Earthquake response analysis of Ankara high speed train station by finite element modeling

Transcription

1 Earthquake response analysis of Ankara high speed train station by finite element modeling Burak Nebil BARUTÇU 1 ; Salih ALAN 2 ; Mehmet ÇALIŞKAN 3 Department of Mechanical Engineering Middle East Technical University, Turkey ABSTRACT A new train station is currently under construction in Ankara, Turkey. The building houses a shopping mall and a luxury hotel in nine stores while serving the function of train station. The earthquake response of the building is sought due to a typical earthquake which measured 5.3 Md and 5.5 ML on December 20, A finite element model of the building is developed for this purpose. A number of spring and damper elements whose characteristics are obtained from the soil-structure interactions are used to model the interaction between the foundation and the building itself. Spectral analysis is conducted on the earthquake time signature data measured in Ankara to obtain displacement amplitudes at corresponding frequencies for the N-S, E-W and U-D directions. These results of the spectral analysis are utilized in harmonic analysis on the constructed model. Also, transient analysis is conducted on the model subjected to the raw earthquake displacement data. Vibration amplitudes for a typical floor of the building are predicted due to this particular earthquake. Keywords: Vibration, Building, Earthquake, I-INCE Classification of Subjects Number(s): INTRODUCTION A strong impetus by the Turkish government is set forth to establish a high speed train network in Turkey. It is decided to have the capital city Ankara to serve as the hub of the network. Upon completion of MARMARAY which also involves tube crossing of Bosporus under the sea the network included rail connection between two major cities Ankara and Istanbul, which is the extension of first leg between Ankara and Eskisehir. Another leg of the network between Ankara- Konya is currently in operation. Plans are underway to extend the network to other cities, to Bursa and İzmir in the West and to Sivas in the East in the near future. Figure 1 shows the status of high speed railroad network in Turkey as of May This study aims to predict the vibration amplitudes for a typical floor of the building due to a typical earthquake recorded at a nearby station. The building is modeled by finite elements to estimate the vibration amplitudes. Soil parameters are also employed to model dynamics of the building on elastic foundations. Spectral analysis is conducted on the earthquake acceleration data in order to get the dominant harmonics and their amplitudes. By using the results of the spectral analysis, harmonic analysis is performed on the model of the train station. Also, transient analysis has been carried on the building model by assigning the raw earthquake data as the base input. This study can be separated into two steps, one is spectral analysis, the other is the vibration analysis on the finite element model. The earthquake data have been taken from the Strong Ground Motion Database of Turkey website [1]. Earthquake is dated on at 23:47: This data is recorded from the station whose coordinates are N E. This particular station is the nearest station to the earthquake coordinates which are N E. 1 burakn@metu.edu.tr 2 salihalan@gmail.com 3 caliskan@metu.edu.tr 6318

2 Figure 1 Map of high speed train lines in Turkey 2. SPECTRAL ANALYSIS Spectral analysis has been conducted on the raw earthquake data in order to find the dominant frequency and its amplitude. These results have been used in the harmonic analysis. Time history data of acceleration in N-S, U-D and E-W directions can be seen from the Figure 2, Figure 3 and Figure 4, respectively. Figure 2 Time history data of acceleration in N-S direction 6319

3 Figure 3 Time history data of acceleration in U-D direction Figure 4 Time history data of acceleration E-W direction Velocity and displacement data can be calculated from the time history data of acceleration. Time history of displacement input can be seen in Figure 5 to

4 Figure 5 Time history data of displacement in N-S direction Figure 6 Time history data of displacement in U-D direction Figure 7 Time history data of displacement in E-W direction 6321

5 The sampling interval of data is taken as 0.01 s. The following procedure has been carried out during the spectral analysis [2]. 1. Specify the critical frequency and maximum frequency of interest by using the following formulas. f c = 1/h (1) f max = f c /2 (2) 2. Specify the effective bandwidth (Be) and the accuracy figure (σ/m). 3. Find the record length (T) by using the below formula. T = (1/(σ/m)) 2 /Be (3) 4. Determine the number of non-zero data points as follows; N = T/h (4) 5. To be able to use FFT algorithm the total number points should be powers of 2. Therefore, as the total number of points, the nearest power of 2 to the value by Equation (4) should be used. For the spectral analysis of the earthquake data, 2048 number of points should be used. 6. After the determination of the total number of points new record length should be determined. T = N new h (5) 7. Next step is specifying the number of adjacent spectral estimates (n) which should be an integer. (2n + 1) = Be T (N new )/N_new (6) Value get by equation (6) should be rounded to the nearest integer in order to get the number of adjacent spectral estimates. 8. Since the acceleration data obtained is a unique time history, this data should be divided into samples with a proper time delay at the beginning of the previous sample. For this case, every 2048 data point sample is taken out from the main time history data by adding time delay at the beginning of the previous sample. By this way, time samples are generated with overlapping of the data. 9. Removal of the trend by subtracting the mean values of the time samples is the next step. x i new = x i x for i = 0,1,2 N new 1 (7) where (x) refers to the displacement samples, (x ) refers to the mean values and (i) indicates the number of samples. 10. Take the Fast Fourier Transformation (FFT) of each sample. 11. Calculate the spectral coefficients (S k ) by S k = X k X k (8) where (X k ) is the Fourier Transform of displacement data and (X k ) is the conjugate of the Fourier Transform of displacement data. 12. Then, determine the estimates of the continuous spectrum from S(ω k ) = (T/2π)S k (9) 13. Final step is carrying out final smoothing by calculating the average of adjacent spectral estimates. S(ω k ) = (1/(2n + 1)) S(ω k+m ) n m= n where values of S(ω k+m ) for k + m > N/2. Results of spectral analysis for acceleration data in N-S, U-D and E-W directions can be seen from Figure 14, Figure 15 and Figure 16. (9) 6322

6 Figure 8 Energy spectrum density estimate of acceleration in N-S direction Figure 9 - Energy spectrum density estimate of acceleration in U-D direction Figure 10 - Energy spectrum density estimate of acceleration in E-W direction 6323

7 3. VIBRATION ANALYSIS In order to perform transient and harmonic vibration analysis train station building, which can be seen from the Figure 11, has been model by finite elements. This building is designed by A-Architectural Design Inc. of Ankara, Turkey. The contractor is the joint venture of Cengiz-Limak-Kolin of Turkey. Building has 9 stores and covers an area of 336 m by 93 m. The height of the building from the basement floor is 53 m and from the ground is 45 m. There are a shopping mall and a 5-star hotel in the upper floors. Finite element model of the train station has been developed on ANSYS Parametric Design Language platform. This model consists of beam elements and shell elements and can be seen from the Figure 12. The soil-structure interaction at the boundary in horizontal and vertical directions is represented by springs and dampers and their equivalent coefficients obtained by employing the procedures outlined in [3]. In the soil-structure interaction model, mechanical properties of the soil, bearing area and embedment height of the building along with its weight are taken into account. (Figure 13) Figure 11 Render of high speed train station in Ankara Figure 12 - Finite element model of the building 6324

8 Amplitude [m] 0,11 7,37 14,63 21,89 29,15 36,41 43,67 50,93 58,19 65,45 72,71 79,97 87,23 94,49 101,75 109,01 116,27 123,53 130,79 138,05 145,31 152,57 159,83 167,09 174,35 181,61 188,87 196,13 INTER-NOISE 2016 Figure 13 - Soil structure interaction model 3.1 Transient Analysis Transient analysis has been conducted on the finite element model of the train station by using the raw displacement data. This analysis has been done on the Ansys Parametric Design Language platform. Response of the upper hotel floor is obtained in N-S, U-D and E-W directions. Full Transient Analysis has been performed on the model. Responses in N-S, U-D and E-W directions can be seen from the figures 14 to 16 below. Although, the vibration amplitudes in N-S and E-W directions are damped out drastically, the response of the system follows the displacement input caused by the earthquake closely in U-D direction. There is not much difference between the input and the response of the system in U-D direction. Response of Train Station in N-S Direction Response of Building Displacement Time History of Earthquake 2,00E-03 1,00E-03 0,00E+00-1,00E-03-2,00E-03-3,00E-03-4,00E-03-5,00E-03 Time [s] Figure 14 - Results of transient analysis in N-S direction for the hotel floor 6325

9 Amplitude [m] 0,11 7,15 14,19 21,23 28,27 35,31 42,35 49,39 56,43 63,47 70,51 77,55 84,59 91,63 98,67 105,71 112,75 119,79 126,83 133,87 140,91 147,95 154,99 162,03 169,07 176,11 183,15 190,19 197,23 0,11 7,15 14,19 21,23 28,27 35,31 42,35 49,39 56,43 63,47 70,51 77,55 84,59 91,63 98,67 105,71 112,75 119,79 126,83 133,87 140,91 147,95 154,99 162,03 169,07 176,11 183,15 190,19 197,23 Amplitude [m] INTER-NOISE 2016 Response of Train Station in U-D Direction Response of Building Displacement Time History of Earthquake 1,80E-02 1,60E-02 1,40E-02 1,20E-02 1,00E-02 8,00E-03 6,00E-03 4,00E-03 2,00E-03 0,00E+00-2,00E-03 Time [s] Figure 15 Results of transient analysis in U-D direction for the hotel floor Response of Train Station in E-W Direction Response of Building Displacement Time History of Earthquake 1,00E-02 0,00E+00-1,00E-02-2,00E-02-3,00E-02-4,00E-02-5,00E-02-6,00E-02 Time [s] Figure 16 Results of transient analysis in E-W direction for the hotel floor 3.2 HARMONIC ANALYSIS The following results have been singled out from the previously conducted spectral analysis in this study as the maximum amplitude and its corresponding frequency. These values are used as inputs to the harmonic analysis. Table 1 - Results of spectral analysis N-S U-D E-W Frequency, Hz Amplitude, m E E E-2 Amplitude values for the response of building can be seen from the Table 2 below. 6326

10 Table 2 Results of harmonic analysis of displacement N-S U-D E-W Real Part, m 3.50E E E-03 Imaginary Part, m -1.87E E E-04 Amplitude, m 3.97E E E RESULTS Vibration amplitudes for the train station building due to the strongest earthquake in the known history of Ankara, Turkey need to be determined. Values of parameters used in the spectral analysis are tabulated in Table 3. Table 4 represents the maximum displacement of raw earthquake data, maximum vibrational response which is got from transient analysis and vibration amplitudes get from the harmonic analysis. The results of the transient and harmonic analysis represent the vibration amplitudes of a hotel room. Table 3 Parameter values in spectral analysis Be, Hz σ/m h N T n 0.5 1/ s s 5 Table 4 Results of analysis for the earthquake response N-S U-D E-W Displacement Raw Data, m 4.34E E E-02 Transient Analysis, m 2.19E E E-02 Harmonic Analysis, m 3.97E E E CONCLUSION Vibration amplitudes of a building due to an earthquake data, which can be specified as random signal, have been obtained by two different methods. Spectral analysis has been conducted on the random data to obtain the dominant harmonics and its corresponding amplitudes. Harmonic analysis has been performed on the finite element model of the train station by inputting the results of spectral analysis. As a second study, the raw displacement data, which is calculated from the recorded raw acceleration data, is exploited in the subsequent transient analysis. Two methods of analysis to describe the earthquake response of the station building are found to yield close and meaningful results. ACKNOWLEDGEMENTS Authors are indebted to Mezzo Stüdyo Ltd, Turkey for the support. Thanks are extended to the architect, Mr. Ali Osman Öztürk of A-Architectural Design Inc. of Ankara and to the contractor, joint venture of CLK (Cengiz-Limak-Kolin) of Turkey for granting authors permission to disseminate the knowledge on vibration isolation design for the station building and for provision of visual materials and drawings. REFERENCES 1. Raw Earthquake Displacement Data for Bala, Ankara, Turkey Earthquake on 2007, December 20. (2016, May 5). Retrieved from 2. Newland D. E., An introduction to random vibrations, spectral & wavelet analysis, 3 rd Edition, Prentice-Hall; 1993, p , Essex, UK. 3. Arya S., O Neill M., Pincus G., Design of structures and foundations for vibrating machines, Gulf Publishing, May 1979, p.57-76, Houston, TX, USA. 4. Alan S., Caliskan M., Vibration isolation design of railroad tracks within Ankara high speed train station. Proc 169 th Meeting of the Acoustical Society of America; May 2015 Pittsburgh, PA 6327