Quantification of Site City Interaction Effects on Responses of Buildings and Basin Under Realistic Earthquake Loading for Development of Economic Smart City


 The paper presents the quantification of site-city-interaction (SCI) effects on the responses of buildings of a city and free field motion under realistic earthquake loading for the economic development of a smart city. The state of the art pseudo-dynamic earthquake rupture is implemented in the existing fourth-order viscoelastic staggered-grid SH-wave finite-difference program, and simulated results validated. SH-wave responses of various homogeneous and heterogeneous cities situated on horizontal sediment layer as well as in 2D heterogeneous basins are simulated and analyzed for different dynamic parameters of the buildings. The simulated SCI effects using realistic earthquake loading reveals a reduction of transfer function (TF) of buildings in a wide frequency bandwidth. This finding is conflicting with the reported splitting of bandwidth of the FoSB in the past SCI studies, carried out using simple plane incident wave-front with a single zero-phase wavelet. The obtained largest SCI effects on a building was highly dependent on the building type, city and basin heterogeneity in contrast to the general perception that it should be maximum at centre of city. It is also obtained that SCI effects are always beneficial to buildings when fundamental frequency of building on rock FoSR <1.4FoB( FoB is the fundamental frequency of basin/sediment layer). The obtained reduction of of building of city as well as free field motion due to the effects of SCI corroborates with the past SCI studies. The increase of coupling between the buildings and basin due to an increase of building density causes an increase of SCI effects on the responses of both the buildings and free field motion. The SCI effects in the case of buildings with low damping are beneficial during an earthquake. It is recommended that the smart city should be homogeneous in nature and of buildings should be less than around 1.4 times the of the underlying basin/sediment deposit and buildings should preferably be a steel one.


INTRODUCTION 51
The explanation of the behaviour of buildings and free field motion during an earthquake loading 52 is a significant challenge for researchers because of the complex soil-structure-soil interaction 53

SGM simulation using PRM2 rupture model 259
In the case of PRM2 model, the STF, rise-time, rake and rupture arrival times for different point 260 sources are the same as used in the PRM1 model (Table 2). Nevertheless, the moment release 261 as per-slip was varied from one-point source to another, and the spatial slip distribution 262 was done using the methodology of Mai and Beroza (2002). Mai and Beroza (2002) concluded 263 based on the study of several past earthquakes that the slip distribution in the wavenumber 264 domain follows the Von Karman autocorrelation function as given bellow 265 ( , ) = [ (1+ 2 ) +1 ] 1 2 ⁄ (6) 266 Where as and ad are the correlation lengths in the strike and dip direction, H is the Hurst exponent 267 which is taken as 0.75, and K is given as 268 in slip is the same as used in the PRM2 model (Table 2). In this PRM5 model, the 338 perturbations to the rake is applied ( Table 2). The rake on the fault plane is varied 339 throughout the fault plane, having a mean value of 180⁰ and a standard deviation of 10⁰. velocity of up to 50% has been found in the damage zone near the fault plane. In the PRM5 347 model, the maximum reduction in velocity is taken as 35% in the fault zone which extends to a 348 depth of 1.5 km beyond the depth of fault where it linearly tapers into the background velocity. 349  The basin is implemented in the form of a horizontal layer or with a varying sediment thickness. 424 The S-wave velocity (VS),) and S-wave quality factor (QS) at the reference frequency (Fr=1.0 Hz), 425 density (), and unrelaxed moduli for the viscoelastic air, BBM, sediment, and rock are given in 426  Table 3. The left panel of Figure 4a shows the recorded 442 ground acceleration and corresponding spectral acceleration on rock at an epicentral distance of 443

528
It is interesting to infer that the SCI effects on the response of building under realistic earthquake 529 loading has caused a plateau like TF in a wide frequency bandwidth. In contrast to this, in most 530 of the past SCI studies using incident plane wave-front and simple source excitation function 531 (Ricker wave or Gabor wavelet), the reduction of TF was maximum at the 0 of building, which 532 buildings is 33 m. The height of buildings of the H1CB-H5CB homogeneous city models is H1-562 H5, respectively as given in Table 4. Similarly, five H1SB-H5SB models with a standalone building 563 at desired location on the same sediment layer with heights as H1-H5, respectively are 564 considered. Table 4 also depicts the 0 of standalone buildings of H1SB-H5SB models. There is 565 no resonance between the buildings of the H1CB and H2CB city models with the sediment layer. 566 The buildings of H3CB and H4CB city models are in partial resonance condition and buildings of 567 responses of all the considered buildings (Fig. 6a). The obtained percentage increase of ATF in 596 the BP of buildings of H1CB city model as compared to that the respective standalone building 597 are given in Table 5

Building-sediment layer in partial resonance 629
A comparison of TF of the 7 th , 15 th , 21 st and 28 th buildings of H3CB and H4CB city models with 630 that of standalone building of the H3SB and H4SB models at the corresponding locations is given 631 in Figure 6c&d, respectively. There is a decrease of TF of all the buildings of H3CB and H4CB 632 city-models, but this decrease of TF is relatively more in the case of H4CB city model. We can 633 infer the reduction of 0 of the buildings of the H3CB and H4CB city-models. Table 5 depicts the 634 percentage reduction of ATF in the BP as compared to that at 0 of the standalone building due 635 to the SCI effects and is highly variable from one building to another building. The obtained range 636 of percentage reduction of ATF in BP is 18.68% to 30.04% and 7.16 to 35.92% for the buildings  (Table 5). For example, its range in the case of H5CB city is 23.38% to 648 38.66%. Analysis of Figure 6 and Table 5 clearly reveals that the SCI effects are maximum in the 649 case of H5CB city-model, and these effects are reducing as we move away from the condition of 650 double resonance. The reason for this can be understood by enquiring about the underlying cause 651 of SCI effects. In the case of double resonance, the motion of the building is relatively high as 652 compared to the motion of a building which is not in complete resonance with the sediment layer.

ROLE OF BASIN HETEROGENEITY IN SCI EFFECTS 738
Nowadays, the city or a particular sector is being developed using a specific design and height of 739 buildings. In nature, the sediment thickness in basin may not be the same everywhere below that 740 city/sector. So, some of the structures may be in double resonance, partial double resonance, 741 and out of double resonance. In order to infer the SCI effects on the responses of a city made up 742 of a particular type of structure but with a varying sediment thickness below it, four B1-B4 basin 743 models are considered. Each basin model is subdivided into five sectors, and the sediment 744 thickness in a particular segment is constant. The thicknesses of sediment in different segments 745 of the basin are given in Table 6. Although the considered step like basin may seem to be 746 unrealistic but the reason why this type of geometry has been selected is to get an exact 747 match of frequencies with the building frequencies considered in the previous section. 748 749 The S-wave velocity in sediment is constant throughout, as given in Table 3. The sediment 754 thickness before and after the city is extending infinitely with the sediment thickness of the first 755 and last segments of different basin models. Figure 11a-d depicts the sketches for the B1-B4 756 basin models, respectively. 757  (Table 7). Even, % reduction of ATF of 28 th 785 building of B4-H5CB is of the order of 70.34%. It is interesting to note that the minimum 786 percentage reduction of ATF is of the order to 13.89% even for buildings which are out of 787 resonance with the underlying basin. The 28 th and 21 st buildings of the B2-H5CB and B4-H5CB 788 cities are in resonance with the underlying basin and the corresponding percentage reduction of 789 ATF is of the order of 41.64% and 38.37% which is comparable or more than that of the buildings 790 of the H5CB city (Table 5). 791 792   (Table 5). For rest of the buildings of both the 817 HT1CB and HT2CB city models, the range of percentage reduction of ATF in the BP of buildings 818 is 8.98% to 37.68% (Table 8). 819 Fig. 13a&b Sketches for the HT1CB and HT2CB heterogeneous site-city models, respectively 822 823 Another interesting result is the obtained percentage reduction of ATF in the case of 7 th 824 building, with as 1.0 Hz and common to both the HT1CB and HT2CB city models, as 825 12.77% and 13.46%, respectively which is much lesser than that obtained in the case of 826 buildings of the H5CB city as 23.38% to 38.66% (Table 5). This may be because there are 827 different buildings (18m and 60m) before the 7 th building, which may modify the ground 828 motion at the location of 7 th building distinctively by radiating motion back to the ground. 829 In contrast to this, the obtained percentage reduction of ATF in the BP of 21 st and 28 th 830 buildings of HT1CB and HT2CB city as 37.68% and 35.63 % (Table 8)   However, an increase of observed reduction of TF in the bandwidth of fundamental mode of 932 vibration of buildings of H4CB model as well as minor apparent increase of 0 of sediment layer 933 can be inferred with an increase of density of the buildings (Figure 16b). Similarly, Figure 16c   model with an increase of damping of the buildings (Figure 18b). Similarly, Figure 18c shows a 1002 substantial decrease of TF function and considerable apparent decrease of 0 of the sediment 1003 layer due to SCI effects in the case of H5CB city model with increase of damping. Further, a 1004 decrease of SCI effects can be inferred with an increase in the damping of the buildings. The 1005 obtained percentage reduction of TF of the sediment layer in the frequency bandwidth of 1006 0.75 -1.25 Hz in H5CB city model were of the order of 19.34%, 18.69%, and 9.51% in the 1007 case of BBM damping as 2.5%, 5%, and 10%, respectively (Table 12). This can be because 1008 buildings with higher damping value radiate lesser motion back to ground which causes the 1009 reduction in TF of the sediment layer.