries without reflections and refractions, as they actually did in the real infinite soil. Other considerations were also addressed to ensure that the computation was reasonable and that the time was acceptable. First, the columns were actually separated from the soil surface with a small spacing of 2 m. The earthquake waves were then input at the element nodes on the bottom of the columns model. As a result, it was possible to improve the computational efficiency because the soil model was not activated until the tower fragments impacted it. The shortcoming of this strategy was that the interaction between the cooling tower and the soil was ignored. Second, contacts and collisions acted among tower fragments as well as between the fragments and soil surface during the collapse process. To describe these, the widely used penalty function method was used to implement the contact-collision algorithm. Third, one center integral point in solid elements was applied to make the computation efficient; however, this resulted in undesired zero energy modes (hourglass modes). To control these modes in a reasonable manner, a viscous damping and small elastic stiffness were used (Hallquist, 2012). Fourth, central difference method (explicit time integration) with consideration of geometric and material nonlinearity was used to solve the dynamic equations. Finally, detailed information about the parameter values used was presented by Lin et al. (2014a).

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acceleration response spectrum specified in the Chinese code GB 50267-97 (1998). As a result, the earthquake wave RG1.60 was adopted in this study due to its common use in nuclear engineering. The peak ground accelerations (PGAs) of the chosen earthquake waves were first normalized as 0.05 g (g denotes the acceleration of gravity) in two horizontal directions and 0.033 g in the vertical direction, with the ratio 0.05:0.05:0.033 = 1:1:0.67 in conformance with the code GB 50267-97 (1998). Then the earthquake wave was input on the bottom nodes of the elements on the column feet of the model in x, y and z directions which meant the east–west, north–south and vertical direction presented in Fig. 2, respectively. Finally, incremental computations were performed gradually with a fixed step increment for PGAs of 0.05 g in two horizontal directions and 0.033 g in the vertical direction until the tower collapsed. The strong winds in this study belong basically to the condition of both normal and typhoon climate. First, the equivalent design values of the wind pressure distributed on the external surface of the cooling towers, w(z, ) , were obtained according to the Chinese code GB/T50102-2003 (2003) with consideration of the reference wind pressure w0 , wind vibration coefficient ˇ, wind pressure distribution coefficient Cp() , wind pressure coefficient z at height z, and in the form of Eq. (2): w(z,) = ˇCp() z w0

(2)

where ˇ equals to 1.9 for B type terrain with consideration for wind vibration effect and gust response. Fig. 3 illustrates the wind pressure distribution coefficient Cp() on the external surface of cooling tower shell in term of the angle in circumferential direction . The obtained results of the wind pressure distribution were also similar to the widely accepted ones presented in the VGB Guideline (VGB-Technical Committee, 2005). It was also assumed that the wind pressure distribution did not change including the collapse process. Afterwards, the wind pressures distributed on the shell surface were applied in x direction in the form of ␭w(z, ) and gradually increased with a scale of 10%, i.e.,  = 1.0, 1.1, . . .. Finally, the cooling towers collapsed with  = 2.2 for Tower 1 and  = 1.9 for Tower 2. These values were similar to the ones in literature, e.g., 2.31 in (Busch et al., 2002). Although winds are rather quasi-static pressure which should be simulated using implicit code, explicit computation was chosen in the study because the subsequent or simultaneous collapse progress featured with significant dynamics. The time duration for increasing each  was 4–5 times of the primary natural period, which was thought to be appropriate with the primary natural period of 1.26 s for Tower 1 and 1.58 s for Tower 2. The primary natural periods were also verified by using another commercial finite element program ABAQUS. The widely operating Boeing 747-400 with a maximum takeoff weight of 396 tons and cruise speed of 940 km/h (261 m/s) was used for the loads type of aircraft impact. The cruise speed applied to a terrorist scenario in which a velocity reduction would not be expected. The airplane was considered as an elastically deformable

2.2. Accidental loads Four types of accidental loads were considered in this study to cause the cooling tower to collapse, i.e., strong earthquakes, strong winds, aircraft impacts and failure of all the columns simultaneously. Strong earthquakes and strong winds go far beyond the design level specified in Chinese codes, and aircraft impacts are usually not taken into account in the codes. In the explicit formulation, the gravity loads of the towers were first applied using a dynamic relaxation method with an artificial and large damping to approximately simulate a static loading. The earthquake wave was first chosen following the general approach with primary consideration of soil properties and

Fig. 3. Wind pressure distribution coefficient Cp() in term of the angle in circumferential direction .

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F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

Fig. 4. Aircraft impact to the cooling tower based on two different approaches.

body with uniform distribution of rigidity and mass because the relevant information was unfortunately unavailable in literature. The aircraft impacted the tower throat in two styles as illustrated in Fig. 4, i.e., impact with airplane head and impact with one airplane wing, since different impact styles could lead to different local collapse forms of a tower. In the computation, the airplane model instead of a force–time curve was used for impact loading because the former could describe two events of impacts, i.e., hitting the front and rear shells of the tower frontally and successively. However, an overestimated impact effect on the towers was expected because hardly any energy was consumed by the elastically deformable aircraft in the model. A possible fire disaster due to the burning fuel was not considered. The last load type was the failure of all the columns simultaneously. In the simulation, all columns failed within 0.04 ms. This time duration was small enough compared to the primary natural period of the two towers of about 1.5 s and thereby could generally be regarded as appropriate.

collapse mode and collapse duration. In addition, the numerical model was also partially verified by test results of a scaled cooling tower model with half number of its columns sudden removed (Li et al., 2013). Falling weight tests were conducted by Lin et al. (2013) and the impact-induced ground vibration at different points at various distances was recorded. The simulated results of ground vibration were obtained using a “falling weight-soil” model. The tested and simulated ground vibrations were compared in historical form and matched well with each other, with respects to the acceleration amplitudes, wave forms, and vibration durations. Aircraft impact action was partially verified by means of a nuclear containment subjected to a large-scale commercial aircraft crash (Lin et al., 2014b). The force-time history curve for the impact action of a Boeing 767-400 was used. The calculated maximum shell deformation was 95 mm which was similar to the result of 92 mm in Sadique et al. (2013).

3. Influencing factors 2.3. Model verification 3.1. Study plan The developed model in Section 2.1 were verified in several aspects, including the numerical techniques, the collapse modes of cooling towers, the ground vibration, and the aircraft impact action. The specific numerical techniques used in the study were checked. The penalty function method was applicable for describing the collisions between concrete blocks. This was confirmed based on a series of experimental and numerical studies (Hou et al., 2007). In addition, the commonly used viscous boundaries in the soil model were proved to be efficient both for the compressive and shear wave. The hourglass was also controlled in a reasonable level (Lin et al., 2014a). A cooling tower located in Xuzhou, China, was demolished by controlled blasting, and the collapse process was videotaped (NEBTSD, 2012). The developed model was used to simulate the collapse process, and partial results are illustrated in Fig. 5 for comparison. Satisfactory agreements were achieved both in the

Five critical factors influencing collapse-induced ground vibration were investigated, i.e., the height and weight of the towers, the accidental loads, the soil properties, the overlying soil, and the isolation trench. These influencing factors were closely related to their vibratory source and the medium for wave propagation. As presented in Table 1, the study plan contained five cases and in each case only one influencing factor varied while the others remained unchanged. On the whole, the study plan included two towers, four types of accidental loads, three types of soils from “soft” to “hard”, two depths of overlying soil, and two cases of isolation trenches. Tables 2–4 present the information for the dimensions and weights of the towers, the reinforcements of the towers, and the soil properties, respectively. The soil properties were excerpted from a practical project. The uniaxial compressive and tensile strength

Fig. 5. The comparison of the collapse process of a demolished cooling tower with simulated results.

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

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Table 1 Study plan. Case

Influencing factor

Model composition

Location in this paper

Tower

Accidental loads

Soil type

Overlying soil

Isolation trench

Earthquake

SWSS

Not available

Not available

Earthquake, wind, aircraft impact, column failure Earthquake Earthquake Earthquake

SWSS

Not available

Not available

C, SWSS, MWSS SWSS SWSS

Not available 5 m, 10 m Not available

Not available Not available Four cases

Section 3.2

2

Height and weight of towers Accidental load

Section 3.3

Tower 1, Tower 2 Tower 1

3 4 5

Soil property Overlying soil Isolation trench

Section 3.4 Section 3.5 Section 3.6

Tower 1 Tower 1 Tower 1

1

Note: The soil type of C, SWSS and MWSS means clay, strongly weathered sandy slate, and moderately weathered sandy slate, respectively.

Table 2 Information for the dimensions and weights of the towers. Tower no.

Tower 1 Tower 2

Height (m)

Thickness of shell body (mm)

Diameter of shell body (m)

Column

Weight (ton)

Total

Column

Bottom

Top

Bottom

Throat

Top

No.

Diameter (mm)

200 251

12.4 14.8

153.0 176.6

96.6 114.2

1400 1700

250 350

350 400

104 112

1300 1600

60,000 120,000

Table 3 Information for the reinforcements of the towers. Tower no.

Reinforcement ratio in shell body Circumferential Inner side

Tower 1 Tower 2

Outer side

0.28–0.62% 0.18–0.31%

Reinforcement ratio in columns Meridional

0.31–0.72% 0.18–0.45%

Inner side

Outer side

0.33–0.68% 0.20–0.80%

0.33–0.70% 0.20–0.84%

for concrete were 29.6 MPa and 2.51 MPa, respectively. The elasticity modulus of concrete was 2.0 × 104 MPa. The yield strength and the ultimate strength of the reinforcing steel bars were 400 MPa and 540 MPa, respectively. The elasticity modulus and the Poisson’s ratio were 2.0 × 105 MPa and 0.3, respectively. The stress–strain relationships for concrete and reinforcing steel bars in the shell subject to loading, unloading and reloading in uniaxial compression and tension referred to Lin et al. (2014a). The earthquake wave RG1.60, before normalization, was adopted with the PGA of 0.100 g, 0.100 g and 0.067 g in x, y and z directions, respectively. The earthquake wave lasted for 25.00 s. 3.2. The heights and weights of the towers Towers 1 and 2 were used to investigate the influence of tower heights and weights on ground vibration. The strongly weathered sandy slate and the earthquake wave RG1.60 were used in the model without overlying soil and isolation trench. As a result, the two towers collapsed with the threshold PGAs both of 0.350 g in x and y directions and 0.233 g in z direction. The threshold PGAs meant the earthquake caused the towers to collapse with minimum acceleration amplitude. Table 5 summarizes the characteristics of the ground vibration at point A at a distance L of 350 m presented in Fig. 2. This distance was of interest because the nuclear island would most likely be located here. As an example,

Longitudinal

Stirrup

2.42% 0.86%

0.31% 0.13%

Figs. 6 and 7 show the acceleration histories and Fourier acceleration amplitude spectra of the collapse-induced vibration at point A in radial direction, respectively. It was found that the maximum acceleration amplitudes of the vibration increased with the increase of the weight and height of the cooling towers. However, a quantitative relationship was difficult to derive for the distance L varied from 250 m to 450 m which was concerned in practice. The tangent acceleration amplitudes were relatively small compared to those in radial and vertical directions, mainly due to the central symmetry of the soil. The dominant frequency bands slightly differed from each other and the maximum Fourier acceleration amplitudes were about 0.008 m/s and 0.015 m/s for Towers 1 and 2, respectively. The vibration durations were similar to each other. These results have a close relationship with the identical collapse mode of the two towers under dead loads and the earthquake. Fig. 8 shows the collapse process of Towers 1 and 2 with fragments not shown for clarity, respectively. The local cracks initiated in the middle part of each tower along both meridional and circumferential directions. The cracks then developed and gradually formed a concave adjacent to the throat of the shell body. Large deformation was observed in the upper part of each shell body. The structure finally collapsed with most of the fragments falling within its interior. From an energy viewpoint, increasing the height and weight of the tower resulted in increasing the input energy of the ground

Table 4 Information for the soil properties. Soil type

Density (kg/m3 )

Dyn. shear modulus (MPa)

Poisson’s ratio

Cohesion (MPa)

Internal friction angle (◦ )

Damping ratio

Shear wave velocity (m/s)

Clay Strongly weathered sandy slate Moderately weathered sandy slate

1930 2350 2510

150 1810 5150

0.40 0.36 0.33

0.007 0.030 1.640

15.00 25.00 36.42

5% 1% 1%

215 849 1406

Note: The properties of the overlying soil were identical to those of the clay.

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F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

Table 5 Characteristics of ground vibration at point A at a distance of 350 m for different cooling towers under earthquake wave RG1.60 with strongly weathered sandy slate. Tower no.

Tower 1 Tower 2 Error

Height (m)

Maximum acceleration amplitude (m/s2 )

Weight (ton)

200 251 +25.5%

60,000 120,000 +100%

r

t

Vertical direction

0.294 0.513 +74.5%

0.176 0.339 +92.6%

0.344 0.733 +113.1%

Dominant frequency band in r direction (Hz)

Vibration duration (s)

2.5–25 2.5–25 Minor differences

Approx. 23 Approx. 27 Close to each other

0.60

0.60

Acc (m/s2)

Acc (m/s2)

Note: (1) error = (value of Tower 2 − value of Tower 1)/value of Tower 1; and (2) r and t directions denote radial and tangent directions, respectively.

0.30 0.00 -0.30 -0.60 10.00

20.00

30.00

40.00

0.30 0.00 -0.30 -0.60 10.00

50.00

T(s)

20.00

30.00

40.00

50.00

T(s)

(a) Tower1

(b) Tower2

0.02

Fourier Amplitude (m/s)

Fourier Amplitude (m/s)

Fig. 6. Acceleration histories of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for the towers under earthquake RG1.60 with strongly weathered sandy slate.

0.01 0.00 0.00

5.00

10.00

15.00

20.00

25.00

0.02 0.01 0.00 0.00

5.00

10.00

15.00

f (Hz)

f (Hz)

(a) Tower 1

(b) Tower 2

20.00

25.00

Fig. 7. Fourier acceleration amplitude spectra of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for the towers under earthquake RG1.60 with strongly weathered sandy slate.

vibration, leading to a stronger ground vibration when the collapse mode of the towers was almost identical. 3.3. Collapse modes Fig. 9 presents the profiles of the collapse initiation and debris of Tower 1 under different accidental loads. Table 6 summarizes the characteristics of the ground vibration at point A for the collapse of Tower 1. As an example, Figs. 10 and 11 show the acceleration histories and Fourier acceleration amplitude spectra of collapse-induced vibration at point A in radial direction, respectively. In particular, in the strong wind case, a majority of the shell failed while a small part of the bottom shell and all the columns survived. This scenario was similar to the collapse mode of the cooling towers in Ferrybridge power station in 1965, which was a well-known disaster due to strong wind (Central Electricity Generating Board, 1966). The collapse mode caused by column failure fell to the category of “collapse in integrity”, while the collapse by other forces was categorized as “collapse in fragments”. Typically, the collapse mode of “collapse in fragments” could happen when the shell body disintegrated gradually before the column failure. The collapse mode

of “collapse in integrity” meant that the columns failed first and then the shell body impacted the ground almost as a whole following the disintegration of the shell body in a relatively short time. This collapse mode is usually associated with relatively high vibration intensity compared to that of “collapse in fragments” (Lin et al., 2013). The maximum acceleration amplitudes of the four cases varied widely, e.g., in the range of 0.175–1.374 m/s2 in radial direction with amplitudes differing by a magnitude of more than seven times. Similar results were also observed for the vibration duration lasted from 8 s to 23 s. As expected, the maximum acceleration amplitude was significantly larger and the vibration duration was significantly shorter due to column failure when compared to the other three accidental loads, which was mainly due to the characteristics of different collapse modes. Finally, dominant frequency bands differed insignificantly for the four cases. In the category of “collapse in fragments”, the maximum acceleration amplitudes of ground vibration caused by strong wind were generally high compared to those of earthquake and aircraft impact. This was possibly attributed to the specific features of the wind acting on the structure surface, i.e., continuously and unidirectionally. Therefore, two results were expected. One was relative heavy shell

Fig. 8. Collapse process of the towers under earthquake wave RG1.60.

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

33

0.60

0.60

Acc (m/s2)

Acc (m/s2)

Fig. 9. Profiles of collapse initiation and debris after the collapse of Tower 1 under different accidental loads.

0.30 0.00 -0.30 -0.60 10.00

0.30 0.00 -0.30 -0.60

20.00

30.00

40.00

0.00

50.00

10.00

20.00

(a) Earthquake wave RG1.60

40.00

50.00

40.00

50.00

(b) Strong wind

0.60

0.60

Acc (m/s2)

Acc (m/s2)

30.00

T(s)

T(s)

0.30 0.00 -0.30

0.30 0.00 -0.30

-0.60

-0.60 0.00

10.00

20.00

30.00

40.00

50.00

0.00

T(s)

10.00

20.00

30.00

T(s)

(c) Aircraft impact with head

(d) Aircraft impact with one wing

Acc (m/s2)

2.00 1.00 0.00 -1.00 -2.00 0.00

10.00

20.00

30.00

40.00

50.00

T(s)

(e) Column failure Fig. 10. Acceleration histories of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under different accidental loads with strongly weathered sandy slate.

fragments (less shell survived as illustrated in Fig. 9(b)) impacting the ground. The other was that the impacted region on the ground was closed to point A. Note that the wind was applied in x direction toward point A in the computation. In general, both results led to vibration enhancement at point A.

3.4. Soil properties Table 7 presents the characteristics of ground vibration at point A for the collapse of Tower 1 under earthquake RG1.60 with different soil properties. As an example, Figs. 12 and 13 show acceleration

Table 6 Characteristics of ground vibration at point A at a distance of 350 m for the collapse of Tower 1 under different accidental loads and with strongly weathered sandy slate. Loads type

Earthquake wave RG1.60 Strong wind With head Aircraft impact With one wing Column failure

Maximum acceleration amplitude (m/s2 ) r

t

Vertical direction

0.294 0.486 0.263 0.175 1.374

0.176 0.151 0.085 0.050 1.022

0.344 0.711 0.358 0.295 1.875

Dominant frequency band in r direction (Hz) 2.5–25 2.5–25 2.5–7.5 and 20–25 2.5–7.5 and 20–25 15–25

Vibration duration (s) Approx. 23 Approx. 20 Approx. 22 Approx. 12 Approx. 8

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39 0.02

Fourier Amplitude (m/s)

Fourier Amplitude (m/s)

34

0.01 0.00 0.00

5.00

10.00

15.00

20.00

0.02 0.01 0.00

25.00

0.00

5.00

10.00

f (Hz)

0.01 0.00 5.00

25.00

0.02 0.01 0.00 0.00

10.00 15.00 20.00 25.00

5.00

10.00 15.00 20.00 25.00

f (Hz)

f (Hz)

(c) Aircraft impact with head Fourier Amplitude (m/s)

20.00

(b) Strong wind Fourier Amplitude (m/s)

Fourier Amplitude (m/s)

(a) Earthquake wave RG1.60 0.02

0.00

15.00

f (Hz)

(d) Aircraft impact with one wing

0.10 0.05 0.00 0.00

5.00

10.00 15.00 20.00 25.00 f (Hz)

(e) Column failure Fig. 11. Fourier acceleration amplitude spectra of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under different accidental loads with strongly weathered sandy slate.

Table 7 Characteristics of ground vibration at point A at a distance of 350 m for the collapse of Tower 1 under earthquake wave RG1.60 with different soil properties. Maximum acceleration amplitude (m/s2 )

Soil property

r

t

Vertical direction

0.048 0.294 2.697

0.020 0.176 0.328

0.043 0.344 4.516

0–5 2.5–25 7.5–15

3.00

3.00

1.50

1.50

1.50

0.00 -1.50 -3.00 10.00

20.00

30.00 T(s)

40.00

0.00 -1.50 -3.00 10.00

50.00

(a) Clay

Acc (m/s2)

3.00

Acc (m/s2)

Acc (m/s2)

Clay Strongly weathered sandy slate Moderately weathered sandy slate

20.00

30.00 T(s)

Vibration duration (s)

Dominant frequency band in r direction (Hz)

40.00

(b) Strongly weathered sandy slate

0.00 -1.50 -3.00 10.00

50.00

Approx. 20 Approx. 23 Approx. 27

20.00

30.00 T(s)

40.00

50.00

(c) Moderately weathered sandy slate

0.05

0.00 0.00

5.00

10.00 15.00 f (Hz)

(a) Clay

20.00

25.00

0.10

Fourier Amplitude (m/s)

0.10

Fourier Amplitude (m/s)

Fourier Amplitude (m/s)

Fig. 12. Acceleration histories of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with different soil properties.

0.05

0.00 0.00

5.00

10.00 15.00 f (Hz)

20.00

25.00

(b) Strongly weathered sandy slate

0.10

0.05

0.00 0.00

5.00

10.00

15.00

20.00

25.00

f (Hz)

(c) Moderately weathered sandy slate

Fig. 13. Fourier acceleration amplitude spectra of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with different soil properties.

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

35

Table 8 Characteristics of ground vibration at point A at a distance of 350 m for the collapse of Tower 1 under earthquake wave RG1.60 with overlying soils of different thicknesses. Maximum acceleration amplitude (m/s2 )

Thickness of overlying soil (m) 0 5 10

r

t

Vertical direction

0.294 0.211 0.117

0.176 0.046 0.027

0.344 0.158 0.082

2.5–25 5–18 4–13

Acc (m/s2)

0.60

Acc (m/s2)

Dominant frequency band in r direction (Hz)

0.30 0.00 -0.30 -0.60 10.00

20.00

30.00

40.00

50.00

T(s)

Vibration duration (s) Approx. 23 Approx. 23 Approx. 23

0.60 0.30 0.00 -0.30 -0.60 10.00

20.00

30.00

40.00

50.00

T(s)

(a) Thickness of 5 m

(b) Thickness of 10 m

0.02

Fourier Amplitude (m/s)

Fourier Amplitude (m/s)

Fig. 14. Acceleration histories of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with overlying soil of different thicknesses.

0.01 0.00 0.00

5.00

10.00

15.00

20.00

25.00

0.02 0.01 0.00 0.00

5.00

10.00

(a) Thickness of 5 m

15.00

20.00

25.00

f (Hz)

f (Hz)

(b) Thickness of 10 m

Fig. 15. Fourier acceleration amplitude spectra of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with overlying soil of different thicknesses.

histories and Fourier acceleration amplitude spectra of collapseinduced vibration at point A in radial direction, respectively. It was found that the maximum acceleration amplitudes increased dramatically when the soil became “hard”. For example, the maximum acceleration amplitudes in the case of “strongly weathered sandy slate” were about 6–8 times greater than that of “clay” in three directions. These results were as expected from our knowledge of soil dynamics. It is generally known that ground vibration becomes intensive and will attenuate slowly in a rock-like medium compared to those vibrations occurring in relatively soft soil where ground vibratory source is under identical impacts. In addition, the variations in dominant frequency bands are thought to be caused by the effect of different soil properties.

3.5. Overlying soil As an application of the results in Section 3.4, “soft” soil (clayey) can be used as overlying soil to reduce collapse-induced vibration. Table 8 summarizes the characteristics of ground vibration at point A for the collapse of Tower 1 under earthquake RG1.60 with overlying soils of different thicknesses, i.e., 0 m, 5 m and 10 m. The underneath soil was strongly weathered sandy slate. Figs. 14 and 15 show the acceleration histories and Fourier acceleration amplitude spectra of collapse-induced vibration at point A in radial direction, respectively. Results proved vibration reduction to be significant when 5–10 m of clayey soil was applied on top of the “hard” soil. The maximum acceleration amplitudes were reduced more than 28% when using a 5 m-thick overlying soil in comparison to cases that it was not used. Further reduction ratios of more than 60% in three directions can be obtained using 10 m-thick overlying soil. Vibration durations were almost identical and dominant frequency bands became small when “soft” overlying soil was used.

3.6. Isolation trench Isolation trenches have been widely applied for the reduction of ground vibration. This application was mainly based on the knowledge that: the R-wave is the main component of the surface wave; the propagation depth of the R-wave is about one wavelength, and most of the R-wave energy is located within a depth that is half of the wavelength (Woods, 1968; Michael et al., 1980). Fig. 16 illustrates the open active and passive isolation trenches used in this study with a length of 220 m and a depth of 20 m. Active isolation trench means the trench located near the vibratory source, while passive isolation trench implies the wave barrier is positioned away from the source but around the structure to be protected. Primary conclusions, e.g., presented by Ahmad and Al-Hussaini (1991), were considered to design the trenches in this study. As the R-wave lengths were about 30.6–43.7 m in this study, a trench depth of 20 m was expected to have an appropriate effect of vibration attenuation. Table 9 presents the characteristics of ground vibration at point A for the collapse of Tower 1 under earthquake RG1.60 with isolation trenches. Figs. 17 and 18 illustrate the acceleration histories and Fourier acceleration amplitude spectra

Fig. 16. Plane layout of an active and a passive isolation trenches used in this study.

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F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

Table 9 Characteristics of ground vibration at point A at a distance of 350 m for the collapse of Tower 1 under earthquake wave RG1.60 with different isolation trenches. Trench type

Depth (m)

No trench Active isolation trench Passive isolation trench

0 20 20

Maximum acceleration amplitude (m/s2 )

Dominant frequency band in r direction (Hz)

r

t

Vertical direction

0.294 0.145 0.259

0.176 0.076 0.135

0.344 0.209 0.234

2.5–25 2.5–25 4–20

Vibration duration (s) Approx. 23 Approx. 23 Approx. 23

Table 10 Characteristics of the ground vibration at point A at distance of 350 m for the collapse of Tower 1 under aircraft impact at different speeds and with strongly weathered sandy slate. Maximum acceleration amplitude (m/s2 )

Impacting shell throat at different speed (m/s) 261 215 150

r

t

Vertical direction

0.263 0.305 0.238

0.085 0.116 0.105

0.358 0.448 0.394

Acc (m/s 2)

Acc (m/s2)

2.5–7.5 and 20–25 2.5–7.5 and 17.5–25 2.5–5 and 17.5–25

0.60

0.60 0.30 0.00 -0.30 -0.60 0.00

Dominant frequency band in r direction (Hz)

10.00

20.00

30.00

40.00

0.30 0.00 -0.30 -0.60 0.00

50.00

10.00

20.00

T(s)

30.00

40.00

50.00

T(s)

(a)Active isolation trench with a depth of 20 m

(b) Passive isolation trench with a depth of 20 m

Fig. 17. Acceleration histories of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with different isolation trenches.

3.7. Effects of impact speed and impact position

Fourier Amplitude (m/s)

Effects of impact speed and impact position on the ground vibration due to tower collapses were investigated. First, the aircraft Boeing 747-400 was assumed to frontally impact the shell throat of Tower 1 with aircraft’s head at different speeds, i.e., 261 m/s, 215 m/s and 150 m/s. After two collisions on the front and rear sides of the shell successively, the aircraft speed slowed down to 162 m/s, 123 m/s and 77 m/s, respectively. Table 10 presents the characteristics of ground vibration at point A at distance of 350 m for the collapse of Tower 1 under aircraft impact at different speeds and with strongly weathered sandy slate. Insignificant differences of the ground vibration were found among the three situations of different impact speeds. This was because the original failure regions, failure development, collapse mode, fragments impacting ground were almost identical as those illustrated in Fig. 9c. 0.02 0.01 0.00 0.00

5.00

10.00

15.00

20.00

25.00

f (Hz)

(a) Active isolation trench with a depth of 20 m

Second, the aircraft was assumed to frontally impact Tower 1 in a different position from the throat, but with identical velocity of 261 m/s. Unlike the impact position in the throat shown in Fig. 4, impact position of 10 m above the column top was assumed for comparison and illustrated in Fig. 19a. It was found that the maximum acceleration amplitudes were 1.030 m/s2 , 0.243 m/s2 and 1.715 m/s2 in radial, tangential and vertical directions, respectively. This meant that the ground vibration was significantly more intensive than that in the case of impact position in the throat (0.263 m/s2 , 0.085 m/s2 and 0.358 m/s2 , respectively). The vibration discrepancy was attributed essentially to the different collapse modes. Unlike “collapse in fragments” in the case of impact position in the throat, the collapse mode of nearly “collapse in integrity” was observed for the case of the impact position of 10 m above the column top, as illustrated in Fig. 19b. The whole shell above the impact position collided with the ground in an integrative and oblique manner, resulting in relatively high vibration intensity as discussed in Section 3.3. 4. NPP planning 4.1. Spacing between a cooling tower and the nuclear island After a cooling tower collapses, two factors must be considered when evaluating the appropriate spacing between the cooling Fourier Amplitude (m/s)

of the collapse-induced vibration at point A in radial direction. It was found that ground vibration was reduced with the maximum acceleration amplitude reduction ratios of 39–57% for the active isolation trench, and 12–32% for the passive isolation trench. The active isolation was more effective than the passive isolation. The vibration duration and Fourier acceleration amplitude spectra were relatively unaffected by isolation trenches.

0.02 0.01 0.00 0.00

5.00

10.00

15.00

20.00

25.00

f (Hz)

(b) Passive isolation trench with a depth of 20 m

Fig. 18. Fourier acceleration amplitude spectra of collapse-induced ground vibration at point A at a distance of 350 m in radial direction for Tower 1 under earthquake RG1.60 with different isolation trenches.

F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

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Fig. 19. Collapse mode of Tower 1 for impact position of 10 m above the column top.

4.2. Control of the collapse modes

Fig. 20. The isopleth map of the maximum ground acceleration amplitudes for Tower 1 in Case 1 of the study plan.

Cooling towers may collapse in different collapse modes associated with significantly different ground vibrations. Therefore, it is meaningful to control the collapse modes for the purpose of vibration reduction. As mentioned above, the collapse modes of cooling towers can be roughly divided into two categories: (1) collapse in integrity and (2) collapse in fragments. In addition, different cooling towers may “collapse in integrity” (Lin et al., 2014a) or “collapse in fragments” as illustrated in Fig. 9a under an identical earthquake, depending primarily on the positions of the structural weak parts. Ground vibration can be reduced by controlling the collapse modes of a cooling tower, which has not been addressed in current design concepts for NPP planning. The expected collapse mode can be achieved by adopting appropriate structural design strategy. As an alternative, the weak parts of a tower are intentionally designed in the shell body instead of the columns. Consequently, the collapse mode of “collapse in fragments” is likely to happen and associates with ground vibration of relatively low intensity. 4.3. Sitting of cooling towers and the nuclear island

tower and the nuclear island it serves: (1) the detrimental influence of collapse-induced ground vibration on the nuclear-related facilities and (2) the debris distribution which could impact the facilities. The information on collapse-induced ground vibration and debris distribution can be obtained by conducting a numerical approach as presented in this study. The vibration effect can then be assessed based on the dynamic responses of the facilities when the vibration information was input. In certain circumstances, an isopleth map of the maximum ground acceleration amplitudes as shown in Fig. 20 and a debris distribution map as shown in Fig. 21 are useful assessment tools. Generally, strong wind, among the four considered accidental loads, leads to the maximum debris distribution because wind attacks the structure surface unidirectionally and continuously. As a result, the nuclear island should be located outside debris distribution region. The maximum mass, size and velocity of the debris blocks can also be estimated by using the numerical approach.

Fig. 21. The debris distribution after the collapse of Tower 1 under strong wind.

In earthquake-prone areas, rock-like soil is desired for the sitting of a NPP from the viewpoint of earthquake engineering. In the event of a site limitation, the rock-like soil is prioritized for the nuclear island and other soils are “left” for the nuclear-unrelated facilities, e.g., cooling towers (GB 50267-97, 1998). However, considerations may be different when vibration risk is involved due to the collapse of a large-scale cooling tower adjacent to the nuclear island. In this case, the vibratory source and the considered vibration points are both on ground surface. As an undesired result, the vibration attenuates slowly in rock-like medium compared to those in soft soil. Based on these knowledge and the results in Section 3.4, “soft soil” is recommended for use as the foundation of cooling towers (or with a pile foundation). Soft soil is also recommended for the intermediate region between cooling towers and the nuclear island as illustrated in Fig. 22. This recommendation is under the condition that collapse-induced ground vibration is the primary concern or threat rather than an earthquake.

Fig. 22. Recommendation of the sitting of a cooling tower and the nuclear island.

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F. Lin et al. / Nuclear Engineering and Design 295 (2015) 27–39

withstand vibration were generally provided by the manufacturers and currently publicly unavailable. On the other hand, the factors influencing the ground vibration were comprehensive. Generally speaking, accidental loads of the failure of all the columns simultaneously provided the upper limit of ground vibration magnitude. The strong wind led to a wide debris distribution compared to other loads cases. 5. Conclusions

Fig. 23. Application of the overlying soil to reduce ground vibration.

4.4. Application of vibration reduction techniques Collapse-induced ground vibration can be significantly reduced by applying vibration reduction techniques, e.g., providing overlying soil (Fig. 23) or setting active or passive isolation trench between source and receiver. The magnitude of the vibration reduction in the case of providing an overlying soil depends mainly on the overlying soil properties and thickness as indicated in Section 3.5 where clay of 5–10 m depth resulting in a significant vibration reduction. The depth of the trench should be 0.5–1.0 times of the wavelength of the R-wave.

This study offers new recommendations for NPP planning due to the hazards of ground vibration caused by the collapse of large-scale cooling towers. The formulated recommendations are comprehensive and logical for the purpose of control and reduction of ground vibration. This was achieved by a parametric analysis of the critical factors that affected collapse-induced ground vibration by means of the verified “cooling tower-soil” numerical model. The proposed recommendations for the NPP planning included the spacing between a cooling tower and the nuclear island, control of the collapse modes, sitting of a cooling tower and the nuclear island, application of vibration reduction techniques, and the influence of tower collapse on surroundings. In certain circumstances, a post-disaster assessment is necessary for performing NPP planning in a more rational way. This issue was not addressed in this paper and needs further study.

4.5. Influence of the tower collapse on the surroundings Acknowledgements The collapse of a cooling tower may have detrimental influences on the surroundings beyond ground vibration, e.g., debris may block transportation routes, damage the pipelines and negatively impact the nuclear-related facilities. Clogged transportation routes may further result in disrupting and hampering rescue efforts. Besides, nuclear safety-related pipelines installed above ground or buried underground could become ineffective due to debris impacts or intensive vibration. To avoid these hazards, the main roads and nuclear safetyrelated pipelines should be designed out of the possible debris distribution region, as interpreted in Fig. 24. Increasing the burial depth of the pipelines can also help to mitigate the vibration. The performance of the pipelines to resist the vibration should be properly assessed if necessary. In addition, barriers such as steel wire netting are also suggested to apply around the periphery of nuclear island to protect it from the debris impact. In summary, these design recommendations were qualitative. A series of quantitative results are currently unavailable. This was because, on the one hand, the nuclear facilities’ abilities to

cooling tower debris distribution region

nuclear safety-related pipeline not constructed here lane

main road for transportation

nuclear safety-related pipeline Fig. 24. The main roads and nuclear safety-related pipelines to be designed out of the possible debris distribution region.

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