In populous cities, construction of multistorey buildings close to each other due to space limitation and increased land cost is a dire need. Such construction methods arise several problems during earthquake excitation. The aim of this study is to investigate the bidirectional seismic responses of fully base-isolated (FBI) adjacent buildings having different heights and segregated foundations. Therefore, two scenarios, namely, (a) investigation of the responses of FBI adjacent buildings compared to those with fixed base (FFB) and (b) the effects of separation distance on FBI adjacent buildings, were studied. Based on these investigations, the results showed that isolation system significantly enhances the overall responses of the BI buildings. Spectacularly, the base isolation system was further efficient to decrease displacement rather than the acceleration. In addition, increase of the seismic gap changed the acceleration, pounding, base shear, base moment, and storey drift, as well as the force-deformation performance of the isolators. Therefore, it seems a need to focus on the effect of the separation distances for the design of base isolators for FBI adjacent buildings in future works.
Adjacent buildings are constructed without any structural link connected to surrounding buildings. However, in few cases, they are rarely connected at the foundation level. As a matter of fact, engineers have taken serious concerns about structural damages caused by devastating earthquakes [
Structural responses of adjacent buildings have been investigated by means of nonlinear techniques which demonstrated that collapse of structures has a significant influence on the performance of light and flexibility of buildings mainly in the pounding direction [
From the literature review, it was found that the seismic responses of FBI adjacent buildings have not been studied thoroughly. In this paper, an attempt was thoroughly made by dividing the scenarios into two cases comprising (i) investigate the seismic response characteristics of FBI adjacent building comparing to FFB buildings (Scenario 1) and (ii) investigate the gap size effect on seismic pounding of FBI adjacent buildings (Scenario 2) having different heights. For this aim, lead rubber bearings (LRB) were designed based on the NEHRP provisions [
In the present study, nonlinear dynamic analysis was done using a typical bidirectional seismic recorded and a finite element (FE) analysis package. That is, SAP2000 was selected as an appropriate tool for aiding the purpose. The main equations of motion were taken deliberating equilibrium of forces at each DOF. The motion equations for superstructure and base isolation were written as
All nonlinearities are only restricted to the elements of the base isolator. In the above dynamic equilibrium equation, the base isolator and superstructure are considered as nonlinear and elastic, respectively. Therefore, (
The gap distance between the buildings was represented by the link element in SAP2000. It is remarkable that the gap (link) element is active only in a compression state. The function of the link element (gap element) is to transfer pounding force through itself only at the moment of the impact of buildings. The force-deformation correlation in nonlinearity form was expressed as follows:
The finite element software SAP2000 was implemented to investigate the response of adjacent buildings under different seismic loads by modelling two adjacent ordinary moment-resisting concrete frame (OMRCF) buildings considering FFB adjacent buildings and FBI adjacent buildings subjected to bidirectional earthquake excitations. Nonlinear dynamic time history analysis was carried out through bilateral seismic recorded of Cape (PGA 2.85 m/s2), Los Angeles Century City, LACC-North (PGA 3.85 m/s2), Santa Monica (PGA 1.20 m/s2), and El-Centro (PGA 3.20 m/s2), as shown in Figure
(a) Time histories and (b) spectral accelerations (5% damping) of the applied earthquakes.
Fast nonlinear analysis procedure proposed by Wilson has been weighed to solve the equilibrium equations [
Base isolator (herein LRB) device is shaped by placing a lead plug into a prepared orifice in the scant damping elastomeric bearing. The lead plug is deformed in shear due to enforcing of steel plates. LRB performance is preserved during repetition of severe ground motions with good reliability and durability. LRB generates the required damping and sophisticated initial stiffness. The LRB behaviour is affected by the horizontal elastomer stiffness, horizontal lead plug stiffness, and the yield strength of the lead plug.
The LRB isolator was designed as suggested by Kelly [
LRB details used in this study.
Typical design procedure of base isolators.
Analysis of linear static, the easiest of all, was carried out as the lowest level of complication. Seismic lateral force was defined by taking the
According to the BHRC, the design base shear must not be less than
To calculate the required lateral force for superstructures, we need to compute the minimum and then the maximum effective stiffness of the base isolators. In this regard, the equations are calculated as follows:
In this study, two adjacent buildings having different heights (4- and 8-storey buildings) were considered for the evaluation of structural pounding. The plan and elevation views of the buildings are shown in Figure
Plan and elevation views of buildings having segregated foundations. (a) Plan view; (b) 8-storey-level elevation view; (c) 4-storey-level elevation view.
Location of gap elements and LRB devices in FFB and FBI buildings. (a) FFB adjacent buildings. (b) FBI adjacent buildings.
As Figure
Structural members of OMRCF adjacent buildings.
Column section | Short building | Tall building | Beam section | Short building | Tall building |
---|---|---|---|---|---|
55 × 55 | 1 | 1 | 40 × 60 | 2 | 2 |
50 × 50 | 2 | 2 | 40 × 50 | 2 | 4 |
45 × 45 | 1 | 2 | 30 × 40 | — | 3 |
40 × 40 | — | 3 | — | — | — |
The comparative results of the present study are divided into two parts, in which each part provides a comprehensive study on the objective: Responses of FBI adjacent buildings compared to the FFB adjacent buildings (Scenario 1). Gap size influence on the responses of the FBI adjacent buildings (Scenario 2).
It has ascertained that the input frequency generates the pounding force. In other words, the pounding force is a function of the frequency [
Natural frequency of FFB and FBI systems considering the governor modes.
Mode | FB | Mode | BI | ||||
---|---|---|---|---|---|---|---|
|
|
Mass part. ratio |
|
|
Mass part. ratio | ||
1 | 2.000 | 0.500 | 0.470 | 1 | 3.524 | 0.284 | 0.628 |
4 | 0.962 | 1.039 | 0.301 | 3 | 2.435 | 0.411 | 0.357 |
7 | 0.795 | 1.258 | 0.100 | 7 | 1.110 | 0.900 | 0.012 |
11 | 0.440 | 2.271 | 0.043 | 10 | 0.558 | 1.791 | 0.001 |
For better understanding, the first modal vibration of the buildings for both FFB and FBI adjacent buildings is illustrated in Figure
First modal response of the adjacent structures. (a) FFB adjacent buildings. (b) FBI adjacent buildings.
The envelope displacement values for each floor level of the taller FB and BI buildings subjected to applied earthquakes are presented in Figure Positive relative displacement of the FBI building: 21.2 cm − 10 cm = 11.2 cm < 12 cm for the FFB building (6.7% reduction). Negative relative displacement of the FBI building: (−18.1) − (−11.4) cm = −6.7 cm < −12.1 for the FFB building (44.7% reduction).
Envelope displacements of the taller buildings in different floors under seismic loads.
Furthermore, the distortion of FFB building under applied motions is not desirable such that the building deformations are not controlled unlike the FBI building which has a smooth deformation under the earthquakes as illustrated in the figure. Overall, taking an average calculation for the relative displacement of the buildings under different applied motions shows that the BI system is capable to reduce displacement responses up to 46% in the pounding (longitudinal) direction. The values are indicated in Table
Relative displacement of the taller FFB and FBI buildings under considered motions.
Earthquake | FFB taller building disp. (cm) | FBI taller building disp. (cm) | Reduction (%) | |||
---|---|---|---|---|---|---|
Pos. | Neg. | Pos. | Neg. | Pos. | Neg. | |
Cape | 6.8 | −5.7 | 3.34 | −4.5 | 51 | 21 |
LACC-N | 17.2 | −18.3 | 8.6 | −8 | 50 | 56 |
S-Monica | 14.2 | −14.3 | 5.4 | −5.6 | 62 | 61 |
El-Centro | 12 | −12.1 | 11.2 | −6.7 | 7 | 45 |
Ave. | 42.5 | 46 |
For a shorter building, it can be seen from Figure Positive relative displacement of the BI building: 13.09 − 11.3 = 1.8 cm < 7.1 cm for the FB building (74.6% reduction). Negative relative displacement of the BI building: (−9.3) − (−8) = −1.3 cm < −5.7 cm for the FB building (77.2% reduction).
Envelope displacements of the shorter buildings in different floors under seismic loads.
Overall, taking an average calculation for the relative displacement of the shorter building under different applied motions shows that the BI system is capable to reduce displacement responses up to 77.5% in the pounding (longitudinal) direction. The values are indicated in Table
Relative displacement of the shorter FFB and FBI buildings under considered motions.
Earthquake | FFB shorter building disp. (cm) | FBI shorter building disp. (cm) | Reduction (%) | |||
---|---|---|---|---|---|---|
Pos. | Neg. | Pos. | Neg. | Pos. | Neg. | |
Cape | 2.6 | −2.5 | 1.1 | −0.8 | 58 | 68 |
LACC-N | 10.5 | −7.9 | 1.7 | −2.2 | 84 | 72 |
S-Monica | 6.6 | −5.8 | 1 | −1.9 | 85 | 67 |
El-Centro | 7.1 | −5.7 | 1.8 | −1.3 | 75 | 77 |
Ave. | 75.5 | 71 |
Figures
Displacement time history response of the taller building at the pounding level under the motions. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Displacement time history response of the shorter building at the pounding level under the motions. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Pounding force at the pounding level of FFB and FBI adjacent buildings. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Stopping the displacement in a moment results a rapid and enormous pulse of acceleration at the pounding level in the opposite side. During earthquake excitations, large accelerations will be produced owing to the energetic ground motions. These accelerations may intensify several times once structural pounding happens. Figure
Maximum accelerations of the floor levels of the adjacent buildings under the earthquakes. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Acceleration response of the shorter FFB and FBI buildings under considered motions.
Earthquake | FFB taller building acc. (m/s2) | FBI taller building acc. (m/s2) | Reduction (%) | |||
---|---|---|---|---|---|---|
8th floor | 4th floor | 8th floor | 4th floor | 8th | 4th | |
Cape | −3.1 | −3.3 | −2.6 | −3.2 | 16 | 3 |
LACC-N | −18 | −31 | −4.6 | −11 | 74 | 65 |
S-Monica | −8.2 | −13.2 | −4.6 | −13.5 | 44 | 2 |
El-Centro | −11 | −17.92 | −7.7 | −13.66 | 30 | 24 |
Ave. | 41 | 22.5 | ||||
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||||||
Earthquake | FFB shorter building acc. (m/s2) | FBI shorter building acc. (m/s2) | Reduction (%) | |||
4th floor | 4th floor | 4th | ||||
|
||||||
Cape | 5.4 | 4.5 | 17 | |||
LACC-N | 41 | 11.5 | 72 | |||
S-Monica | 18.6 | 16.8 | 10 | |||
El-Centro | 28.4 | 17 | 40 | |||
Ave. | 35 |
The greater pounding force increases the collapse risk of buildings during ground motions; therefore, it is much favourable to reduce the pounding force between structures. In addition, pounding is too less important in the transverse direction compared to the perpendicular (principal or longitudinal) direction. An investigation of structural pounding between stairway tower and main building revealed that the main structure with considerable stiffness and large mass would response for independent vibration and pounding in the transverse direction [
One of the significant issues in seismic design of structures is controlling or reducing base shear and base moment response of structures. Figure
Base shear for FFB and FBI adjacent buildings under applied earthquakes. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Absolute base shear (kN) of the adjacent buildings under applied earthquakes.
Earthquake | FFB system | FBI system | Reduction (%) | |||
---|---|---|---|---|---|---|
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|
|
|
|
|
|
Cape | 5043 | 5330 | 2910 | 3036 | 42 | 43 |
LACC-N | 21,298 | 19,159 | 5646 | 4629 | 73 | 76 |
S-Monica | 7163 | 7137 | 4223 | 3331 | 41 | 53 |
El-Centro | 11,495 | 12,679 | 5472 | 4246 | 52 | 67 |
Ave. | 52 | 60 |
Absolute base shear reduction in FBI adjacent buildings. (a) Longitudinal direction. (b) Transverse direction.
The base moment response has direct relationship to the base shear of the structure. Thus, it is predicted that the reduction in values of base moment for the FBI buildings be lesser than that of the FFB buildings in both directions. From Figure
Base moment for FFB and FBI adjacent buildings under applied earthquakes. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
Absolute base moment (kN·m) of the adjacent buildings under applied earthquakes.
Earthquake | FFB shorter building disp. (cm) | FBI shorter building disp. (cm) | Reduction (%) | |||
---|---|---|---|---|---|---|
|
|
|
|
|
|
|
Cape | 37,819 | 133,587 | 21,826 | 57,920 | 42 | 57 |
LACC-N | 159,732 | 450,658 | 42,346 | 112,108 | 73 | 75 |
S-Monica | 53,719 | 167,263 | 31,674 | 94,593 | 41 | 43 |
El-Centro | 86,210 | 332,957 | 41,036 | 102,045 | 52 | 69 |
Ave. | 52 | 61 |
Absolute base moment in FFB and FBI adjacent buildings. (a) Longitudinal direction. (b) Transverse direction.
Structural pounding of buildings demonstrated that the transverse direction has insignificant effect in storey drift [
Storey drift for FFB and FBI buildings. (a) Cape. (b) LACC-N. (c) S-Monica. (d) El-Centro.
The variation of shear force for both the FFB and FBI adjacent buildings along the storey levels was compared through Figure
Storey shear force in the adjacent buildings subjected to the different ground motions.
According to previous results, significant reductions were observed for relative displacements, accelerations, pounding forces, base shear, and base moment responses of FBI adjacent buildings. In this section, the FBI adjacent buildings studied above (Figure 30 mm (Case A) 170 mm (Case B) 300 mm (Case C)
By considering the displacement response of the FBI adjacent building, the taller building had more movement; thus, the authors decided to investigate the displacement responses of the taller building. The displacement response along the floor levels is indicated in Figure
Envelope displacement response of the tall BI buildings considering different seismic gaps.
Figure
Acceleration response of BI buildings considering different seismic gaps.
From Table
Effect of different seismic gaps on the pounding force at the pounding level.
Storey level | Separation distance (mm) | Pounding force (kN) | Time (s) |
---|---|---|---|
4th | 30 | 2289.81 | 4.74 |
4th | 170 | 1920.70 | 4.93 |
4th | 300 | 1366.15 | 5.24 |
Pounding force considering different seismic gaps.
Figure
Effect of seismic gaps on base shear and base moment. (a) Longitudinal direction. (b) Transverse direction. (c) Longitudinal direction. (d) Transverse direction.
The storey drift in Cases A and B had approximately the same tendency; however, it had different trends in Case C as shown in Figure
Storey drift in each floor level for different separation distances.
The hysteresis response of the base isolators used in the current study under longitudinal component of the El-Centro earthquake is shown in Figure
Hysteresis behaviour of LRB devices considering different seismic gaps. (a) Shorter building. (b) Taller building.
In the shorter building, the force-deformation (F-D) carried by the isolators was 130 kN-11 mm in Case A. For both 170 mm and 300 mm separation distance, the F-D was similarly 91 kN-7 mm.
In the taller building, the F-D for Case A was 119 kN-10 mm, and for both Case B and C the F-D was 145 kN-13 mm and 147 kN-13 mm, respectively. The behavioural fluctuations of the F-D of isolators were noticeable, spectacularly, for the shorter building, the values of the F-D were decreased as the gap distance between buildings was increased. In contrary, for the taller building, the values of the F-D were increased as the gap distance was increased. Based on these consequences, in design of base isolators for FBI adjacent buildings, it is felt to take the effect of seismic gaps between buildings into consideration.
The overall seismic responses of FBI adjacent buildings considering the effect of different separation gaps are summarized in Table
Summarized responses of fully BI adjacent buildings considering seismic gaps.
Response | Gap distance (mm) | ||
---|---|---|---|
30 | 170 | 300 | |
Pounding force (kN) | 2289.81 | 1920.70 | 1366.15 |
Dis.(taller building−) |
21.21 | 21.33 | 21.14 |
Dis.(taller building+) |
−18.09 | −16.88 | −16.88 |
Acc.(taller building−) |
−15.14 | −11.27 | −7.85 |
Acc.(taller building+) |
5.16 | 4.192 | 4.192 |
Base shear( |
5471.6 | 4351.6 | 4351.6 |
Base shear( |
4246 | 4246 | 4246 |
Base moment( |
41,037 | 30,567 | 30,567 |
Base moment( |
102,044 | 102,319 | 102,573 |
Storey drift ratio | 0.000741 | 0.000535 | 0.000428 |
F-D of base isolators(taller building) (kN·mm) | 119–10 | 145–13 | 147–13 |
F-D of base isolators(shorter building) (kN·mm) | 130–11 | 91–7 | 91–7 |
The present study has been divided into two scenarios. In the first scenario, the nonlinear time history responses of the FFB and FBI adjacent buildings under bilateral excitations have been carried out. To study the effect of the base isolation system on seismic response of the FBI adjacent buildings, their performance has been compared to those with FFB support. In the second scenario, three different seismic gaps have been modelled for the FBI adjacent buildings to investigate the effect of separation gaps on response of the FBI adjacent buildings subjected to earthquake load. From both the scenarios and comparative results of the free vibration and time history analyses, the following conclusions can be drawn: The most impressive option in the study showed that the base isolators resulted in a lower frequency which led the FBI adjacent buildings to have a lower acceleration. All the displacement, storey drift, acceleration, base shear, and base moment responses of the superstructure of the FBI buildings were much less sensitive, whilst these responses for FFB buildings were increased significantly. From the relative displacement analysis and acceleration responses of FBI adjacent buildings, it could be concluded that the base isolation system was further efficient to decrease displacement compared to acceleration. Shear force in the vertical members and maximum base shear of FBI buildings were reduced significantly. So, it anticipates fine to save a number of structures as well as supplies economic aid. Reduction of overturning moment in FBI adjacent buildings makes the buildings more stable in comparison to the FFB adjacent buildings. This leads the buildings to experience less contact in both the transverse and longitudinal directions. Allowance of transitionary displacement of support suddenly mutates the trend of entire building deformation. Closer gap resulted in undesired movements for the middle floors for FBI adjacent buildings. Moreover, closer seismic gap resulted in higher base shear and base moment in the FBI adjacent buildings in the longitudinal (pounding) direction. As seismic gap increases in FBI adjacent buildings, the number of collisions decreases because of time delay in pounding. As base isolators affected the displacement pattern of substructure of buildings, the storey drift of the taller BI adjacent building comes into a favourable trend. The values of the F-D of the base isolators were changed as the seismic gap between buildings was altered. Thus, it is a need to focus on the effect of the seismic gaps on the design of base isolators in future studies.
The authors have no conflicts of interest regarding preparation, contribution, and authorship of the present manuscript.
The authors gratefully acknowledge the support given by Fundamental Research Grant Scheme, Ministry of Education, Malaysia (FRGS project no. FP004-2014B), Postgraduate Research Grant (PPP project no. PG177-2016A), and University of Malaya Research Grant (UMRG project no. RP004A-13AET).