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Prediction of ground vibration due to the collapse of a 235 m high cooling tower under accidental loads
Nuclear Engineering and Design 258 (2013) 89–101
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Prediction of ground vibration due to the collapse of a 235 m high cooling tower under accidental loads Feng Lin a , Yi Li a , Xianglin Gu a,∗ , Xinyuan Zhao a , Dongsheng Tang b a b
Department of Building Engineering, Tongji University, No. 1239 Siping Road, Shanghai 200092, China Guangdong Electric Power Design Institute, No. 1 Tianfeng Road, Guangzhou, Guangdong 510663, China
h i g h l i g h t s Ground vibration due to the collapse of a huge cooling tower was predicted. Accidental loads with different characteristics caused different collapse modes. Effect of ground vibration on the nuclear-related facilities cannot be ignored.
a r t i c l e
i n f o
Article history: Received 7 December 2011 Received in revised form 17 December 2012 Accepted 8 January 2013
a b s t r a c t A comprehensive approach is presented in this study for the prediction of the ground vibration due to the collapse of a 235 m high cooling tower, which can be caused by various accidental loads, e.g., explosion or strong wind. The predicted ground motion is to be used in the safety evaluation of nuclear-related facilities adjacent to the cooling tower, as well as the plant planning of a nuclear power station to be constructed in China. Firstly, falling weight tests were conducted at a construction site using the dynamic compaction method. The ground vibrations were measured in the form of acceleration time history. A finite element method based “falling weight-soil” model was then developed and verified by field test results. Meanwhile, the simulated collapse processes of the cooling tower under two accidental loads were completed in a parallel study, the results of which are briefly introduced in this paper. Furthermore, based on the “falling weight-soil” model, “cooling tower-soil” models were developed for the prediction of the ground vibrations induced by two collapse modes of the cooling tower. Finally, for a deep understanding of the vibration characteristics, a parametric study was also conducted with consideration of different collapse profiles, soil geologies as well as the arrangements of an isolation trench. It was found that severe ground vibration occurred in the vicinity of the cooling tower when the collapse happened. However, the vibration attenuated rapidly with the increase in distance from the cooling tower. Moreover, the “collapse in integrity” mode and the rock foundation contributed to exciting intense ground vibration. By appropriately arranging an isolation trench, the ground vibration can be significantly reduced. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In earthquake-prone areas, seismic design should be carefully performed for the design of a nuclear power station (Bommer et al., 2011). However, the ground vibration due to the collapse of a huge structure, e.g., a cooling tower, is usually not considered. With increases in the height and mass of a tower-like structure, the ground vibration may become more intensive when collapse happens. Hence, it is reasonable to be concerned about whether this kind of ground vibration may damage the safe operation of nearby nuclear-related facilities. Unfortunately, this particular
∗ Corresponding author. Tel.: +86 21 6598 2928; fax: +86 21 6598 2928. E-mail address: [email protected] (X. Gu). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.01.022
issue has not been given serious attention, as few studies have addressed it. As a contribution to the mentioned problematic concern, this study presents a comprehensive approach for the prediction of the ground vibration due to the collapse of a cooling tower. The study motivation comes from a new water cooling tower with an overall height of 235 m, which will be built as a part of the construction of a planned nuclear power station in southern China. A cooling tower of such a great height, probably the highest planned one worldwide, raises a number of questions. One of the most interesting issues is the proper predication of collapse-induced ground vibrations, because the planned cooling tower is to be adjacent to the nuclear island with their spacing to be about 200 m, which is also the usual distance for other planned nuclear power stations in China due to limited space. In the event of the collapse of the
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Fig. 1. Methodology applied in this study.
cooling tower, the collapse-induced vibration may detrimentally affect the safe operation of the nuclear-related facilities. The causes that may induce the tower to collapse could be various accidental loads, such as an explosion or strong wind. The study results, in terms of the characteristics of the vibration, will be used as input data for the safety evaluation of nuclear-related facilities, as well as the plant planning of nuclear power stations. Studies on the ground vibration induced by a falling weight can be traced back to at least Lamb (1904). He studied the vibration of a semi-infinite body under a vertically concentrated harmonic force and derived an analytical solution for the displacement in an integral form. Subsequently, with the rapid development of computational technology, numerical simulation is being applied with increasingly frequency for the description of the ground motion. Gu and Lee (2002) studied the ground response to the dynamic compaction (DC) of dry sand, using two-dimensional finite element analyses with a large-strain dynamic formulation and a cap model for the soil behavior. As a result, the stress wave attenuation and improvement effects were realistically predicted. Pan and Selby (2002) numerically simulated the DC of loose soils under dynamic loads. A full axisymmetric elasto-plastic finite element representation was generated for the soils. The impact of the drop mass was modeled in two ways – a force–time input and a rigid body – both resulting in well simulated results of DC. On the other hand, a few measurements of ground vibration from field tests were also performed, with different vibration sources, e.g., a chimney with a height of 140 m and a weight of 2600 tons (Stangenberg and Zinn, 1998) or a falling weight of 25 tons weight used in DC (Kwang and Tu, 2006). For the evaluation of the ground vibration induced by the collapse of a cooling tower, which is characterized as a huge thin-walled reinforced concrete structure, few studies and suggestions were found in either technical handbooks or research papers. Therefore, the executed study has both academic and engineering significance. It is assumed that the cooling towers, like these in Germany and in France, will not collapse when built under the conditions of rational site selection, design, construction and maintenance, without suffering severe natural or man-made disasters. However, China is among the most natural disaster prone countries in the world. In extreme circumstances, e.g., explosion or strong wind, the cooling tower may partially or totally collapse (Gould, 2012; Krätzig and Zhuang, 1992). The explosion may be executed by terrorist attack, and the strong wind happens occasionally in China, such as typhoon, tornado, downburst (Fu et al., 2010) and squall line (Mitsuta et al., 1995). These accidental loads are usually not considered in practice according to the current design concept (VGB Guideline, 2005; JGJ22-2012, 2012), but they may occur in the small probability cases. For instance, nuclear accident happened at Fukushima, Japan, 2010, because of both strong earthquake and tsunami.
(1) Conducting the falling weight tests. (2) Developing a “falling weight-soil” model and verifying it with the tests. (3) Simulating the collapse of the cooling tower. (4) Developing “cooling tower-soil” models based on the “falling weight-soil” model. (5) Predicting the ground vibration using the “cooling tower-soil” models. (6) Performing a parametric study of the ground vibration. (7) Proposing suggestions for the design of the nuclear-related facilities and for plant planning. The gray contents in Fig. 1, including the collapse of the cooling tower (step (3)) and the application of this study (step (7)), are not presented in detail in this paper. Moreover, to keep the numerical computation in step (5) at an acceptable level for the current commonly used personal computer, appropriate numerical strategies, as described in Section 6, were employed to keep the computational cost down. 3. Falling weight tests 3.1. Dynamic compaction Dynamic compaction (DC) is a well-known method of site improvement by treating loose soils on site (Gu and Lee, 2002; Pan and Selby, 2002). The construction procedure involves dropping a heavy weight (pounder) from a certain height over the ground surface to be compacted. A number of researchers have studied the design and assessment of DC, mainly focusing on the load bearing capacity or improvement depth of the site soils. In this regard, falling weight tests were conducted by the authors in a construction site near Hangzhou, China, where DC was being used for soil improvement. As illustrated in Fig. 2, the DC facilities included a crawler crane and a falling weight with a self-release
2. Study methodology The methodology applied in this study is schematically illustrated in Fig. 1 and was achieved through the following steps:
Fig. 2. DC facilities.
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
5m
5m
5m
5m
tamping direction tamping points conducted in DC L
considered vibration point
tamping points used in falling weight test Fig. 3. Tamping sequence of the second pass of DC.
mechanism. The falling weight was about 12 tons with a diameter of 2.5 m and was made of a concrete-filled steel shell. In the tests, the pounder was slowly slung to a height of about 6 m and then freely dropped, impacting the soil surface and, consequently, inducing ground vibration. As often used, three phases of impact (normally called passes) were conducted. In each pass, each tamping point was tamped twice. The tests were executed in the second pass, with the tamping sequence shown in Fig. 3. In this pass, the arrangement of the tamping points followed an approximate square-grid pattern with a spacing of about 5 m from center to center. The ground vibrations were measured when each tamping point used in the tests was first tamped in the second pass to ensure measurement consistency. 3.2. Equipment for vibration measurement The equipment layout of the falling weight tests is shown schematically in Fig. 4. The considered vibration point was L far from the tamping points. The distance L varied from 80 m to 155 m, due to the limitations of the maximum length of the site. A recording, storing and data processing system was used. This system included acceleration sensors that were placed in the position of the considered vibration point as accurately as possible and were used to measure the acceleration time histories of the vibration point in the vertical and radial directions. The vibrations in the tangential direction were not measured, because they were relatively small compared to those in the vertical and radial directions and, hence, were regarded as insignificant in this study, due to the approximate axisymmetry of the site soil. Similar results were also found by Kwang and Tu (2006). A type of KD1100LC acceleration sensor, manufactured by Yangzhou Kedong Electronics Technology Corporation, was used. The frequency range of the sensors was 0.2–1000 Hz, and the sensitivities of the sensors were 1000 mV/g. The maximum measurement of acceleration was 5g (where g is the gravitational acceleration). The recording, storing and data processing system was a UA302A system, with sixteen channel data logging and an amplifier system connected to a PC-XP notebook computer for storing
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and processing data. The resolution of the analog-to-digital (A/D) interface was 16 bits, and the maximum sampling rate was 100 kHz. The electronic total station was used to measure the falling heights, H, of the pounder in the tests. This was executable because the pounder was slung and then intentionally controlled to be stationary for a short period of time at its maximum height for the convenience of the measurement. The falling heights, H, were also controlled to be approximately identical. In the tests, the position of the considered vibration point was not changed, whereas the tamping points were moved (see Fig. 4). In this manner, it can be regarded that the vibration exciter was approximately the same for different test cases, whereas the distances (L) from the vibration sources to the considered sole vibration point were reduced gradually. 3.3. Geological conditions The site soil was coastal plain soil. Table 1 shows the surveyed soil layout and the physical and mechanical properties of the soil layers. In order from top to bottom, the soil formation consisted mainly of clayey silt, sandy silt and mucky silt clay. The topography of the test site was rather flat with the ground surface elevations between 4.3 m and 4.8 m. 3.4. Test results and analysis The ground vibrations were recorded in the form of acceleration histories of the considered vibration point at various distances in the vertical and radial directions. The results of four typical test cases are presented in Figs. 5 and 6, at distances (L) of 80 m, 100 m, 120 m and 150 m with falling heights (H) of 5.917 m, 5.968 m, 5.903 m and 5.975 m, respectively. A comparison on the maximum acceleration amplitudes in the two directions for the four test cases is presented in Table 2. It can be seen that: (1) The wave forms were typical vibration responses under a heavy impact, particularly one sharp acceleration peak at the nearest distance, i.e., L = 80 m, was recognizable for each direction. (2) The maximum acceleration amplitude occurred in the radial direction and reached a remarkable level of about 0.16 m/s2 at the distance of 80 m. However, the acceleration amplitudes in both directions decreased significantly with increases in distance, indicating a quick attenuation of the wave during propagation. (3) The main part of the vibration durations lasted for about 0.5 s and 1.0 s in the case of distances (L) of 80 m and 150 m, respectively, partially due to the results of multiple reflections and refractions in the layered soils. The considered vibration point then tended to return to its stationary position.
Fig. 4. Equipment layout of falling weight tests.
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Table 1 Soil layout and soil properties in the falling weight tests. Property
Symbol
Unit
Thickness of soil layer Density Shear elastic modulus Poisson’s ratiob Cohesion Internal friction angle Damping ratio
hi Gd0 c
m kg/m3 MPa – kPa
a b
◦
%
Values Clayey silt (uppermost)
Sandy silt
Mucky silt clay
7.8(8)a 1929 28.88 0.4 7.40 30.9 1.15
10 1948 77.22 0.4 5.89 30.4 0.92
12 1813 99.30 0.4 13.85 13.8 1.13
Thickness of the soil layers in parenthesis was actually used in this study to fit the mesh size. Poisson’s ratio was determined empirically.
Fig. 5. Test and simulation acceleration histories of the vibration point in the vertical direction at various distances in the falling weight tests (“—” denotes the test results and “- -” denotes the simulation results).
Fig. 6. Test and simulation acceleration histories of vibration point in the radial direction at various distances in the falling weight tests (“—” denotes the test results and “- -” denotes the simulation results).
(4) The maximum acceleration amplitudes in the radial direction were larger than the corresponding ones in the vertical direction in the considered ground region, similar to the results observed by Kwang and Tu (2006).
The Fourier amplitude spectra of the acceleration histories of the considered vibration point for the four test cases were derived and are shown in Figs. 7 and 8. A uniform shape for these spectra curves was not found, and a dominant frequency peak was not obvious. This is probably because the considered vibration point was actually located in the relatively far field, leading to an occurrence of multiple refractions and reflections. However, a primary
frequency band for both directions was recognizable, i.e., in the range of 5–15 Hz, similar to other test records (Gu and Lee, 2002; Kwang and Tu, 2006).
Table 2 Maximum acceleration amplitudes of the ground vibrations in the falling weight tests. Direction
Vertical Radial
Maximum acceleration amplitudes (m/s2 ) L = 80 m
L = 100 m
L = 120 m
L = 150 m
0.080 0.160
0.045 0.087
0.030 0.057
0.017 0.033
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Fig. 7. Fourier acceleration amplitude spectra of vibration point in the vertical direction at various distances in the falling weight tests (“—” denotes the tested results and “- -” denotes the simulated results).
L=80m
0.010 0.005 0.000 0.00
5.00
0.015
a (m/s2)
a (m/s2)
0.015
L=100m
0.010 0.005 0.000 5.00
0.00
10.00 15.00 20.00 25.00 f (Hz) L=120m
0.010 0.005 0.000 0.00
5.00
0.015 a (m/s2)
a (m/s2)
0.015
10.00 15.00 20.00 25.00 f (Hz) L=150m
0.010 0.005 0.000 5.00
0.00
10.00 15.00 20.00 25.00
10.00 15.00 20.00 25.00 f (Hz)
f (Hz)
Fig. 8. Fourier acceleration amplitude spectra of vibration point in the radial direction at various distances in the falling weight tests (“—” denotes the tested results and “- -” denotes the simulated results).
4. “Falling weight-soil” model 4.1. Modeling of soil and falling weight A finite element method (FEM) based “falling weight-soil” model was developed for the prediction of the impact-induced ground vibration. The model was built using a commercial finite element program, ANSYS/LS-DYNA, as illustrated in Fig. 9. Firstly, for the modeling of the soil, the mechanical behaviors of the layered soils were assumed to be ideal elasto-plastic, which can be described using the Drucker–Prager model (Drucker and Prager, 1952). Gu and Lee (2002) applied this model and successfully predicted the ground response to the DC of dry sand. Additionally, the eight-node isoparametric element Solid164 was used for the soil elements.
Fig. 9. “Falling weight-soil” model.
For the determination of the mesh size of the soil, it was suggested that the accuracy and numerical efficiency should be both considered. In general, 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 wave length corresponding to the dominant frequency, fT , of the wave; and v denotes the propagation velocity of the wave under consideration. The Rayleigh wave (R-wave) played a predominant role in the ground vibration for these tests (Bolt, 1988); hence, its propagation velocity can be taken as 172 m/s, following a calculation according to the properties of the layered soils in Table 1. When the dominant wave frequency, fT , was conservatively considered as 5 Hz, the mesh size, le , was derived and varied in the range of 2.9–5.8 m, according to Eq. (1). Based on this, two general mesh sizes – 5 m × 5 m × 5 × m and 2.5 m × 2.5 m × 2.5 m – were tested, resulting in very similar results. However, the former offered better numerical efficiency and was, therefore, adopted. In addition, mesh sizes of 4–5 m were also used in the soil model, in order to fit the actual thickness of different soil layers. The commonly used non-reflecting boundaries (transmitting boundaries) were set in the undersurface and the four vertical surfaces of the soil model, so that the waves could transmit through
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these boundaries without reflections and refractions, as they actually did in the real soil without artificial boundaries. The dimensions of the soil model were adopted as 400 m × 400 m in the horizontal plane with a thickness of 30 m, based on the theory of R-wave propagation and trial computations. Secondly, for the modeling of the falling weight, the eight-node isoparametric element Solid164 was also used, together with a rigid material model (compared to soft soil). Mesh sizes of about 1 m were used. Finally, contact and collision actions occurred between the falling weight and the soil during DC. To describe these actions, the widely used penalty function method was adopted to implement the contact-collision algorithm (Hallquist, 2006). The dynamic equations were solved using a central difference scheme, in which a default time step, t, of 9.59 × 10−5 s was applied. 4.2. Simulated results and discussion With the aid of the developed FEM model, the acceleration histories of the considered vibration point at various distances in the falling weight tests could be simulated. The simulation results of the four test cases are illustrated in Figs. 5 and 6 and compared with the test data. One can see that satisfactory agreement was achieved both in the acceleration amplitudes and vibration durations. Additionally, comparisons of the derived Fourier acceleration amplitude spectra of the vibration point in the vertical and radial directions between the simulated and test results are presented in Figs. 7 and 8, respectively. Although the simulated curves did not fit the test ones very well, their dominant frequency band was quite similar, i.e., 5–15 Hz. The reasons for the differences may be mainly attributed to the following aspects: (1) The falling weight may have fallen down onto the ground surface with a minor obliquity, which has not been considered in the model. (2) In the tests, the sensors may not have been exactly placed in the expected vibration point and in the desired directions. Moreover, the sensors were probably not in perfect contact with the soft surface of the ground to ensure a synchronous motion due to the inertia of the sensors. (3) The soil parameters and thickness of the soil layers used in the model may not have been exactly in conformance with those of the site soil, due to survey errors or quality variation of the soil specimens.
Fig. 10. Profile of the cooling tower.
of the whole tower shell. Meanwhile, the residual 60 columns were crushed into pieces sequentially, due to the action of the tower gravity. The tower shell then contacted the ground surface with an inclination angle of about 3◦ . Subsequently, the tower strongly struck the ground and finally disintegrated. This collapse mode is labeled as “collapse in integrity” in this study. Dissimilarly, after the wind load was applied for load case 2, a large part of the upper shell became concaved and cracked. The tower then disintegrated, broke into fragments and finally dropped on the ground. However, the lower portion of the shell did not break up and survived the disaster. This collapse mode is labeled as “collapse in fragments” in this study. It is meaningful to distinguish between the two collapse modes. As mentioned above, the columns failed in the collapse mode of “collapse in integrity”, but survived in that of “collapse in fragments”. In order to simulate the failure of the columns, we had to use many solid elements, due to the limitation of the used program, i.e., a column contained 432 elements for concrete and 288 elements for steel bars. In total, the 120 columns contained 86,400 elements, resulting in tremendous numerical computation. This disadvantage is corrected in Section 6, based on the different collapse modes.
5. Collapse simulation of the cooling tower The planned cooling tower was designed to be constructed with reinforced concrete, with 120 columns that are 18 m high at the bottom. Its profile is illustrated in Fig. 10. Two accidental loads that may cause the tower to collapse were considered in this study. One was the sudden removal of 60 columns (simply named as load case 1), as a result of, for example, a bomb attack or foundation settlement. The other was an extremely strong wind load (wind velocity of 44.3 m/s, Beaufort Scale 14, simply named as load case 2). The simulations indicated that the cooling tower collapsed under the two load cases. However, for brevity, the details of the cooling tower, the structural model as well as the collapse simulation are not presented here, but were described by Li et al. (2011). The simulation also indicated that the collapse modes of the tower exhibited different characteristics under the two load cases, as demonstrated by the two pictures from the collapse simulation in Fig. 11. For load case 1, firstly, the tower shell began to incline in the “removal” direction after the sudden removal of the columns, sinking in integrity, almost without changing the profile
Fig. 11. Collapse of the cooling tower in load case of (a) a sudden removal of 60 columns and (b) an extremely strong wind.
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Table 3 Maximum acceleration amplitudes and vibration durations of the ground vibrations in the event of the collapse of the cooling tower. Load case
1 2
Fig. 12. “Cooling tower-soil” model for the prediction of ground vibration caused by the collapse of the cooling tower in load case of (a) a sudden removal of 60 columns and (b) an extremely strong wind.
6. “Cooling tower-soil” models Two “cooling tower-soil” models were developed from the “falling weight-soil” model for the prediction of the ground vibrations caused by the two collapse modes of the cooling tower. The difference between the two models lay only in the modeling of the cooling tower for the purposes of avoiding tremendous numerical computation. The “cooling tower-soil” model for load case 1 is illustrated in Fig. 12(a) with the modeling of the tower shell being identical to that in (Li et al., 2011). In Fig. 12(a), a small distance, i.e., 0.5 m, was set between the lowest point of the tower shell and the ground in the model for load case 1 for convenience of computation. The residual 60 columns were intentionally removed from the model, so that the element number could be reduced remarkably; and the computational time was limited to within one day for the current commonly used personal computer. When the collapsed cooling tower just contacted the ground surface, the whole tower shell hold its profile almost in integrity and reached a motion state with an inclination angle of 3◦ and a vertical velocity of approximately 16.3 m/s (Li et al., 2011). The horizontal velocities of the tower shell were relatively small and could be ignored. As a result, the collapse process of the cooling tower was believed to have no significant change in comparison to that using the model with the 60 columns retained, based on a comparative trial. In the simulation, when the tower shell impacted the ground, it disintegrated into fragments under gravity. Eventually, the fragments dropped onto the ground and may have also broken into pieces, and formed debris. The model for load case 2 is illustrated in Fig. 12(b). In this model, the modeling of the tower shell was also identical to that in Li et al. (2011), while the modeling of the columns was different. Each column was simulated as one beam element, instead of a number of solid elements used in the model in Fig. 11(b). The column model using the beam element overestimated the load bearing capacity of the real column. However, the collapse processes of the cooling tower were almost the same between the collapse modes illustrated in Figs. 11(b) and 12(b), because actually all the columns and the lower portion of the tower shell did not fail. By doing this, the element number of the columns was reduced remarkably; thus, the numerical computation was also reduced significantly. In the simulation, the tower shell disintegrated into fragments under wind and gravity, dropped on the ground and formed debris. In Fig. 12, the foundation of the planned cooling tower was rock, described using a linear elastic material model. The soil parameters were considered to be density () of 2700 kg/m3 , elastic modulus (E) of 4.00 × 104 MPa, Poisson’s ratio () of 0.2 and damping ratio () of 5%. The dimensions of the rock model were 1000 m × 1000 m in the horizontal plane with a thickness of 50 m. The mesh size was 5 m × 5 m × 5 m, which was accurate enough in comparison with that of the “falling weight-soil” model, because the R-wave of rock
Direction
Vertical Radial Vertical Radial
Maximum acceleration amplitudes (m/s2 )
L = 200 m
L = 300 m
L = 400 m
L = 500 m
2.96 1.97 0.57 0.38
1.10 1.52 0.16 0.07
0.54 0.50 0.06 0.04
0.15 0.25 0.01 0.02
Vibration duration (s)
6.8 9.0
has a much large propagation velocity. Non-reflecting boundaries were also set, as adopted in the “falling weight-soil” model. A strategy was devised to counteract the reduction of the amount of contributed structural elements during the numerical computation and was achieved by increasing the material density of the residual tower, because the model was based on FEM. As generally known, when cracked or crushed, the elements are “killed” and then “disappear” from the model. As a result, the sum of the contributing structural elements and the total mass and impulse were gradually reduced during the simulation process. However, such a result is inconsistent with reality. This inconsistency was approximately eliminated by means of the following steps: (1) Dividing the whole simulation time into several time periods, (2) Checking the disappeared mass of the structure at each end of the time period, and (3) Increasing the material density of the residual tower to keep the total mass constant and partly, to compensate for the loss of impulse. 7. Ground vibration With the aid of the “cooling tower-soil” models, the ground vibrations were obtained in the form of acceleration histories of vibration points at various distances in the vertical and redial directions. Some results are illustrated in Figs. 13 and 14 for load cases 1 and 2, respectively, at distances (L) of 200 m, 300 m, 400 m and 500 m. These distances denote the horizontal length from the considered vibration point to the ground center of the cooling tower, in the collapse direction of the tower. This region was of interest because this is the most likely location of the nuclear island. The derived Fourier acceleration amplitude spectra of the vibration points are presented in Figs. 15 and 16 for load cases 1 and 2, respectively. For clarity, the maximum acceleration amplitudes and vibration durations are listed in Table 3. It was found that: (1) The considered ground region may experience a severe vibration. With load case 1, the maximum acceleration amplitudes were about 0.3g and 0.2g in the field at a distance (L) of 200 m in the vertical and radial directions, respectively. This was mainly due to the tremendous impulse that was transferred from the cooling tower to the ground. (2) The excited ground vibration was more intense in load case 1 than that in load case 2. This may be primarily attributed to the different collapse modes of the tower. For load case 1, the whole part of the tower shell impacted the ground and then disaggregated, following the drop of the fragments on the ground successively in a relative short time; whereas, for load case 2, only the upper part of the tower shell disaggregated with the fragments dropping on the ground, thus resulting in a relatively light ground vibration. (3) The vibration attenuated rapidly in both directions with increases in distance. The attenuation rate in the vertical direction was greater than that in the radial direction. In relation
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
vertical direction L=200m
3.00 1.50 0.00 -1.50 -3.00
a (m/s2)
a (m/s2)
96
4.00 t (s)
6.00
8.00
0.00
vertical direction L=400m
3.00 1.50 0.00 -1.50 -3.00 0.00
2.00
4.00 t (s)
6.00
0.00
2.00
4.00
6.00
4.00 t (s)
2.00
4.00 t (s)
0.00
2.00
a (m/s2)
a (m/s2)
radial direction L=400m
0.00
2.00
4.00
6.00
8.00
4.00
6.00
8.00
t (s)
t (s) 2.00 1.00 0.00 -1.00 -2.00
8.00
radial direction L=500m
2.00 1.00 0.00 -1.00 -2.00
8.00
6.00
vertical direction L=500m
0.00
radial direction L=200m
2.00 1.00 0.00 -1.00 -2.00
2.00
3.00 1.50 0.00 -1.50 -3.00
8.00
a (m/s2)
a (m/s2)
2.00
a (m/s2)
a (m/s2)
0.00
vertical direction L=300m
3.00 1.50 0.00 -1.50 -3.00
6.00
8.00
radial direction L=500m
2.00 1.00 0.00 -1.00 -2.00 0.00
2.00
4.00 t (s)
t (s)
6.00
8.00
Fig. 13. Simulated acceleration histories of vibration points in the event of the collapse of the cooling tower in load case 1.
to this, in the “near” field (L = 200–300 m), the acceleration amplitudes in the vertical direction were larger than the corresponding ones in the radial direction. However, these results were reversed in the “far” field (L = 500 m), because the amplitude of the surficial particle motion, either in the vertical or in the radial direction, is the result of the propagation of different types of waves (Raleigh, primary and secondary waves). As is generally known, the wave propagations are direction oriented and exhibit different attenuation rates that generally depend on the frequency of the vibration, the type of soil and radiation damping (Athanasopoulos et al., 2000). As a result, the acceleration amplitude of the ground vibration in each direction, which is one of the forms to describe the surficial particle motion, attenuated depending on individual characteristics. Based on this knowledge, the authors believe that the characteristics of the vibration attenuation observed in this study cannot be considered as general rules and may vary from case to case. (4) The vibration duration lasted for about 6.8 s and 9.0 s for load cases 1 and 2, respectively. Both were much shorter than the duration time of a common earthquake. For comparison, the ground vibration, induced by the blasting demolition of a 140 m high chimney with the foundation dominantly consisting of clay marl overlaying moisture sand, lasted for about 2 s (Stangenberg and Zinn, 1998). (5) The frequency band of the vibration lay mainly in the range of 0–25 Hz and 0–8 Hz for load cases 1 and 2, respectively, showing an appreciable difference. This indicated different impact
effects between the tower shell and the ground, essentially due to the different collapse modes of the two load cases. The underground vibration was also investigated for the safety evaluation of the facilities embedded in the subsoil. Table 4 presents the maximum acceleration amplitudes of the underground vibrations in the event of a collapse of the cooling tower as in load case 1, with respect to the depth, H, of the observed vibration points. One can see that the vibration attenuated rapidly with a rate greater than linearity. These results imply that increasing the burial depth contributes to the efficient reduction of vibration, which may be used as a possible design method for vibration reduction of nuclearrelated facilities. Table 4 Maximum acceleration amplitudes of the underground vibrations in the event of the collapse of the cooling tower in load case 1. Depth (m)
Direction
0
Vertical Radial Vertical Radial Vertical Radial Vertical Radial
10 20 30
Maximum acceleration amplitudes (m/s2 ) L = 200 m
L = 300 m
L = 400 m
L = 500 m
2.96 1.97 2.28 1.01 1.53 0.71 0.97 0.66
1.10 1.52 0.99 0.52 0.72 0.30 0.41 0.27
0.54 0.50 0.50 0.21 0.39 0.11 0.24 0.10
0.15 0.25 0.14 0.16 0.13 0.06 0.11 0.04
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
97
Fig. 14. Simulated acceleration histories of vibration points in the event of the collapse of the cooling tower in load case 2.
8. Parametric study and vibration reduction
8.1. Collapse profiles
A parametric study was conducted for the purposes of investigating the influential factors affecting the ground vibration and of exploring the possible methods for vibration reduction. As is generally known, the ground vibration depends on the characteristics of the vibration source and the soils that are the medium for the wave propagation (Woods and Jedele, 1985; Athanasopoulos et al., 2000). The characteristics of the vibration source are associated with the collapse modes and profiles. The mode of “collapse in integrity” was chosen for this study, since it excited more intense ground vibration than the “collapse in fragments” mode. From the study in Sections 6 and 7, we knew that ground vibration was excited mainly due to the impact of the tower shell and its fragments dropping on the ground, while the columns affected the inclination angle and vertical velocity of the tower shell. Therefore, the collapse profiles may be described with the inclination angle and vertical velocity. In this regard, three influential factors affecting the ground vibration were considered, i.e., collapse profile, site geology and arrangement of an isolation trench. The “cooling tower-soil” model for the chosen collapse mode used in Section 6 was also adopted, with all the columns in the lower part of the tower not being included in the model for brevity and clarity.
The inclination angle and vertical velocity were considered as two critical factors for the collapse profile of the tower shell when it just reached the ground surface. The rock foundation of Section 6 was adopted. 8.1.1. Inclination angles Two inclination angles of the tower shell (i.e., 0◦ and 6◦ ) were chosen for comparison to the 3◦ in Section 6. For the three considered inclination angles, it was assumed that the tower shells freely dropped in integrity with the same height of the center of mass. Consideration that the columns were 18 m high and the diameter of the bottom part of the tower shell was 176 m led to a theoretically maximum inclination angle of the tower shell of about 6◦ . As a result, the falling tower shell with a larger inclination angle would reach the ground surface earlier with a slower vertical velocity. In summary, for the three considered cases, the inclination angles of the tower shell were 0◦ , 3◦ and 6◦ with vertical velocities of 18.8 m/s, 16.3 m/s and 13.4 m/s, as illustrated in Fig. 17(a), Fig. 12(a) and Fig. 17(b), respectively. A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the three considered cases is presented in Table 5. A result similar to result (3) in Section 7 was found. Moreover, it was also found that the case with an inclination angle of 0◦
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F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
Fig. 15. Fourier acceleration amplitude spectra of vibration points in the event of the collapse of cooling tower in load case 1.
led to the most intensive ground vibration with the maximum acceleration amplitude, even up to about 1g. However, its vibration duration, i.e., of about 5.7 s, was the shortest one of the three. This result can be mainly attributed to the different collapse profiles of the tower shell. For the collapse profile with an inclination angle of 0◦ , the impact was finished in the shortest time with a possible complete impact area, among the three considered cases. Thus, under the condition that there were no extraordinary differences of the total impulses among the three cases, the excited ground vibration was most intensive with the maximum acceleration amplitude. On the other hand, this collapse profile was probably the most adverse among the three cases, because, as the simulation indicated, the tower shell disintegrated in the shortest time, leading to the shortest ground vibration duration.
8.1.2. Vertical velocities Assuming that all the columns in the bottom part of the cooling tower fail simultaneously, we can consider that the tower shell freely falls and reaches a vertical velocity of 18.8 m/s at the moment when it just touches the ground surface, since the height of the columns was 18 m. However, the actual vertical velocity at this moment is always less than the free-fall velocity, due to the obstructive effect of the residual parts of the columns. For comparison, three vertical velocities at this moment were chosen, i.e., 18.8 m/s, 15.3 m/s and 10.8 m/s, with an inclination angle all of 0◦ . A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the three considered cases is presented in Table 6. Again, a result similar to result (3) in Section 7 was found. Moreover, not surprisingly, the case with the most rapid velocity led to the most intensive ground vibration and the shortest vibration duration. This
Table 5 Maximum acceleration amplitudes of the ground vibrations at various distances for the collapse profiles of the cooling tower with different inclination angles. Inclination angle (◦ )
Direction
0
Vertical Radial Vertical Radial Vertical Radial
3 6
Maximum acceleration amplitudes (m/s2 )
Vibration durations (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 2.96 1.97 2.17 1.79
2.17 2.20 1.10 1.52 0.91 0.83
1.38 1.27 0.54 0.50 0.48 0.27
0.44 0.57 0.15 0.25 0.11 0.22
5.7 6.8 7.6
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
vertical direction L=200m
0.024 0.012 0.00
2.00
4.00 6.00 f (Hz)
0.012 0.00
10.00
0.024 0.012
2.00
4.00 6.00 f (Hz)
8.00
10.00
vertical direction L=500m
0.036
a (m/s2 )
a (m/s2 )
8.00
vertical direction L=400m
0.036
0.024 0.012 0.000
0.000 0.00
2.00
4.00 6.00 f (Hz)
8.00
0.00
10.00
radial direction L=200m
2.00
0.020 0.010 0.000
4.00 6.00 f (Hz)
8.00
10.00
radial direction L=300m
0.030
a (m/s2 )
0.030
a (m/s2 )
0.024
0.000
0.000
0.020 0.010 0.000
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
0.00
radial direction L=400m
2.00
0.020 0.010 0.000
4.00 6.00 f (Hz)
8.00
10.00
radial direction L=500m
0.030
a (m/s2 )
0.030
a (m/s2 )
vertical direction L=300m
0.036
a (m/s2 )
a (m/s2 )
0.036
99
0.020 0.010 0.000
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
Fig. 16. Fourier acceleration amplitude spectra of vibration points in the event of the collapse of cooling tower in load case 2.
is because, among the three considered cases, the fastest velocity means the largest impulse, generally exciting the most intensive ground vibration. On the other hand, the greatest velocity initiated the strongest interaction between the cooling tower and the ground, resulting in the shortest time for the disintegration of the tower collapse as well as for the duration of the ground vibration. The study results in Section 8.1 indicate that, for the possible collapse profiles of the cooling tower in load case 1, increasing the load bearing capacity and the ductility of the columns may weaken the impact of the collapsed tower on the ground, helping to efficiently reduce the ground vibration.
8.2. Site geologies It is usually desired that the cooling tower in a nuclear power station be constructed on a rock-like foundation, sometimes with overlaying soft soil due to the geological limitations of the plant. In general, the overlaying soft soil may aggravate the effect of the structural damage compared to a solely rock-like foundation in the event of an earthquake (Eurocode 8, 2003). However, this is not the case when the vibration source and the considered vibration points are all on the ground surface. In this condition, the overlaying soft soil seems to
Table 6 Maximum acceleration amplitudes of the ground vibrations at various distances for the collapse profiles of the cooling tower with different vertical velocities. Vertical velocity (m/s)
Direction
18.8
Vertical Radial Vertical Radial Vertical Radial
15.3 10.8
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 4.45 3.64 4.03 3.39
2.17 2.20 2.07 1.45 1.92 1.15
1.38 1.27 0.91 0.97 0.69 0.77
0.44 0.57 0.22 0.43 0.19 0.39
5.7 6.7 7.5
100
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
Fig. 17. “Cooling tower-soil” model with the inclination angle of the tower shell of (a) 0◦ and (b) 6◦ . Fig. 18. “Cooling tower-soil” model with the arrangement of isolation trench with a depth of 5 m or 10 m.
Table 7 Assumed soil properties for “soil-rock” foundation. Property
Unit
Value
Density Shear elastic modulus Poisson’s ratio Cohesion Internal friction angle Damping ratio
kg/m3 MPa – kPa
1800 100 0.35 10 15 5.00
◦
%
work as a flexible gas cushion, resulting in vibration reduction. To demonstrate this, two types of site geology were considered here. One was a solely rock foundation; and the other was a “soilrock” foundation, i.e., overlying soft soil to a depth of 10 m with the same rock foundation underneath. The material model for rock was described in Section 6. The mechanical properties of the soil were depicted using the Drucker–Prager model with the assumed parameters listed in Table 7. The inclination angle was 0◦ with a vertical velocity of 18.8 m/s when the tower shell just reached the ground surface. A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the two considered cases is presented in Table 8. It was found that the ground vibration was dramatically reduced for the soil-rock foundation and that the vibration duration became shorter, compared to those of the solely rock foundation. In particular, for a distance (L) of greater than or equal to 300 m, the ground vibration of the foundation with overlaying soil was so small that the structures in this region may hardly suffer any damage. From the viewpoint of application, this finding also suggests an efficient method for vibration reduction. 8.3. Arrangement of an isolation trench An open or filled isolation trench is often used in engineering practice to reduce ground vibration generated by various factors. This method of vibration isolation can be classified into two categories: source isolation and receiver isolation (Klein et al., 1997; Adam and Estorff, 2005). The former is used to reduce the vibrations at their source; whereas, on the other hand, the latter is
usually built away from the source, surrounding the structure to be protected. A good deal of research efforts, both experimental and numerical, have been devoted to the vibration screening by open trenches (Ahmad and Al-Hussaini, 1991; Klein et al., 1997; Adam and Estorff, 2005; Celebi et al., 2009). These studies concluded that using an open isolation trench could reduce the ground vibrations significantly. Generally, the effect of vibration reduction depends mainly on the depth and width of the trench. The trench depth is the governing factor compared to the trench width. An analytical approach has rarely been used, because its solutions are usually limited to ideal conditions. In this part of the parametric study, we chose an open isolation trench as a method of source isolation, because it provides effective and low-cost isolation measures. Two different isolation trenches, both with a length of 220 m and a width of 5 m, were set in the model, as illustrated in Fig. 18. Their width was determined in conformance with the mesh size of the foundation model. The difference between the two trenches was their depth: one was 5 m, and the other was 10 m. For each trench, the distance between the ground center of the cooling tower and the neighboring edge of the trench was approximately 100 m, ensuring that almost all the fragments fell to one side of the trench, i.e., did not cross the trench. A rock foundation, an inclination angle of 0◦ and a vertical velocity of 18.8 m/s when the tower shell just reached the ground surface, were adopted. Table 9 presents the comparative results of the maximum acceleration amplitudes of the ground vibrations for different points located on the side of the trench. It can be seen that the ground vibrations were significantly reduced by adding an isolation trench. For trench depths of 5 m and 10 m, the reduction percentages of the maximum acceleration amplitudes of the ground points at different distances were in the range of 23–49% and 48%–70% compared to those without a trench, respectively. These results were comparable to Ahmad and Al-Hussaini’s results (1991). The vibration durations of the three considered cases had almost no significant change and were all around 5.7 s. Similarly, it was also observed in a numerical study by Adam and Estorff (2005) that hardly any change in the ground vibration durations occurred when different depths of open trenches were used.
Table 8 Maximum acceleration amplitudes of the ground vibrations at various distances for different site geologies. Site geology
Direction
Rock
Vertical Radial Vertical Radial
Soil + rock
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 0.25 1.16
2.17 2.20 0.03 0.29
1.38 1.27 0.01 0.07
0.44 0.57 0.01 0.03
5.7 4.3
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
101
Table 9 Maximum acceleration amplitudes of the ground vibrations for open trenches with different depths. Trench depth (m)
0 5 10
Direction
Vertical Radial Vertical Radial Vertical Radial
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 6.82 2.85 4.37 1.89
2.17 2.20 1.41 1.70 0.89 1.15
1.38 1.27 0.77 0.65 0.55 0.60
0.44 0.57 0.24 0.30 0.13 0.19
9. Conclusions This study presents a comprehensive approach for the prediction of the ground vibration caused by the collapse of a huge cooling tower. The adopted “cooling tower-soil” model was based on the “falling weight-soil” model verified by the falling weight tests. The ground vibration was predicted in the form of acceleration histories and vibration durations of points at different distances from the ground center of the cooling tower. The following conclusions can be drawn from the study: (1) A severe ground vibration may occur in the considered region, with maximum acceleration amplitudes being about 0.3g and 0.2g at a distance (L) of 200 m in the vertical and radial directions in load case 1, respectively. (2) Different accidental loads may lead to different collapse modes of the cooling tower, resulting in ground vibrations that significantly differ from each other. (3) The vibrations in the vertical and radial directions exhibit different characteristics. For distances (L) from 200 m to 300 m, the maximum acceleration amplitudes in the vertical direction were larger than the corresponding ones in the radial direction. For a distance (L) of 500 m, however, the results were reversed. (4) The collapse profiles, site geologies and arrangements of an isolation trench may significantly affect the ground vibration. On the other hand, the results from the parametric study provide potential methods for vibration reduction. The current study has been aimed at providing a complete approach and a few general suggestions for the prediction of collapse-induced ground vibration. However, it should be noted that, in many practical cases, it seems appropriate to perform a similar investigation for the cooling tower–soil system under consideration, as has been done in this contribution. The results may vary from case to case, because the ground vibration mainly depends on the characteristics of the vibration source and the soil properties. In the conventional design of nuclear power stations, the considered accidental loads do not include the ground vibration due to the collapse of adjacent large-scale structures. However, this study has indicated that, with the increasing height of the cooling tower and the relatively small distance between the nuclear island and the cooling tower, the effect of collapse-induced ground vibration on the nuclear-related facilities cannot be ignored. Acknowledgements This research was sponsored by the National High-Tech Development Plan (863 Programme) under Grant No. 2012AA050903 and the Kwang-Hua Fund for the College of Civil Engineering, Tongji
5.7 5.7 5.7
University. The authors would like to extend their sincere gratitude to the Ministry of Science and Technology, China, and to Tongji University for their supports. References Adam, M., Estorff, O., 2005. Reduction of train-induced building vibrations by using open and filled trenches. Comp. Struct. 83, 11–24. Ahmad, S., Al-Hussaini, T.M., 1991. Simplified design for vibration screening by open and in-filled trenches. J. Geotech. Eng. (ASCE) 117 (1), 67–88. Athanasopoulos, G.A., Pelekisa, P.C., Anagnostopoulos, G.A., 2000. Effect of soil stiffness in the attenuation of Rayleigh-wave motions from field measurements. Soil Dyn. Earthq. Eng. 19, 277–288. Bolt, B.A., 1988. Earthquake. Freeman, New York. Bommer, J.J., Papaspiliou, M., Price, W., 2011. Earthquake response spectra for seismic design of nuclear power plants in the UK. Nucl. Eng. Des. 241, 968–977. Celebi, E., Firat, S., Beyhan, G., Cankaya, I., Vural, I., Kirtel,.O., 2009. Field experiments on wave propagation and vibration isolation by using wave barriers. Soil Dyn. Earthq. Eng. 29, 824–833. Drucker, D.C., Prager, W., 1952. Soil mechanics and plastic analysis for limit design. Quart. Appl. Math. 10 (2), 157–165. European Committee for Standardisation, 2003. Eurocode 8: Design of Structures in Seismic Regions, Part 1—General Rules and Rules for Buildings (prEN 19981:2003). Fu, D.J., Yang, F.L., Li, Q.H., et al., 2010. Simulations for tower collapses of 500 kV Zhengxiang transmission line induced by the downburst. In: International Conference on Power System Technology, Hangzhou, October 24–28, pp. 1–6. Gould, P.L., 2012. The influence of R&D on the design, construction and damage assessment of large cooling towers. In: 6th International Symposium on Cooling Tower (ISCT2012), Cologne, Germany, June 20–23, pp. 3–15. Gu, Q., Lee, F.H., 2002. Ground response to dynamic compaction of dry sand. Geotechnique 52 (7), 481–493. Hallquist, J.O., 2006. ANSYS/LS-DYNA Theoretical Manual. Livermore Software Technology Corporation, United States. JGJ 22-Committee, 2012. Specification for Design of Reinforced Concrete Shell Structures (JGJ22-2012). China Architecture & Building Press, Beijing, China. Kausel, E., Manolis, G., 2000. Wave Motion in Earthquake Engineering. WIT Press, Boston. Klein, R., Antes, H., Le Houedec, D., 1997. Efficient 3D modelling of vibration isolation by open trenches. Comp. Struct. 64 (1–4), 809–817. Krätzig, W.B., Zhuang, Y., 1992. Collapse simulation of reinforced concrete natural draught cooling tower. Eng. Struct. 14 (5), 291–299. Kwang, J.H., Tu, T.Y., 2006. Ground vibration due to dynamic compaction. Soil Dyn. Earthq. Eng. 26, 337–346. Lamb, H., 1904. On the propagation of tremors over the surface of an elastic solid. Philos. Trans. R. Soc. Lond. 203, 359–371. Li, Y., Lu, X.Q., Lin, F., Gu, X.L., 2011. Numerical simulation analysis on collapse of a super large cooling tower subjected to accidental loads. In: 21st International Conference on Structural Mechanics in Reactor Technology (SMiRT 21), New Delhi, India, November 6–11, pp. 349–357. Mitsuta, Y., Hayashi, T., Takemi, T., 1995. Two severe local storms as observed in the arid area of Northwest China. J. Meteor. Res. Japan 73 (6), 1269–1284. Pan, J.L., Selby, A.R., 2002. Simulation of dynamic compaction of loose granular soils. Adv. Eng. Software 33, 631–640. Stangenberg, F., Zinn, R., 1998. Bodenerschütterungen beim sprengtechnischen Abbruch von 140 m hohen Stahlbetonschornsteinen. In: Finite Elemente in der Baupraxis. Modellierung, Berechnung und Konstruktion. Beiträge zur Tagung FEM’98, Technischen Universität Darmstadt, Berlin, Ernst und Sohn, March 5–6, pp. 471–480. VGB-Technical Committee, 2005. VGB-Guideline, Structural Design of Cooling Towers. VGB PowerTech e.V., Germany. Woods, R.D., Jedele, L.P., 1985. Energy – attenuation from construction vibrations. In: Gazetas, G., Selig, E.T. (Eds.), Vibration Problems in Geotechnical Engineering. Special Publication of ASCE, pp. 229–246.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Prediction of ground vibration due to the collapse of a 235 m high cooling tower under accidental loads Feng Lin a , Yi Li a , Xianglin Gu a,∗ , Xinyuan Zhao a , Dongsheng Tang b a b
Department of Building Engineering, Tongji University, No. 1239 Siping Road, Shanghai 200092, China Guangdong Electric Power Design Institute, No. 1 Tianfeng Road, Guangzhou, Guangdong 510663, China
h i g h l i g h t s Ground vibration due to the collapse of a huge cooling tower was predicted. Accidental loads with different characteristics caused different collapse modes. Effect of ground vibration on the nuclear-related facilities cannot be ignored.
a r t i c l e
i n f o
Article history: Received 7 December 2011 Received in revised form 17 December 2012 Accepted 8 January 2013
a b s t r a c t A comprehensive approach is presented in this study for the prediction of the ground vibration due to the collapse of a 235 m high cooling tower, which can be caused by various accidental loads, e.g., explosion or strong wind. The predicted ground motion is to be used in the safety evaluation of nuclear-related facilities adjacent to the cooling tower, as well as the plant planning of a nuclear power station to be constructed in China. Firstly, falling weight tests were conducted at a construction site using the dynamic compaction method. The ground vibrations were measured in the form of acceleration time history. A finite element method based “falling weight-soil” model was then developed and verified by field test results. Meanwhile, the simulated collapse processes of the cooling tower under two accidental loads were completed in a parallel study, the results of which are briefly introduced in this paper. Furthermore, based on the “falling weight-soil” model, “cooling tower-soil” models were developed for the prediction of the ground vibrations induced by two collapse modes of the cooling tower. Finally, for a deep understanding of the vibration characteristics, a parametric study was also conducted with consideration of different collapse profiles, soil geologies as well as the arrangements of an isolation trench. It was found that severe ground vibration occurred in the vicinity of the cooling tower when the collapse happened. However, the vibration attenuated rapidly with the increase in distance from the cooling tower. Moreover, the “collapse in integrity” mode and the rock foundation contributed to exciting intense ground vibration. By appropriately arranging an isolation trench, the ground vibration can be significantly reduced. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In earthquake-prone areas, seismic design should be carefully performed for the design of a nuclear power station (Bommer et al., 2011). However, the ground vibration due to the collapse of a huge structure, e.g., a cooling tower, is usually not considered. With increases in the height and mass of a tower-like structure, the ground vibration may become more intensive when collapse happens. Hence, it is reasonable to be concerned about whether this kind of ground vibration may damage the safe operation of nearby nuclear-related facilities. Unfortunately, this particular
∗ Corresponding author. Tel.: +86 21 6598 2928; fax: +86 21 6598 2928. E-mail address: [email protected] (X. Gu). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.01.022
issue has not been given serious attention, as few studies have addressed it. As a contribution to the mentioned problematic concern, this study presents a comprehensive approach for the prediction of the ground vibration due to the collapse of a cooling tower. The study motivation comes from a new water cooling tower with an overall height of 235 m, which will be built as a part of the construction of a planned nuclear power station in southern China. A cooling tower of such a great height, probably the highest planned one worldwide, raises a number of questions. One of the most interesting issues is the proper predication of collapse-induced ground vibrations, because the planned cooling tower is to be adjacent to the nuclear island with their spacing to be about 200 m, which is also the usual distance for other planned nuclear power stations in China due to limited space. In the event of the collapse of the
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F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
Fig. 1. Methodology applied in this study.
cooling tower, the collapse-induced vibration may detrimentally affect the safe operation of the nuclear-related facilities. The causes that may induce the tower to collapse could be various accidental loads, such as an explosion or strong wind. The study results, in terms of the characteristics of the vibration, will be used as input data for the safety evaluation of nuclear-related facilities, as well as the plant planning of nuclear power stations. Studies on the ground vibration induced by a falling weight can be traced back to at least Lamb (1904). He studied the vibration of a semi-infinite body under a vertically concentrated harmonic force and derived an analytical solution for the displacement in an integral form. Subsequently, with the rapid development of computational technology, numerical simulation is being applied with increasingly frequency for the description of the ground motion. Gu and Lee (2002) studied the ground response to the dynamic compaction (DC) of dry sand, using two-dimensional finite element analyses with a large-strain dynamic formulation and a cap model for the soil behavior. As a result, the stress wave attenuation and improvement effects were realistically predicted. Pan and Selby (2002) numerically simulated the DC of loose soils under dynamic loads. A full axisymmetric elasto-plastic finite element representation was generated for the soils. The impact of the drop mass was modeled in two ways – a force–time input and a rigid body – both resulting in well simulated results of DC. On the other hand, a few measurements of ground vibration from field tests were also performed, with different vibration sources, e.g., a chimney with a height of 140 m and a weight of 2600 tons (Stangenberg and Zinn, 1998) or a falling weight of 25 tons weight used in DC (Kwang and Tu, 2006). For the evaluation of the ground vibration induced by the collapse of a cooling tower, which is characterized as a huge thin-walled reinforced concrete structure, few studies and suggestions were found in either technical handbooks or research papers. Therefore, the executed study has both academic and engineering significance. It is assumed that the cooling towers, like these in Germany and in France, will not collapse when built under the conditions of rational site selection, design, construction and maintenance, without suffering severe natural or man-made disasters. However, China is among the most natural disaster prone countries in the world. In extreme circumstances, e.g., explosion or strong wind, the cooling tower may partially or totally collapse (Gould, 2012; Krätzig and Zhuang, 1992). The explosion may be executed by terrorist attack, and the strong wind happens occasionally in China, such as typhoon, tornado, downburst (Fu et al., 2010) and squall line (Mitsuta et al., 1995). These accidental loads are usually not considered in practice according to the current design concept (VGB Guideline, 2005; JGJ22-2012, 2012), but they may occur in the small probability cases. For instance, nuclear accident happened at Fukushima, Japan, 2010, because of both strong earthquake and tsunami.
(1) Conducting the falling weight tests. (2) Developing a “falling weight-soil” model and verifying it with the tests. (3) Simulating the collapse of the cooling tower. (4) Developing “cooling tower-soil” models based on the “falling weight-soil” model. (5) Predicting the ground vibration using the “cooling tower-soil” models. (6) Performing a parametric study of the ground vibration. (7) Proposing suggestions for the design of the nuclear-related facilities and for plant planning. The gray contents in Fig. 1, including the collapse of the cooling tower (step (3)) and the application of this study (step (7)), are not presented in detail in this paper. Moreover, to keep the numerical computation in step (5) at an acceptable level for the current commonly used personal computer, appropriate numerical strategies, as described in Section 6, were employed to keep the computational cost down. 3. Falling weight tests 3.1. Dynamic compaction Dynamic compaction (DC) is a well-known method of site improvement by treating loose soils on site (Gu and Lee, 2002; Pan and Selby, 2002). The construction procedure involves dropping a heavy weight (pounder) from a certain height over the ground surface to be compacted. A number of researchers have studied the design and assessment of DC, mainly focusing on the load bearing capacity or improvement depth of the site soils. In this regard, falling weight tests were conducted by the authors in a construction site near Hangzhou, China, where DC was being used for soil improvement. As illustrated in Fig. 2, the DC facilities included a crawler crane and a falling weight with a self-release
2. Study methodology The methodology applied in this study is schematically illustrated in Fig. 1 and was achieved through the following steps:
Fig. 2. DC facilities.
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
5m
5m
5m
5m
tamping direction tamping points conducted in DC L
considered vibration point
tamping points used in falling weight test Fig. 3. Tamping sequence of the second pass of DC.
mechanism. The falling weight was about 12 tons with a diameter of 2.5 m and was made of a concrete-filled steel shell. In the tests, the pounder was slowly slung to a height of about 6 m and then freely dropped, impacting the soil surface and, consequently, inducing ground vibration. As often used, three phases of impact (normally called passes) were conducted. In each pass, each tamping point was tamped twice. The tests were executed in the second pass, with the tamping sequence shown in Fig. 3. In this pass, the arrangement of the tamping points followed an approximate square-grid pattern with a spacing of about 5 m from center to center. The ground vibrations were measured when each tamping point used in the tests was first tamped in the second pass to ensure measurement consistency. 3.2. Equipment for vibration measurement The equipment layout of the falling weight tests is shown schematically in Fig. 4. The considered vibration point was L far from the tamping points. The distance L varied from 80 m to 155 m, due to the limitations of the maximum length of the site. A recording, storing and data processing system was used. This system included acceleration sensors that were placed in the position of the considered vibration point as accurately as possible and were used to measure the acceleration time histories of the vibration point in the vertical and radial directions. The vibrations in the tangential direction were not measured, because they were relatively small compared to those in the vertical and radial directions and, hence, were regarded as insignificant in this study, due to the approximate axisymmetry of the site soil. Similar results were also found by Kwang and Tu (2006). A type of KD1100LC acceleration sensor, manufactured by Yangzhou Kedong Electronics Technology Corporation, was used. The frequency range of the sensors was 0.2–1000 Hz, and the sensitivities of the sensors were 1000 mV/g. The maximum measurement of acceleration was 5g (where g is the gravitational acceleration). The recording, storing and data processing system was a UA302A system, with sixteen channel data logging and an amplifier system connected to a PC-XP notebook computer for storing
91
and processing data. The resolution of the analog-to-digital (A/D) interface was 16 bits, and the maximum sampling rate was 100 kHz. The electronic total station was used to measure the falling heights, H, of the pounder in the tests. This was executable because the pounder was slung and then intentionally controlled to be stationary for a short period of time at its maximum height for the convenience of the measurement. The falling heights, H, were also controlled to be approximately identical. In the tests, the position of the considered vibration point was not changed, whereas the tamping points were moved (see Fig. 4). In this manner, it can be regarded that the vibration exciter was approximately the same for different test cases, whereas the distances (L) from the vibration sources to the considered sole vibration point were reduced gradually. 3.3. Geological conditions The site soil was coastal plain soil. Table 1 shows the surveyed soil layout and the physical and mechanical properties of the soil layers. In order from top to bottom, the soil formation consisted mainly of clayey silt, sandy silt and mucky silt clay. The topography of the test site was rather flat with the ground surface elevations between 4.3 m and 4.8 m. 3.4. Test results and analysis The ground vibrations were recorded in the form of acceleration histories of the considered vibration point at various distances in the vertical and radial directions. The results of four typical test cases are presented in Figs. 5 and 6, at distances (L) of 80 m, 100 m, 120 m and 150 m with falling heights (H) of 5.917 m, 5.968 m, 5.903 m and 5.975 m, respectively. A comparison on the maximum acceleration amplitudes in the two directions for the four test cases is presented in Table 2. It can be seen that: (1) The wave forms were typical vibration responses under a heavy impact, particularly one sharp acceleration peak at the nearest distance, i.e., L = 80 m, was recognizable for each direction. (2) The maximum acceleration amplitude occurred in the radial direction and reached a remarkable level of about 0.16 m/s2 at the distance of 80 m. However, the acceleration amplitudes in both directions decreased significantly with increases in distance, indicating a quick attenuation of the wave during propagation. (3) The main part of the vibration durations lasted for about 0.5 s and 1.0 s in the case of distances (L) of 80 m and 150 m, respectively, partially due to the results of multiple reflections and refractions in the layered soils. The considered vibration point then tended to return to its stationary position.
Fig. 4. Equipment layout of falling weight tests.
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Table 1 Soil layout and soil properties in the falling weight tests. Property
Symbol
Unit
Thickness of soil layer Density Shear elastic modulus Poisson’s ratiob Cohesion Internal friction angle Damping ratio
hi Gd0 c
m kg/m3 MPa – kPa
a b
◦
%
Values Clayey silt (uppermost)
Sandy silt
Mucky silt clay
7.8(8)a 1929 28.88 0.4 7.40 30.9 1.15
10 1948 77.22 0.4 5.89 30.4 0.92
12 1813 99.30 0.4 13.85 13.8 1.13
Thickness of the soil layers in parenthesis was actually used in this study to fit the mesh size. Poisson’s ratio was determined empirically.
Fig. 5. Test and simulation acceleration histories of the vibration point in the vertical direction at various distances in the falling weight tests (“—” denotes the test results and “- -” denotes the simulation results).
Fig. 6. Test and simulation acceleration histories of vibration point in the radial direction at various distances in the falling weight tests (“—” denotes the test results and “- -” denotes the simulation results).
(4) The maximum acceleration amplitudes in the radial direction were larger than the corresponding ones in the vertical direction in the considered ground region, similar to the results observed by Kwang and Tu (2006).
The Fourier amplitude spectra of the acceleration histories of the considered vibration point for the four test cases were derived and are shown in Figs. 7 and 8. A uniform shape for these spectra curves was not found, and a dominant frequency peak was not obvious. This is probably because the considered vibration point was actually located in the relatively far field, leading to an occurrence of multiple refractions and reflections. However, a primary
frequency band for both directions was recognizable, i.e., in the range of 5–15 Hz, similar to other test records (Gu and Lee, 2002; Kwang and Tu, 2006).
Table 2 Maximum acceleration amplitudes of the ground vibrations in the falling weight tests. Direction
Vertical Radial
Maximum acceleration amplitudes (m/s2 ) L = 80 m
L = 100 m
L = 120 m
L = 150 m
0.080 0.160
0.045 0.087
0.030 0.057
0.017 0.033
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
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Fig. 7. Fourier acceleration amplitude spectra of vibration point in the vertical direction at various distances in the falling weight tests (“—” denotes the tested results and “- -” denotes the simulated results).
L=80m
0.010 0.005 0.000 0.00
5.00
0.015
a (m/s2)
a (m/s2)
0.015
L=100m
0.010 0.005 0.000 5.00
0.00
10.00 15.00 20.00 25.00 f (Hz) L=120m
0.010 0.005 0.000 0.00
5.00
0.015 a (m/s2)
a (m/s2)
0.015
10.00 15.00 20.00 25.00 f (Hz) L=150m
0.010 0.005 0.000 5.00
0.00
10.00 15.00 20.00 25.00
10.00 15.00 20.00 25.00 f (Hz)
f (Hz)
Fig. 8. Fourier acceleration amplitude spectra of vibration point in the radial direction at various distances in the falling weight tests (“—” denotes the tested results and “- -” denotes the simulated results).
4. “Falling weight-soil” model 4.1. Modeling of soil and falling weight A finite element method (FEM) based “falling weight-soil” model was developed for the prediction of the impact-induced ground vibration. The model was built using a commercial finite element program, ANSYS/LS-DYNA, as illustrated in Fig. 9. Firstly, for the modeling of the soil, the mechanical behaviors of the layered soils were assumed to be ideal elasto-plastic, which can be described using the Drucker–Prager model (Drucker and Prager, 1952). Gu and Lee (2002) applied this model and successfully predicted the ground response to the DC of dry sand. Additionally, the eight-node isoparametric element Solid164 was used for the soil elements.
Fig. 9. “Falling weight-soil” model.
For the determination of the mesh size of the soil, it was suggested that the accuracy and numerical efficiency should be both considered. In general, 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 wave length corresponding to the dominant frequency, fT , of the wave; and v denotes the propagation velocity of the wave under consideration. The Rayleigh wave (R-wave) played a predominant role in the ground vibration for these tests (Bolt, 1988); hence, its propagation velocity can be taken as 172 m/s, following a calculation according to the properties of the layered soils in Table 1. When the dominant wave frequency, fT , was conservatively considered as 5 Hz, the mesh size, le , was derived and varied in the range of 2.9–5.8 m, according to Eq. (1). Based on this, two general mesh sizes – 5 m × 5 m × 5 × m and 2.5 m × 2.5 m × 2.5 m – were tested, resulting in very similar results. However, the former offered better numerical efficiency and was, therefore, adopted. In addition, mesh sizes of 4–5 m were also used in the soil model, in order to fit the actual thickness of different soil layers. The commonly used non-reflecting boundaries (transmitting boundaries) were set in the undersurface and the four vertical surfaces of the soil model, so that the waves could transmit through
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these boundaries without reflections and refractions, as they actually did in the real soil without artificial boundaries. The dimensions of the soil model were adopted as 400 m × 400 m in the horizontal plane with a thickness of 30 m, based on the theory of R-wave propagation and trial computations. Secondly, for the modeling of the falling weight, the eight-node isoparametric element Solid164 was also used, together with a rigid material model (compared to soft soil). Mesh sizes of about 1 m were used. Finally, contact and collision actions occurred between the falling weight and the soil during DC. To describe these actions, the widely used penalty function method was adopted to implement the contact-collision algorithm (Hallquist, 2006). The dynamic equations were solved using a central difference scheme, in which a default time step, t, of 9.59 × 10−5 s was applied. 4.2. Simulated results and discussion With the aid of the developed FEM model, the acceleration histories of the considered vibration point at various distances in the falling weight tests could be simulated. The simulation results of the four test cases are illustrated in Figs. 5 and 6 and compared with the test data. One can see that satisfactory agreement was achieved both in the acceleration amplitudes and vibration durations. Additionally, comparisons of the derived Fourier acceleration amplitude spectra of the vibration point in the vertical and radial directions between the simulated and test results are presented in Figs. 7 and 8, respectively. Although the simulated curves did not fit the test ones very well, their dominant frequency band was quite similar, i.e., 5–15 Hz. The reasons for the differences may be mainly attributed to the following aspects: (1) The falling weight may have fallen down onto the ground surface with a minor obliquity, which has not been considered in the model. (2) In the tests, the sensors may not have been exactly placed in the expected vibration point and in the desired directions. Moreover, the sensors were probably not in perfect contact with the soft surface of the ground to ensure a synchronous motion due to the inertia of the sensors. (3) The soil parameters and thickness of the soil layers used in the model may not have been exactly in conformance with those of the site soil, due to survey errors or quality variation of the soil specimens.
Fig. 10. Profile of the cooling tower.
of the whole tower shell. Meanwhile, the residual 60 columns were crushed into pieces sequentially, due to the action of the tower gravity. The tower shell then contacted the ground surface with an inclination angle of about 3◦ . Subsequently, the tower strongly struck the ground and finally disintegrated. This collapse mode is labeled as “collapse in integrity” in this study. Dissimilarly, after the wind load was applied for load case 2, a large part of the upper shell became concaved and cracked. The tower then disintegrated, broke into fragments and finally dropped on the ground. However, the lower portion of the shell did not break up and survived the disaster. This collapse mode is labeled as “collapse in fragments” in this study. It is meaningful to distinguish between the two collapse modes. As mentioned above, the columns failed in the collapse mode of “collapse in integrity”, but survived in that of “collapse in fragments”. In order to simulate the failure of the columns, we had to use many solid elements, due to the limitation of the used program, i.e., a column contained 432 elements for concrete and 288 elements for steel bars. In total, the 120 columns contained 86,400 elements, resulting in tremendous numerical computation. This disadvantage is corrected in Section 6, based on the different collapse modes.
5. Collapse simulation of the cooling tower The planned cooling tower was designed to be constructed with reinforced concrete, with 120 columns that are 18 m high at the bottom. Its profile is illustrated in Fig. 10. Two accidental loads that may cause the tower to collapse were considered in this study. One was the sudden removal of 60 columns (simply named as load case 1), as a result of, for example, a bomb attack or foundation settlement. The other was an extremely strong wind load (wind velocity of 44.3 m/s, Beaufort Scale 14, simply named as load case 2). The simulations indicated that the cooling tower collapsed under the two load cases. However, for brevity, the details of the cooling tower, the structural model as well as the collapse simulation are not presented here, but were described by Li et al. (2011). The simulation also indicated that the collapse modes of the tower exhibited different characteristics under the two load cases, as demonstrated by the two pictures from the collapse simulation in Fig. 11. For load case 1, firstly, the tower shell began to incline in the “removal” direction after the sudden removal of the columns, sinking in integrity, almost without changing the profile
Fig. 11. Collapse of the cooling tower in load case of (a) a sudden removal of 60 columns and (b) an extremely strong wind.
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
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Table 3 Maximum acceleration amplitudes and vibration durations of the ground vibrations in the event of the collapse of the cooling tower. Load case
1 2
Fig. 12. “Cooling tower-soil” model for the prediction of ground vibration caused by the collapse of the cooling tower in load case of (a) a sudden removal of 60 columns and (b) an extremely strong wind.
6. “Cooling tower-soil” models Two “cooling tower-soil” models were developed from the “falling weight-soil” model for the prediction of the ground vibrations caused by the two collapse modes of the cooling tower. The difference between the two models lay only in the modeling of the cooling tower for the purposes of avoiding tremendous numerical computation. The “cooling tower-soil” model for load case 1 is illustrated in Fig. 12(a) with the modeling of the tower shell being identical to that in (Li et al., 2011). In Fig. 12(a), a small distance, i.e., 0.5 m, was set between the lowest point of the tower shell and the ground in the model for load case 1 for convenience of computation. The residual 60 columns were intentionally removed from the model, so that the element number could be reduced remarkably; and the computational time was limited to within one day for the current commonly used personal computer. When the collapsed cooling tower just contacted the ground surface, the whole tower shell hold its profile almost in integrity and reached a motion state with an inclination angle of 3◦ and a vertical velocity of approximately 16.3 m/s (Li et al., 2011). The horizontal velocities of the tower shell were relatively small and could be ignored. As a result, the collapse process of the cooling tower was believed to have no significant change in comparison to that using the model with the 60 columns retained, based on a comparative trial. In the simulation, when the tower shell impacted the ground, it disintegrated into fragments under gravity. Eventually, the fragments dropped onto the ground and may have also broken into pieces, and formed debris. The model for load case 2 is illustrated in Fig. 12(b). In this model, the modeling of the tower shell was also identical to that in Li et al. (2011), while the modeling of the columns was different. Each column was simulated as one beam element, instead of a number of solid elements used in the model in Fig. 11(b). The column model using the beam element overestimated the load bearing capacity of the real column. However, the collapse processes of the cooling tower were almost the same between the collapse modes illustrated in Figs. 11(b) and 12(b), because actually all the columns and the lower portion of the tower shell did not fail. By doing this, the element number of the columns was reduced remarkably; thus, the numerical computation was also reduced significantly. In the simulation, the tower shell disintegrated into fragments under wind and gravity, dropped on the ground and formed debris. In Fig. 12, the foundation of the planned cooling tower was rock, described using a linear elastic material model. The soil parameters were considered to be density () of 2700 kg/m3 , elastic modulus (E) of 4.00 × 104 MPa, Poisson’s ratio () of 0.2 and damping ratio () of 5%. The dimensions of the rock model were 1000 m × 1000 m in the horizontal plane with a thickness of 50 m. The mesh size was 5 m × 5 m × 5 m, which was accurate enough in comparison with that of the “falling weight-soil” model, because the R-wave of rock
Direction
Vertical Radial Vertical Radial
Maximum acceleration amplitudes (m/s2 )
L = 200 m
L = 300 m
L = 400 m
L = 500 m
2.96 1.97 0.57 0.38
1.10 1.52 0.16 0.07
0.54 0.50 0.06 0.04
0.15 0.25 0.01 0.02
Vibration duration (s)
6.8 9.0
has a much large propagation velocity. Non-reflecting boundaries were also set, as adopted in the “falling weight-soil” model. A strategy was devised to counteract the reduction of the amount of contributed structural elements during the numerical computation and was achieved by increasing the material density of the residual tower, because the model was based on FEM. As generally known, when cracked or crushed, the elements are “killed” and then “disappear” from the model. As a result, the sum of the contributing structural elements and the total mass and impulse were gradually reduced during the simulation process. However, such a result is inconsistent with reality. This inconsistency was approximately eliminated by means of the following steps: (1) Dividing the whole simulation time into several time periods, (2) Checking the disappeared mass of the structure at each end of the time period, and (3) Increasing the material density of the residual tower to keep the total mass constant and partly, to compensate for the loss of impulse. 7. Ground vibration With the aid of the “cooling tower-soil” models, the ground vibrations were obtained in the form of acceleration histories of vibration points at various distances in the vertical and redial directions. Some results are illustrated in Figs. 13 and 14 for load cases 1 and 2, respectively, at distances (L) of 200 m, 300 m, 400 m and 500 m. These distances denote the horizontal length from the considered vibration point to the ground center of the cooling tower, in the collapse direction of the tower. This region was of interest because this is the most likely location of the nuclear island. The derived Fourier acceleration amplitude spectra of the vibration points are presented in Figs. 15 and 16 for load cases 1 and 2, respectively. For clarity, the maximum acceleration amplitudes and vibration durations are listed in Table 3. It was found that: (1) The considered ground region may experience a severe vibration. With load case 1, the maximum acceleration amplitudes were about 0.3g and 0.2g in the field at a distance (L) of 200 m in the vertical and radial directions, respectively. This was mainly due to the tremendous impulse that was transferred from the cooling tower to the ground. (2) The excited ground vibration was more intense in load case 1 than that in load case 2. This may be primarily attributed to the different collapse modes of the tower. For load case 1, the whole part of the tower shell impacted the ground and then disaggregated, following the drop of the fragments on the ground successively in a relative short time; whereas, for load case 2, only the upper part of the tower shell disaggregated with the fragments dropping on the ground, thus resulting in a relatively light ground vibration. (3) The vibration attenuated rapidly in both directions with increases in distance. The attenuation rate in the vertical direction was greater than that in the radial direction. In relation
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
vertical direction L=200m
3.00 1.50 0.00 -1.50 -3.00
a (m/s2)
a (m/s2)
96
4.00 t (s)
6.00
8.00
0.00
vertical direction L=400m
3.00 1.50 0.00 -1.50 -3.00 0.00
2.00
4.00 t (s)
6.00
0.00
2.00
4.00
6.00
4.00 t (s)
2.00
4.00 t (s)
0.00
2.00
a (m/s2)
a (m/s2)
radial direction L=400m
0.00
2.00
4.00
6.00
8.00
4.00
6.00
8.00
t (s)
t (s) 2.00 1.00 0.00 -1.00 -2.00
8.00
radial direction L=500m
2.00 1.00 0.00 -1.00 -2.00
8.00
6.00
vertical direction L=500m
0.00
radial direction L=200m
2.00 1.00 0.00 -1.00 -2.00
2.00
3.00 1.50 0.00 -1.50 -3.00
8.00
a (m/s2)
a (m/s2)
2.00
a (m/s2)
a (m/s2)
0.00
vertical direction L=300m
3.00 1.50 0.00 -1.50 -3.00
6.00
8.00
radial direction L=500m
2.00 1.00 0.00 -1.00 -2.00 0.00
2.00
4.00 t (s)
t (s)
6.00
8.00
Fig. 13. Simulated acceleration histories of vibration points in the event of the collapse of the cooling tower in load case 1.
to this, in the “near” field (L = 200–300 m), the acceleration amplitudes in the vertical direction were larger than the corresponding ones in the radial direction. However, these results were reversed in the “far” field (L = 500 m), because the amplitude of the surficial particle motion, either in the vertical or in the radial direction, is the result of the propagation of different types of waves (Raleigh, primary and secondary waves). As is generally known, the wave propagations are direction oriented and exhibit different attenuation rates that generally depend on the frequency of the vibration, the type of soil and radiation damping (Athanasopoulos et al., 2000). As a result, the acceleration amplitude of the ground vibration in each direction, which is one of the forms to describe the surficial particle motion, attenuated depending on individual characteristics. Based on this knowledge, the authors believe that the characteristics of the vibration attenuation observed in this study cannot be considered as general rules and may vary from case to case. (4) The vibration duration lasted for about 6.8 s and 9.0 s for load cases 1 and 2, respectively. Both were much shorter than the duration time of a common earthquake. For comparison, the ground vibration, induced by the blasting demolition of a 140 m high chimney with the foundation dominantly consisting of clay marl overlaying moisture sand, lasted for about 2 s (Stangenberg and Zinn, 1998). (5) The frequency band of the vibration lay mainly in the range of 0–25 Hz and 0–8 Hz for load cases 1 and 2, respectively, showing an appreciable difference. This indicated different impact
effects between the tower shell and the ground, essentially due to the different collapse modes of the two load cases. The underground vibration was also investigated for the safety evaluation of the facilities embedded in the subsoil. Table 4 presents the maximum acceleration amplitudes of the underground vibrations in the event of a collapse of the cooling tower as in load case 1, with respect to the depth, H, of the observed vibration points. One can see that the vibration attenuated rapidly with a rate greater than linearity. These results imply that increasing the burial depth contributes to the efficient reduction of vibration, which may be used as a possible design method for vibration reduction of nuclearrelated facilities. Table 4 Maximum acceleration amplitudes of the underground vibrations in the event of the collapse of the cooling tower in load case 1. Depth (m)
Direction
0
Vertical Radial Vertical Radial Vertical Radial Vertical Radial
10 20 30
Maximum acceleration amplitudes (m/s2 ) L = 200 m
L = 300 m
L = 400 m
L = 500 m
2.96 1.97 2.28 1.01 1.53 0.71 0.97 0.66
1.10 1.52 0.99 0.52 0.72 0.30 0.41 0.27
0.54 0.50 0.50 0.21 0.39 0.11 0.24 0.10
0.15 0.25 0.14 0.16 0.13 0.06 0.11 0.04
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
97
Fig. 14. Simulated acceleration histories of vibration points in the event of the collapse of the cooling tower in load case 2.
8. Parametric study and vibration reduction
8.1. Collapse profiles
A parametric study was conducted for the purposes of investigating the influential factors affecting the ground vibration and of exploring the possible methods for vibration reduction. As is generally known, the ground vibration depends on the characteristics of the vibration source and the soils that are the medium for the wave propagation (Woods and Jedele, 1985; Athanasopoulos et al., 2000). The characteristics of the vibration source are associated with the collapse modes and profiles. The mode of “collapse in integrity” was chosen for this study, since it excited more intense ground vibration than the “collapse in fragments” mode. From the study in Sections 6 and 7, we knew that ground vibration was excited mainly due to the impact of the tower shell and its fragments dropping on the ground, while the columns affected the inclination angle and vertical velocity of the tower shell. Therefore, the collapse profiles may be described with the inclination angle and vertical velocity. In this regard, three influential factors affecting the ground vibration were considered, i.e., collapse profile, site geology and arrangement of an isolation trench. The “cooling tower-soil” model for the chosen collapse mode used in Section 6 was also adopted, with all the columns in the lower part of the tower not being included in the model for brevity and clarity.
The inclination angle and vertical velocity were considered as two critical factors for the collapse profile of the tower shell when it just reached the ground surface. The rock foundation of Section 6 was adopted. 8.1.1. Inclination angles Two inclination angles of the tower shell (i.e., 0◦ and 6◦ ) were chosen for comparison to the 3◦ in Section 6. For the three considered inclination angles, it was assumed that the tower shells freely dropped in integrity with the same height of the center of mass. Consideration that the columns were 18 m high and the diameter of the bottom part of the tower shell was 176 m led to a theoretically maximum inclination angle of the tower shell of about 6◦ . As a result, the falling tower shell with a larger inclination angle would reach the ground surface earlier with a slower vertical velocity. In summary, for the three considered cases, the inclination angles of the tower shell were 0◦ , 3◦ and 6◦ with vertical velocities of 18.8 m/s, 16.3 m/s and 13.4 m/s, as illustrated in Fig. 17(a), Fig. 12(a) and Fig. 17(b), respectively. A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the three considered cases is presented in Table 5. A result similar to result (3) in Section 7 was found. Moreover, it was also found that the case with an inclination angle of 0◦
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F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
Fig. 15. Fourier acceleration amplitude spectra of vibration points in the event of the collapse of cooling tower in load case 1.
led to the most intensive ground vibration with the maximum acceleration amplitude, even up to about 1g. However, its vibration duration, i.e., of about 5.7 s, was the shortest one of the three. This result can be mainly attributed to the different collapse profiles of the tower shell. For the collapse profile with an inclination angle of 0◦ , the impact was finished in the shortest time with a possible complete impact area, among the three considered cases. Thus, under the condition that there were no extraordinary differences of the total impulses among the three cases, the excited ground vibration was most intensive with the maximum acceleration amplitude. On the other hand, this collapse profile was probably the most adverse among the three cases, because, as the simulation indicated, the tower shell disintegrated in the shortest time, leading to the shortest ground vibration duration.
8.1.2. Vertical velocities Assuming that all the columns in the bottom part of the cooling tower fail simultaneously, we can consider that the tower shell freely falls and reaches a vertical velocity of 18.8 m/s at the moment when it just touches the ground surface, since the height of the columns was 18 m. However, the actual vertical velocity at this moment is always less than the free-fall velocity, due to the obstructive effect of the residual parts of the columns. For comparison, three vertical velocities at this moment were chosen, i.e., 18.8 m/s, 15.3 m/s and 10.8 m/s, with an inclination angle all of 0◦ . A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the three considered cases is presented in Table 6. Again, a result similar to result (3) in Section 7 was found. Moreover, not surprisingly, the case with the most rapid velocity led to the most intensive ground vibration and the shortest vibration duration. This
Table 5 Maximum acceleration amplitudes of the ground vibrations at various distances for the collapse profiles of the cooling tower with different inclination angles. Inclination angle (◦ )
Direction
0
Vertical Radial Vertical Radial Vertical Radial
3 6
Maximum acceleration amplitudes (m/s2 )
Vibration durations (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 2.96 1.97 2.17 1.79
2.17 2.20 1.10 1.52 0.91 0.83
1.38 1.27 0.54 0.50 0.48 0.27
0.44 0.57 0.15 0.25 0.11 0.22
5.7 6.8 7.6
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
vertical direction L=200m
0.024 0.012 0.00
2.00
4.00 6.00 f (Hz)
0.012 0.00
10.00
0.024 0.012
2.00
4.00 6.00 f (Hz)
8.00
10.00
vertical direction L=500m
0.036
a (m/s2 )
a (m/s2 )
8.00
vertical direction L=400m
0.036
0.024 0.012 0.000
0.000 0.00
2.00
4.00 6.00 f (Hz)
8.00
0.00
10.00
radial direction L=200m
2.00
0.020 0.010 0.000
4.00 6.00 f (Hz)
8.00
10.00
radial direction L=300m
0.030
a (m/s2 )
0.030
a (m/s2 )
0.024
0.000
0.000
0.020 0.010 0.000
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
0.00
radial direction L=400m
2.00
0.020 0.010 0.000
4.00 6.00 f (Hz)
8.00
10.00
radial direction L=500m
0.030
a (m/s2 )
0.030
a (m/s2 )
vertical direction L=300m
0.036
a (m/s2 )
a (m/s2 )
0.036
99
0.020 0.010 0.000
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
0.00
2.00
4.00 6.00 f (Hz)
8.00
10.00
Fig. 16. Fourier acceleration amplitude spectra of vibration points in the event of the collapse of cooling tower in load case 2.
is because, among the three considered cases, the fastest velocity means the largest impulse, generally exciting the most intensive ground vibration. On the other hand, the greatest velocity initiated the strongest interaction between the cooling tower and the ground, resulting in the shortest time for the disintegration of the tower collapse as well as for the duration of the ground vibration. The study results in Section 8.1 indicate that, for the possible collapse profiles of the cooling tower in load case 1, increasing the load bearing capacity and the ductility of the columns may weaken the impact of the collapsed tower on the ground, helping to efficiently reduce the ground vibration.
8.2. Site geologies It is usually desired that the cooling tower in a nuclear power station be constructed on a rock-like foundation, sometimes with overlaying soft soil due to the geological limitations of the plant. In general, the overlaying soft soil may aggravate the effect of the structural damage compared to a solely rock-like foundation in the event of an earthquake (Eurocode 8, 2003). However, this is not the case when the vibration source and the considered vibration points are all on the ground surface. In this condition, the overlaying soft soil seems to
Table 6 Maximum acceleration amplitudes of the ground vibrations at various distances for the collapse profiles of the cooling tower with different vertical velocities. Vertical velocity (m/s)
Direction
18.8
Vertical Radial Vertical Radial Vertical Radial
15.3 10.8
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 4.45 3.64 4.03 3.39
2.17 2.20 2.07 1.45 1.92 1.15
1.38 1.27 0.91 0.97 0.69 0.77
0.44 0.57 0.22 0.43 0.19 0.39
5.7 6.7 7.5
100
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
Fig. 17. “Cooling tower-soil” model with the inclination angle of the tower shell of (a) 0◦ and (b) 6◦ . Fig. 18. “Cooling tower-soil” model with the arrangement of isolation trench with a depth of 5 m or 10 m.
Table 7 Assumed soil properties for “soil-rock” foundation. Property
Unit
Value
Density Shear elastic modulus Poisson’s ratio Cohesion Internal friction angle Damping ratio
kg/m3 MPa – kPa
1800 100 0.35 10 15 5.00
◦
%
work as a flexible gas cushion, resulting in vibration reduction. To demonstrate this, two types of site geology were considered here. One was a solely rock foundation; and the other was a “soilrock” foundation, i.e., overlying soft soil to a depth of 10 m with the same rock foundation underneath. The material model for rock was described in Section 6. The mechanical properties of the soil were depicted using the Drucker–Prager model with the assumed parameters listed in Table 7. The inclination angle was 0◦ with a vertical velocity of 18.8 m/s when the tower shell just reached the ground surface. A comparison of the maximum acceleration amplitudes of the ground vibrations at various distances in the two directions for the two considered cases is presented in Table 8. It was found that the ground vibration was dramatically reduced for the soil-rock foundation and that the vibration duration became shorter, compared to those of the solely rock foundation. In particular, for a distance (L) of greater than or equal to 300 m, the ground vibration of the foundation with overlaying soil was so small that the structures in this region may hardly suffer any damage. From the viewpoint of application, this finding also suggests an efficient method for vibration reduction. 8.3. Arrangement of an isolation trench An open or filled isolation trench is often used in engineering practice to reduce ground vibration generated by various factors. This method of vibration isolation can be classified into two categories: source isolation and receiver isolation (Klein et al., 1997; Adam and Estorff, 2005). The former is used to reduce the vibrations at their source; whereas, on the other hand, the latter is
usually built away from the source, surrounding the structure to be protected. A good deal of research efforts, both experimental and numerical, have been devoted to the vibration screening by open trenches (Ahmad and Al-Hussaini, 1991; Klein et al., 1997; Adam and Estorff, 2005; Celebi et al., 2009). These studies concluded that using an open isolation trench could reduce the ground vibrations significantly. Generally, the effect of vibration reduction depends mainly on the depth and width of the trench. The trench depth is the governing factor compared to the trench width. An analytical approach has rarely been used, because its solutions are usually limited to ideal conditions. In this part of the parametric study, we chose an open isolation trench as a method of source isolation, because it provides effective and low-cost isolation measures. Two different isolation trenches, both with a length of 220 m and a width of 5 m, were set in the model, as illustrated in Fig. 18. Their width was determined in conformance with the mesh size of the foundation model. The difference between the two trenches was their depth: one was 5 m, and the other was 10 m. For each trench, the distance between the ground center of the cooling tower and the neighboring edge of the trench was approximately 100 m, ensuring that almost all the fragments fell to one side of the trench, i.e., did not cross the trench. A rock foundation, an inclination angle of 0◦ and a vertical velocity of 18.8 m/s when the tower shell just reached the ground surface, were adopted. Table 9 presents the comparative results of the maximum acceleration amplitudes of the ground vibrations for different points located on the side of the trench. It can be seen that the ground vibrations were significantly reduced by adding an isolation trench. For trench depths of 5 m and 10 m, the reduction percentages of the maximum acceleration amplitudes of the ground points at different distances were in the range of 23–49% and 48%–70% compared to those without a trench, respectively. These results were comparable to Ahmad and Al-Hussaini’s results (1991). The vibration durations of the three considered cases had almost no significant change and were all around 5.7 s. Similarly, it was also observed in a numerical study by Adam and Estorff (2005) that hardly any change in the ground vibration durations occurred when different depths of open trenches were used.
Table 8 Maximum acceleration amplitudes of the ground vibrations at various distances for different site geologies. Site geology
Direction
Rock
Vertical Radial Vertical Radial
Soil + rock
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 0.25 1.16
2.17 2.20 0.03 0.29
1.38 1.27 0.01 0.07
0.44 0.57 0.01 0.03
5.7 4.3
F. Lin et al. / Nuclear Engineering and Design 258 (2013) 89–101
101
Table 9 Maximum acceleration amplitudes of the ground vibrations for open trenches with different depths. Trench depth (m)
0 5 10
Direction
Vertical Radial Vertical Radial Vertical Radial
Maximum acceleration amplitudes (m/s2 )
Vibration duration (s)
L = 200 m
L = 300 m
L = 400 m
L = 500 m
9.48 3.80 6.82 2.85 4.37 1.89
2.17 2.20 1.41 1.70 0.89 1.15
1.38 1.27 0.77 0.65 0.55 0.60
0.44 0.57 0.24 0.30 0.13 0.19
9. Conclusions This study presents a comprehensive approach for the prediction of the ground vibration caused by the collapse of a huge cooling tower. The adopted “cooling tower-soil” model was based on the “falling weight-soil” model verified by the falling weight tests. The ground vibration was predicted in the form of acceleration histories and vibration durations of points at different distances from the ground center of the cooling tower. The following conclusions can be drawn from the study: (1) A severe ground vibration may occur in the considered region, with maximum acceleration amplitudes being about 0.3g and 0.2g at a distance (L) of 200 m in the vertical and radial directions in load case 1, respectively. (2) Different accidental loads may lead to different collapse modes of the cooling tower, resulting in ground vibrations that significantly differ from each other. (3) The vibrations in the vertical and radial directions exhibit different characteristics. For distances (L) from 200 m to 300 m, the maximum acceleration amplitudes in the vertical direction were larger than the corresponding ones in the radial direction. For a distance (L) of 500 m, however, the results were reversed. (4) The collapse profiles, site geologies and arrangements of an isolation trench may significantly affect the ground vibration. On the other hand, the results from the parametric study provide potential methods for vibration reduction. The current study has been aimed at providing a complete approach and a few general suggestions for the prediction of collapse-induced ground vibration. However, it should be noted that, in many practical cases, it seems appropriate to perform a similar investigation for the cooling tower–soil system under consideration, as has been done in this contribution. The results may vary from case to case, because the ground vibration mainly depends on the characteristics of the vibration source and the soil properties. In the conventional design of nuclear power stations, the considered accidental loads do not include the ground vibration due to the collapse of adjacent large-scale structures. However, this study has indicated that, with the increasing height of the cooling tower and the relatively small distance between the nuclear island and the cooling tower, the effect of collapse-induced ground vibration on the nuclear-related facilities cannot be ignored. Acknowledgements This research was sponsored by the National High-Tech Development Plan (863 Programme) under Grant No. 2012AA050903 and the Kwang-Hua Fund for the College of Civil Engineering, Tongji
5.7 5.7 5.7
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