# Suitability of Seismic Isolation for Buildings Founded on Soft Soil. Case Study of a RC Building in Shanghai

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*Buildings*: 10th Anniversary)

## Abstract

**:**

## 1. Introduction

## 2. Building under Consideration

#### 2.1. Superstructure

_{ck}= 30 MPa and the deformation modulus is estimated as E

_{c}= 30 GPa. The reference [16] contains deeper information on the structural parameters. The live (variable) gravity load is established according to the Chinese design code [22], ranging between 2 and 2.5 kN/m

^{2}, except for stairs and other highly crowded areas. The seismic weight corresponds to the combination D + 0.5 L where D and L account for dead (permanent) and live (variable) loads, respectively. For this loading level, the building mass is 9576 t; from the first to top (6th) floor, the masses are 1569, 1652, 1607, 1621, 1854 and 1273 t, respectively. To analyze the influence in the plan symmetry of irregular columns arrangements and other unevenness (e.g., balconies), the eccentricities between the mass and rigidity centers of each floor are determined: in the x direction, the eccentricity ranges between 0.15% (first floor) and 0.70% (top floor) while in the y direction, it ranges between 3.75% (top floor) and 5.14% (first floor).

#### 2.2. Isolation Layer

^{2}for all the devices; Table 1 displays the other main geometric and mechanic parameters of the rubber isolators.

#### 2.3. Soil and Foundation

_{s30}) ranges between 84 and 256 m/s [24]. For the seismic design, the soil is categorized as type IV; this is the softest class, according to the Chinese code [12]. Section 3.3 discusses more deeply the ground parameters that are relevant to the soil–structure interaction.

## 3. Numerical Modeling of the Isolated Building Dynamic Behavior

#### 3.1. Model of the Superstructure

#### 3.2. Model of Isolators and Dampers

#### 3.3. Soil–Structure Interaction Modelling

_{p}A

_{p}/L

_{p}(E

_{p}, A

_{p}and L

_{p}refer to modulus of deformation, cross section area and length of the pile, respectively), and (b) since the piles do not actually reach the bedrock, only the friction stiffness is accounted for. In this last case, the vertical stiffness K

_{vf}of a pile can be calculated by the formulation proposed in [32]:

_{s}is the soil modulus of elasticity, D

_{p}is the pile diameter, λ is the ratio between the pile length and diameter (λ = L

_{p}/D

_{p}), η is the ratio between the soil and pile moduli of elasticity (η = E

_{p}/E

_{s}), and the exponent b is given by b = λ/η. In the analyzed case, E

_{p}= 26 GPa, L

_{p}= 28 m, D

_{p}= 0.60 m, and E

_{s}is calculated after the shear modulus G

_{s}based on the weighted average shear wave velocity (v

_{s}) and the soil density (ρ

_{s}) on the top 28 m. Table 3 displays the soil properties of each layer in the top 28 m:

_{s}= 171.8 m/s and ρ

_{s}= 1795 kg/m

^{3}, respectively; therefore: G

_{s}= 53 MPa, and, by assuming that the Poisson ratio is ν = 0.25, E

_{s}= 132.5 MPa. Finally, E

_{p}A

_{p}/L

_{p}= 263 kN/mm and K

_{vf}= 338 kN/mm; thus, the friction stiffness (K

_{vf}) is 1.29 times higher than the axial one (E

_{p}A

_{p}/L

_{p}), what is consistent with the estimations in [33]. Finally, for each cap, the vertical spring stiffness is obtained as the sum of those of each pile.

## 4. Modal Analysis of the Building

- ▪
**Fixed-base building**. The first mode corresponds basically to motion along the y direction (also some torsion), the second mode involves motion along the x direction (there is torsion as well), and the third mode contains mainly torsion. The relatively long period of the third mode (1.106 s) indicates a low torsional stiffness; this is coherent with the absence of any important stiffening element in the façades. Therefore, further verifications are carried out. The simplified expression for regular reinforced concrete frames that are contained in the European [19] and American [35] codes (among others) provide a fundamental period equal to 0.676 s; since the building is rather flexible (as base isolation allows for significant reductions in the lateral design forces), the difference among this value and those in Table 4 is feasible. For further verification, the building has been also modelled with the PKPM Chinese software code [36]; the obtained periods are highly similar to those from SAP.- ▪
**Base-isolated building**. The first three modes correspond basically to motion along the y, x and φ directions, respectively. Such modes gather most of the mass; this indicates a rather satisfactory performance of base isolation, since those modes correspond basically to rigid-body motion (i.e., without any structural damage).- ▪
**Fixed-base vs. base-isolated building**. Comparison among the periods of the first three modes of the base-isolated building and those of the fixed-base building shows that base isolation elongates the periods as expected. Similar comparison among the modal mass factors shows that the base-isolated building vibrates more symmetrically; this can be read as a proper design of the isolation system, in the sense that the slight plan asymmetry of the fixed-base building is corrected in the isolated solution.

^{−3}are indicated as “-”; SSI-a and SSI-b correspond to the consideration of axial and friction stiffness of the piles, respectively (Section 3.3). As in Table 4, the highlighted values correspond to the biggest component, in terms of modal mass factor, of each mode. Table 5 shows that the influence of SSI on the periods and modal mass ratios of the first three modes can be ignored. Also, comparison between both models of SSI shows little influence of the vertical stiffness of piles; therefore, the SSI results are reliable.

## 5. Seismic Inputs for the Dynamic Analyses

^{2}(moderate earthquake); for the second set, the soil period is 1.1 s and the acceleration is 2.2 m/s

^{2}(rare earthquake). Table 6 and Table 7 display the main features of both sets, respectively; the information in such Tables is described next. In the left column, “NR” accounts for “Natural Record” while “AW” means “Artificial Wave”. x/y directions correspond to strong/weak components, respectively. PGV and PGD refer to Peak Ground Velocity and Displacement, respectively. I

_{A}is the Arias intensity [39] given by ${I}_{\mathrm{A}}=\frac{\mathsf{\pi}}{2g}\int \text{}{\ddot{x}}_{\mathrm{g}}^{2}dt$, where ${\ddot{x}}_{\mathrm{g}}$ is the input ground acceleration; the Arias intensity is an estimator of the input severity. I

_{D}is the dimensionless seismic index [40] given by ${I}_{\mathrm{D}}=\frac{\int \text{}{\ddot{x}}_{\mathrm{g}}^{2}dt}{PGAPGV}$; I

_{D}accounts for the relevance of the velocity pulses. The Trifunac duration is the elapsed time between 5% and 95% of the Arias intensity I

_{A}[41]. The closest distance corresponds to the shortest way to the rupture surface. The hypocentral distance is the straight separation between the hypocentre and the recording station. v

_{s30}is the harmonic weighted average shear wave velocity in the top 30 m; this parameter characterizes the soil type.

^{2}; therefore, the plots in Figure 4c,d are reduced by a factor of 2.2. Figure 4 shows a rather satisfactory fit between the spectra of the scaled inputs and the code spectrum, particularly in the main (x) direction.

## 6. Time-History Analysis

#### 6.1. Global Description of the Analyses

#### 6.2. General Overview of the Results

_{ζ}, E

_{HD}, E

_{HI}) and the input energy E

_{I}. E

_{ζ}, E

_{HD}and E

_{HI}are the energy dissipated by the structural damping, the viscous dampers and the rubber bearings, respectively; at the end of the shake, the energy balance reads E

_{I}≈ E

_{ζ}+ E

_{HD}+ E

_{HI}.

_{I}, E

_{ζ}, E

_{HD}and E

_{HI}(Table 10) for the input NR0.9-6 (Table 6); “Input Energy”, “Damping Energy”, “Dampers Energy” and “Isolators Energy” account for E

_{I}, E

_{ζ}, E

_{HD}and E

_{HI}, respectively.

- ▪
**Drift angle in the superstructure**. Except in few cases, the isolation reduces the drift displacements; for the 0.22 g inputs (Table 9), that lessening is higher in the top stories. In base isolation conditions, the drift is rather moderate, even for the strongest inputs (Table 9); this trend confirms that the assumption of linear behavior for the superstructure is correct. Finally, comparison between the results for inputs with maximum acceleration 0.1 g and 0.22 g shows that the reduction generated by the isolation is greater for the strongest inputs; this difference can be explained by the non-linear behavior of the lead-rubber bearings: the higher the shear strain, the higher the equivalent damping and the lower the effective secant stiffness, thus leading to a more intense isolation.- ▪
**Drift angle in the isolators**. The shear strains for the inputs with acceleration 0.22 g (Table 9) are more than 2.2 times higher than those for the inputs with 0.1 g (Table 8). Obviously, this circumstance implies non-linear behavior of the lead-rubber bearings. On the other hand, no relevant permanent displacements are observed; this can be read as a satisfactory behavior of the isolation units.- ▪
**Shear coefficient in the superstructure**. The isolation diminishes significantly the story shear forces; that decreasing is higher for the top stories and the strongest inputs. For the base-isolated building, the shear coefficient is near-constant along the building height; this seems to indicate a high participation of the first mode.- ▪
**Base shear coefficient**. As expected, the isolation reduces appreciably the base shear force. For the less severe inputs (0.1 g, Table 8), the diminution ranges between 55% (“y” case) and 70% (“x” case); for the strongest inputs (0.22 g, Table 9), the lessening is roughly 75% in all the cases. This difference can be explained by the non-linear behavior of the lead-rubber bearings.- ▪
**Absolute acceleration in the superstructure**. The absolute acceleration at the ground floor (above the isolation layer) is not reduced, compared to the driving input; in numerous cases, it is even slightly increased. This undesired circumstance might be due to the soft soil influence. However, in the other floors, the absolute acceleration is decreased, compared to the fixed-base case; more precisely, as is common in seismically isolated buildings, the reduction is higher in the top stories. As well, such decreasing is more important for the inputs with acceleration 0.22 g (Table 9). It is well known that the spectral ordinate is roughly equivalent to the ratio between the ground and the top floor acceleration; accordingly, the percentages of reduction of the top floor absolute acceleration and the base shear force are rather similar.- ▪
**Dissipated energy**. Table 10 shows that the percentage of energy dissipated at the isolation interface (E_{HD}+ E_{HI}, corresponding to viscous dampers and lead-rubber bearings, respectively) is above 80% of the input energy, being slightly higher for the stronger inputs (Table 9). Comparison with the ordinary values of the ratio between the input and hysteretic energies [45] shows that this percentage is clearly above the common demands in terms of energy contributable to damage. Plots from Figure 7 show that the maximum values are obtained at the end of shake; this observation confirms that, for energy-based design, using the final values of energy is an adequate strategy.- ▪
**Simultaneity of the x and y inputs**. As expected, for both the fixed-base and base-isolated buildings, the average drift ratios and shear coefficients for the simultaneous action of the x and y inputs are bigger than those generated by the x and y inputs acting separately. Conversely, regarding the absolute acceleration, the balance is unclear; this apparent inconsistency can be explained by the small building asymmetry (Section 2.1), as any unidirectional input can generate responses containing x, y and torsion (φ) components (Table 4). Broadly speaking, the strategy of combining the full value in one direction with 30% of the value in the orthogonal direction seems to be sufficiently conservative.

#### 6.3. Results for the Rubber Bearings

**Buckling stability**. The Chinese code [12] indicates that the average drift displacement in the rubber isolators should not exceed 0.55 times the rubber diameter. This condition is fulfilled in almost all the cases; more precisely, that threshold is only (slightly) exceeded in one case (corresponding to a “x + y” case). The Chinese code does not explicitly require consideration of that coincident actuation; for this unclear situation, the European regulation [21] is considered instead. In that code, it is required that the demanding axial force does not exceed the critical load of each isolator unit; such force is given by P

_{cr}= λ G A

_{r}a′ S/T

_{q}, where λ = 1.1 (for circular devices), G is the rubber shear deformation modulus, A

_{r}is the rubber bearing plan area, a′ is the device diameter, S is the shape factor (ratio between the diameter of the device and the thickness of each rubber layer) and T

_{q}is the total rubber thickness. By neglecting (conservatively) the stiffening effect of the lead plug, the following two values of the critical load are obtained:

_{Ed,max}= 4536 kN (device No. 24, input NR1.1-7, case “x + y”) and N

_{Ed,max}= 6099 kN (device No. 17, input NR1.1-7, case “x + y”), respectively; thus, in both cases N

_{Ed,max}< P

_{cr}/4. On the other hand, [21] prescribes that it should be also checked that δ ≤ 0.7, where δ is the ratio between the design drift displacement d

_{bd}and the device diameter; the design drift is conservatively taken as the maximum value in Table 11: δ = 0.7 and 0.61 for 700 and 800 mm isolators, respectively. Therefore, this criterion is fulfilled in both types of device.

**Maximum shear strain**. In the European code [21], the maximum design shear strain is given by ε

_{t,d}= ε

_{c,E}+ ε

_{q,max}+ ε

_{α,d}; in this expression, ε

_{c,E}= 6 S/A

_{r}E′

_{c}, E′

_{c}= 3 G (1 +2 S

^{2}), ε

_{q,max}= d

_{bd}/T

_{q}≤ 2.5, and ε

_{α,d}= 0.003 (a′

^{2}+ b′

^{2}) t

_{r}/2 Σ t

^{3}

_{r}, where a′ = b′ (for circular devices), and t

_{r}is the thickness of each rubber layer. For the 700 mm diameter isolators, E′

_{c}= 2882 MPa, and for the 800 mm ones, E′

_{c}= 2614 MPa; then:

_{m}(where γ

_{m}is a safety factor, being γ

_{m}= 1 in this case), this criterion is fulfilled.

#### 6.4. Influence of Soil–Structure Interaction

#### 6.5. Influence of Changes of the Isolation Units’ Parameters

## 7. Conclusions

- ▪
**Global**. Isolation reduces significantly the base shear force, being more efficient for the strongest inputs; also, the SSI effect is rather negligible. Additionally, the simultaneous actuation of both input horizontal components is compared with the usual simplified combination criteria; it is concluded that they frequently underestimate the demand.- ▪
**Isolation layer**. The demand on the isolators is checked in terms of buckling instability and shear strain; on the other hand, the percentage of hysteretic energy that is dissipated by the isolation interface is high, clearly above common demands. Finally, it is observed that there are no relevant permanent displacements.- ▪
**Superstructure**. Relative displacements, shear forces and absolute accelerations are significantly reduced, except the ground floor accelerations.

## Author Contributions

## Funding

## Conflicts of Interest

## List of Symbols

A_{r} | Rubber bearing plan area |

a′, b′ | Rubber bearing diameter |

b | Exponent is given by b = λ/η (Equation (2)) |

c | Dampers damping coefficient |

D, L | Dead (permanent) and live (variable) loads |

d_{bd} | Design drift displacement |

E_{c}, E_{s}, E′_{c} | Concrete (soil, rubber) deformation modulus |

E_{p}, A_{p}, L_{p} | Modulus of deformation, cross section area and length of a pile |

E_{ζ}, E_{HD}, E_{HI} | Energy dissipated by the structural damping, the viscous dampers and the rubber bearings |

f | Damper force (Equation (1)) |

f_{ck} | Characteristic value of the concrete compressive strength |

G, G_{s} | Rubber (soil) shear modulus |

I_{A}, I_{D} | Arias Intensity, dimensionless seismic index (Table 6) |

K_{vf} | Vertical stiffness of a pile |

N_{Ed,max} | Demanding axial force in the isolator units (rubber bearings) |

P_{cr} | Critical load for each isolator unit (rubber bearing) |

PGA, PGD, PGV | Peak Ground Acceleration (Displacement, Velocity) |

S | Shape factor of a rubber bearing (ratio between the diameter of the device and the thickness of each rubber layer) |

T_{q} | Total rubber thickness of a rubber bearing |

t_{r} | Thickness of each rubber layer of a rubber bearing |

v_{s} | Weighted harmonic average shear wave velocity (v_{s30} refers to the top 30 m) |

x_{g} | Ground displacement |

x, y | Horizontal coordinates along the longitudinal and transverse directions of the building (Figure 1, Figure 2 and Figure 4). Directions of the strong/weak components of the seismic inputs (Table 6 and Table 7). |

α | Exponent (Equation (1)) |

Δt | Time step |

δ | Ratio between the design drift displacement (d_{bd}) and the device (rubber bearing) diameter |

ε_{t,d}, ε_{c,E}, ε_{q,max}, ε _{α,d} | Shear strain coefficients for the rubber bearing |

φ | Torsion angle |

γ_{m} | Safety factor for the rubber bearings (γ_{m} = 1) |

λ | Ratio between the pile length and diameter (λ = L_{p}/D_{p}, Equation (2)). Coefficient for the critical load of an isolator unit (rubber bearing). Factor modifying the mechanical parameters of the rubber bearings. |

η | Ratio between the soil and pile moduli of elasticity (η = E_{p}/E_{s}, Equation (2)) |

ρ_{s} | Soil density |

## References

- Kelly, J.M. Aseismic base isolation: Review and bibliography. Soil Dyn. Earthq. Eng.
**1986**, 5, 202–217. [Google Scholar] [CrossRef] - Buckle, I.G.; Mayes, R.L. Seismic isolation: History, application, and performance. A world overview. Earthq. Spectra
**1990**, 6, 161–202. [Google Scholar] [CrossRef] - Koh, H.M.; Song, J.; Ha, D.H. Cost effectiveness of seismic isolation for bridges in low and moderate seismic region. In Proceedings of the 12th World Conference on Earthquake Engineering (12WCEE), Auckland, New Zealand, 30 January–4 February 2000; p. 1100. [Google Scholar]
- Deb, S.K. Seismic base isolation—An overview. Curr. Sci.
**2004**, 87, 1426–1430. [Google Scholar] - Higashino, M.; Okamoto, S. (Eds.) Response Control and Seismic Isolation of Buildings; Taylor & Francis: Milton Park, UK, 2006. [Google Scholar]
- Constantinou, M.; Kneifati, M. Dynamics of Soil-Base-Isolated-Structure Systems. J. Struct. Eng. ASCE
**1988**, 114, 211–221. [Google Scholar] [CrossRef] - Vlassis, A.G.; Spyrakos, C.C. Seismically isolated bridge piers on shallow stratum with soil–structure interaction. Comput. Struct.
**2001**, 79, 2847–2861. [Google Scholar] [CrossRef] - Spyrakos, C.C.; Koutromanos, I.A.; Maniatakis, C.A. Seismic response of base-isolated buildings including soil–structure interaction. Soil Dyn. Earthq. Eng.
**2009**, 29, 658–668. [Google Scholar] [CrossRef] - Spyrakos, C.C.; Maniatakis, C.A.; Koutromanos, I.A. Soil-structure interaction effects on base-isolated buildings founded on soil stratum. Eng. Struct.
**2009**, 31, 729–737. [Google Scholar] [CrossRef] - Enomoto, T.; Yamamoto, T.; Ninomiya, M.; Miyamoto, Y.; Navarro, M. Seismic Response Analysis of Base Isolated RC Building Building Considering Dynamical Interaction Between Soil and Structure. In Proceedings of the 15th World Conference on Earthquake Engineering (15WCEE), Lisbon, Portugal, 24–28 September 2012; p. 3611. [Google Scholar]
- Alavi, E.; Alidoost, M. Soil-Structure Interaction Effects on Seismic Behavior of Base-Isolated Buildings. In Proceedings of the 15th World Conference on Earthquake Engineering (15WCEE), Lisbon, Portugal, 24–28 September 2012; p. 4982. [Google Scholar]
- GB50011. Code for Seismic Design of Buildings; Ministry of Housing and Urban-Rural Development: Beijing, China, 2010. [Google Scholar]
- E.030. Norma Técnica de Edificación E.030 Diseño Sismorresistente; Ministerio de Vivienda, Construcción y Saneamiento: Madrid, Spain, 2014. [Google Scholar]
- ASCE 7–16. Minimum Design Loads and Associated Criteria for Buildings and Other Structures; American Society of Civil Engineers: Reston, VA, USA, 2016. [Google Scholar]
- Zhou, Y.; Wu, C.X.; Zhang, C.L. Analysis and Design of Seismic Isolation Structure in Outpatient Building of the Lushan County People’s Hospital. Build. Struct.
**2013**, 43, 23–27. (In Chinese) [Google Scholar] - Weng, D.; Zhang, S.; Hu, X.; Chen, T.; Zhou, Y. Seismic Isolation Design Soil of a Teaching Building for Shanghai Foreign Language School; Research Institute of Structural Engineering and Disaster Reduction, Tongji University: Shanghai, China, 2012. (In Chinese) [Google Scholar]
- Weng, D.; Tao, L.; Alfarah, B.; López-Almansa, F. Nonlinear time-history analysis of a base-isolated RC building in Shanghai founded on soft soil. In Proceedings of the 16th World Conference on Earthquake Engineering (16WCEE), Santiago de Chile, Chile, 9–13 January 2017; p. 2634. [Google Scholar]
- CSI Analysis Reference Manual for SAP2000
^{®}, ETABS^{®}, and SAFE^{®}; CSI (Computers and Structures, Inc.): Berkeley, CA, USA, 2010. - EN 1998-1. Eurocode 8: Design of Structures for Earthquake Resistance; European Committee for Standardization: Brussels, Belgium, 2004. [Google Scholar]
- EN 15129. Anti-Seismic Devices; European Committee for Standardization: Brussels, Belgium, 2009. [Google Scholar]
- EN 1337-3. Structural Bearings. Part 3: Elastomeric Bearings; European Committee for Standardization: Brussels, Belgium, 2005. [Google Scholar]
- GB50009. Load Code for Design of Building Structures; Ministry of Housing and Urban-Rural Development: Beijing, China, 2010. [Google Scholar]
- Inaudi, J.A.; Kelly, J.M. Optimum damping in linear isolation systems. Earthq. Eng. Struct. Dyn.
**1993**, 22, 583–598. [Google Scholar] [CrossRef] - DGJ 08-37. Code for Investigation of Geotechnical Engineering; Shanghai Geotechnical Investigations & Design Institute Co, Ltd.: Shanghai, China, 2012. [Google Scholar]
- FEMA 356. Prestandard and Commentary for the Seismic Rehabilitation of Buildings; Federal Emergency Management Agency: Washington, DC, USA, 2000. [Google Scholar]
- Castaldo, P.; De Iuliis, M. Optimal integrated seismic design of structural and viscoelastic bracing-damper systems. Earthq. Eng. Struct. Dyn.
**2014**, 43, 1809–1827. [Google Scholar] [CrossRef] - Ou, J.P.; Long, X.; Li, Q.S. Seismic response analysis of structures with velocity-dependent dampers. J. Constr. Steel Res.
**2007**, 63, 628–638. [Google Scholar] [CrossRef] - Luco, J.E. Effects of soil–structure interaction on seismic base isolation. Soil Dyn. Earthq. Eng.
**2014**, 66, 167–177. [Google Scholar] [CrossRef] - Hatami, F.; Nademi, H.; Rahaie, M. Effects of Soil-Structure Interaction on the Seismic Response of Base Isolated in High-Rise Buildings. Int. J. Struct. Civ. Eng. Res.
**2015**, 4, 237–242. [Google Scholar] [CrossRef] [Green Version] - Sayyad, S.T.; Bhusare, V. Effectiveness of base isolator in high-rise building for different soil conditions using FEM. Int. J. Sci. Dev. Res.
**2016**, 1, 291–295. [Google Scholar] - FEMA 273. NEHRP Guidelines for the Seismic Rehabilitation of Buildings; Federal Emergency Management Agency: Washington, DC, USA, 1997. [Google Scholar]
- Gazetas, G.; Makris, N. Dynamic pile-soil-pile interaction. Part I: Analysis of axial vibration. J. Earthq. Eng. Struct. Dyn.
**1991**, 20, 115–132. [Google Scholar] [CrossRef] - ATC-40. Seismic Evaluation and Retrofit of Concrete Buildings; Applied Technology Council: Redwood City, CA, USA, 1996. [Google Scholar]
- Gazetas, G. Formulas and charts for impedances of surface and embedded foundations. J. Geotech. Eng. ASCE
**1991**, 117, 1363–1381. [Google Scholar] [CrossRef] - UBC (Uniform Building Code); International Council of Building Officials: Lansing, MI, USA, 1997.
- PKPM. SATWE Users’ Manual. 2014. Available online: http://www.pkpm.cn/ (accessed on 12 December 2020).
- DGJ 08-9. Code for Seismic Design of Buildings; Tongji University Shanghai Urban Construction and Communication Commission: Shanghai, China, 2013. [Google Scholar]
- PEER. Users Manual for the PEER Ground Motion Database Web Application; Technical Report; Pacific Earthquake Engineering Research Center (PEER): Berkeley, CA, USA, 2011. [Google Scholar]
- Arias, A. A Measure of Earthquake Intensity. Seismic Design for Nuclear Power Plants; MIT Press: Cambridge, MA, USA, 1970; pp. 438–443. [Google Scholar]
- Manfredi, G. Evaluation of seismic energy demand. Earthq. Eng. Struct. Dyn.
**2001**, 30, 485–499. [Google Scholar] [CrossRef] - Trifunac, M.D.; Brady, A.G. Study on the duration of strong earthquake ground motion. Bull. Seismol. Soc. Am.
**1975**, 65, 581–626. [Google Scholar] - Gomase, O.; Bakre, S. Performance of Non-Linear Elastomeric Base-Isolated building structure. Int. J. Civ. Struct. Eng.
**2011**, 2, 280–291. [Google Scholar] - Castaldo, P.; Gino, D.; Mancini, G. Safety formats for non-linear finite element analysis of reinforced concrete structures: Discussion, comparison and proposals. Eng. Struct.
**2019**, 193, 136–153. [Google Scholar] [CrossRef] - Haukaas, T.; Gardoni, P. Model uncertainty in finite-element analysis: Bayesian finite elements. J. Eng. Mech.
**2011**, 137, 519–526. [Google Scholar] [CrossRef] - López Almansa, F.; Yazgan, U.; Benavent Climent, A. Design energy input spectra for moderate-to-high seismicity regions based on Turkish registers. Bull. Earthq. Eng.
**2013**, 11, 885–912. [Google Scholar] [CrossRef] [Green Version]

**Figure 4.**Comparison between the response spectra of the natural selected inputs and the code design spectra.

**Figure 5.**Dynamic responses of two isolators and a damper for input NR1.1-7 in the x direction (Table 7).

**Figure 7.**Time-history of the energy components for the input NR0.9-6 (Table 6).

Name | Diameter (mm) | Height (mm) | Rubber Layer Height (mm) | Rubber Height (mm) | Lead Plug Diameter (mm) | Horizontal Stiffness (kN/m) | Critical Shear Strain/Stress (%/MPa) | Yielding Force (kN) | After-Yielding Horizontal Stiffness (kN/m) |
---|---|---|---|---|---|---|---|---|---|

NRB700 | 700 | 451.5 | 5 | 200 | - | 742 | 280/8 | - | - |

NRB800 | 800 | 438.5 | 6 | 204 | - | 951 | 301/10 | - | - |

LRB700 | 700 | 451.5 | 5 | 200 | 160 | 1565 | 282/8 | 160 | 764 |

LRB800 | 800 | 438.5 | 6 | 204 | 160 | 1758 | 304/10 | 160 | 972 |

Direction | Exponent α | Initial Stiffness (kN/mm) * | Maximum Stroke (mm) | Damping Coefficient c (kN/(mm/s)^{0.4}) | Speed (mm/s) | Maximum Damping Force (kN) | Design Life (Years) |
---|---|---|---|---|---|---|---|

x | 0.4 | 49 | ±350 | 70 | 600 | 900 | 50 |

y | 0.4 | 42 | ±350 | 60 | 600 | 800 | 50 |

Layer Type | Cumulated Depth (m) | Density (kg/m^{3}) | Shear Wave Velocity (m/s) |
---|---|---|---|

Filled earth | 4.2 | 1870 | 112 |

Muddy-silty clay | 9.5 | 1820 | 128 |

Muddy clay | 22.5 | 1760 | 178 |

Muddy-silty clay | 32.8 | 1800 | 245 |

Mode No. | Period (s) | Modal Mass Factor x | Modal Mass Factor y | Modal Mass Factor φ |
---|---|---|---|---|

-/1 | -/3.586 | -/0.046 | -/0.910 | -/0.03561 |

-/2 | -/3.528 | -/0.940 | -/0.053 | -/0.0039 |

-/3 | -/2.983 | -/0.011 | -/0.029 | -/0.96049 |

1/4 | 1.229/0.571 | 0.010/7.25 × 10^{−7} | 0.717/0.004 | 0.074/1.142 |

2/5 | 1.163/0.502 | 0.621/2.29 × 10^{−3} | 0.046/1.02 × 10^{−6} | 0.156/2.23 × 10^{−6} |

3/6 | 1.106/0.177 | 0.196/7.08 × 10^{−8} | 0.037/0.39 × 10^{−6} | 0.569/8.59 × 10^{−8} |

**Table 5.**Modal parameters of the base-isolated building considering and without considering soil–structure interaction (SSI).

Mode No. | Period (s) | Modal Mass Factor x | Modal Mass Factor y | Modal Mass Factor φ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

SSI-a | SSI-b | No SSI | SSI-a | SSI-b | No SSI | SSI-a | SSI-b | No SSI | SSI-a | SSI-b | No SSI | |

1 | 3.603 | 3.608 | 3.586 | 0.032 | 0.053 | 0.046 | 0.942 | 0.877 | 0.910 | 0.023 | 0.067 | 0.036 |

2 | 3.544 | 3.540 | 3.528 | 0.957 | 0.922 | 0.940 | 0.036 | 0.067 | 0.053 | 0.004 | 0.008 | 0.004 |

3 | 2.892 | 3.178 | 2.983 | 0.008 | 0.022 | 0.011 | 0.018 | 0.052 | 0.029 | 0.972 | 0.921 | 0.961 |

4 | 0.443 | 0.661 | 0.571 | 0.002 | - | - | - | 0.003 | 0.004 | - | - | - |

5 | 0.306 | 0.600 | 0.502 | - | 0.002 | - | 0.004 | - | - | 0.001 | 0.001 | - |

6 | 0.193 | 0.580 | 0.177 | - | 0.001 | - | - | - | - | - | 0.003 | - |

**Table 6.**Seismic inputs for soil predominant period 0.9 s and scaled to maximum acceleration 1 m/s

^{2}.

Code | Earthquake | Date | M_{w} | Hypocentral Depth (km) | Station | Component | PGV (m/s) | PGD (cm) | I_{A}(m/s) | I_{D} | Trifunac Duration (s) | Closest Distance (km) | Hypocentral Distance (km) | v_{s30}(m/s) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

NR0.9-3 | Kocaeli, Turkey | 17-08-1999 | 7.51 | 15.0 | USAK | x | USK090 | 0.272 | 4.831 | 0.451 | 10.36 | 35.52 | 226.7 | 237.0 | 274.5 |

y | USK180 | 0.310 | 7.700 | 0.264 | 5.32 | 35.36 | |||||||||

NR0.9-4 | Hector Mine, USA | 16-10-1999 | 7.13 | 5.0 | San Bernardino Fire Station #9 | x | 0688c090 | 0.262 | 3.967 | 0.317 | 7.56 | 20.44 | 108.0 | 114.8 | 271.4 |

y | 0688a360 | 0.123 | 7.532 | 0.280 | 14.22 | 28.10 | |||||||||

NR0.9-5 | Denali, USA | 03-11-2002 | 7.9 | 4.9 | Anchorage New Fire Station #7 | x | 1734090 | 0.262 | 3.967 | 0.499 | 11.89 | 31.72 | 275.9 | 296.55 | 274.5 |

y | 1734360 | 0.228 | 2.060 | 0.561 | 15.37 | 29.80 | |||||||||

NR0.9-6 | Chichi, Taiwan | 20-09-1999 | 6.02 | 18.0 | CHY039 | x | CHY039-N | 0.197 | 14.260 | 0.349 | 11.06 | 35.70 | 46.8 | 52.53 | 201.2 |

y | CHY039-E | 0.244 | 18.919 | 0.299 | 7.65 | 36.72 | |||||||||

NR0.9-7 | Chichi, Taiwan | 20-09-1999 | 7.62 | 18.0 | CHY059 | x | CHY059-N | 0.185 | 14.162 | 0.398 | 13.44 | 38.56 | 86.3 | 88.53 | 191.1 |

y | CHY059-E | 0.190 | 6.717 | 0.361 | 11.87 | 33.94 | |||||||||

AW0.9-2 | Loma Prieta, USA | 18-10-1989 | 6.93 | 17.5 | Foster City Menhaden Court | x | MEN270 | 0.272 | 2.138 | 0.317 | 7.28 | 22.08 | 45.4 | 68.0 | 126.4 |

y | MEN360 | 0.242 | 2.211 | 0.308 | 7.95 | 20.10 | |||||||||

AW0.9-1 | Hokkaido, Japan | 29-11-2004 | 7.1 | 48 | HKD085 | x | HKD085EW | 0.274 | 2.127 | 0.344 | 7.84 | 41.68 | 98.1 | - | 150.0 |

y | HKD085NS | 0.242 | 2.762 | 0.183 | 4.72 | 33.04 |

**Table 7.**Seismic inputs for soil predominant period 1.1 s and scaled to maximum acceleration 2.2 m/s

^{2}.

Code | Earthquake | Date | M_{w} | Hypocentral Depth (km) | Station | Component | PGV (m/s) | PGD (cm) | I_{A}(m/s) | I_{D} | Trifunac Duration (s) | Closest Distance (km) | Hypocentral Distance (km) | v_{s30}(m/s) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

NR1.1-3 | Imperial Valley, USA | 15-10-1979 | 7.62 | 10.0 | El Centro Array #12 | x | H-E12140 | 0.443 | 25.937 | 1.390 | 8.91 | 19.38 | 17.9 | 33.5 | 196.9 |

y | H-E12230 | 0.284 | 20.607 | 0.975 | 9.75 | 19.14 | |||||||||

NR1.1-4 | Chichi, Taiwan | 20-09-1999 | 7.62 | 6.8 | CHY058 | x | CHY058-E | 0.467 | 34.299 | 3.615 | 21.97 | 45.64 | 59.8 | 91.4 | 237.6 |

y | CHY058-N | 0.490 | 32.451 | 2.896 | 16.78 | 45.88 | |||||||||

NR1.1-5 | Chichi, Taiwan | 20-09-1999 | 7.62 | 6.8 | CHY090 | x | CHY090-E | 0.446 | 28.146 | 2.917 | 18.57 | 38.78 | 58.4 | 89.8 | 201 |

y | CHY090-N | 0.556 | 40.618 | 2.569 | 13.12 | 45.32 | |||||||||

NR1.1-6 | Chichi, Taiwan | 20-09-1999 | 7.62 | 6.8 | KAU008 | x | KAU008-E | 0.575 | 68.312 | 3.230 | 15.95 | 46.06 | 107.0 | 143.7 | 285.9 |

y | KAU008-N | 0.633 | 57.951 | 3.054 | 13.70 | 46.06 | |||||||||

NR1.1-7 | Chichi, Taiwan | 20-09-1999 | 7.62 | 6.8 | KAU058 | x | KAU058-E | 0.584 | 76.979 | 3.172 | 15.42 | 40.16 | 107.8 | 143.3 | 201 |

y | KAU058-N | 0.717 | 72.504 | 4.263 | 16.88 | 46.84 | |||||||||

AW1.1-2 | Morgan Hill | 24-04-1984 | 6.19 | 8.5 | Foster City APEEL 1 | x | A01040 | 0.450 | 55.382 | 1.528 | 9.64 | 26.82 | 53.9 | 55.0 | 116.4 |

y | A01310 | 0.552 | 50.816 | 1.558 | 8.01 | 26.56 | |||||||||

AW1.1-1 | Hokkaido, Japan | 26-09-2003 | 8.0 | 42 | HKD066 | x | HKD066EW | 0.423 | 34.131 | 1.202 | 8.07 | 39.74 | 226.5 | - | 116.1 |

y | HKD066NS | 0.396 | 45.887 | 1.756 | 12.59 | 45.56 |

**Table 8.**Average maximum * response values for the records NR0.9-3, NR0.9-6 and AW0.9-1 (Table 6).

Story | Input Direction | Drift Angle (%) | Shear Force/Supported Weight | Absolute Acceleration/Input Acceleration | |||
---|---|---|---|---|---|---|---|

Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | ||

Ground | x | - | 22.0 ** | - | 0.042 | 1 | 1.035 |

y | - | 42.5 ** | - | 0.052 | 1 | 1.034 | |

x + y | - | 46.5 ** | - | 0.059 | 1 | 1.124 | |

1 | x | 0.306 | 0.161 | 0.147 | 0.054 | 1.178 | 0.726 |

y | 0.247 | 0.193 | 0.122 | 0.058 | 0.963 | 0.745 | |

x + y | 0.350 | 0.219 | 0.170 | 0.069 | 1.088 | 0.749 | |

2 | x | 0.472 | 0.160 | 0.174 | 0.054 | 1.347 | 0.481 |

y | 0.452 | 0.219 | 0.134 | 0.058 | 1.031 | 0.569 | |

x + y | 0.559 | 0.240 | 0.197 | 0.072 | 1.230 | 0.543 | |

3 | x | 0.464 | 0.133 | 0.200 | 0.054 | 1.405 | 0.438 |

y | 0.468 | 0.195 | 0.147 | 0.058 | 1.277 | 0.530 | |

x + y | 0.553 | 0.210 | 0.221 | 0.069 | 1.399 | 0.513 | |

4 | x | 0.408 | 0.106 | 0.222 | 0.054 | 1.819 | 0.580 |

y | 0.410 | 0.157 | 0.159 | 0.058 | 1.517 | 0.615 | |

x + y | 0.486 | 0.169 | 0.241 | 0.070 | 1.758 | 0.607 | |

5 | x | 0.277 | 0.068 | 0.238 | 0.055 | 2.188 | 0.694 |

y | 0.296 | 0.108 | 0.170 | 0.059 | 1.721 | 0.736 | |

x + y | 0.340 | 0.114 | 0.257 | 0.071 | 2.041 | 0.696 | |

6 | x | 0.147 | 0.036 | 0.262 | 0.059 | 2.426 | 0.762 |

y | 0.176 | 0.063 | 0.188 | 0.062 | 1.923 | 0.831 | |

x + y | 0.192 | 0.066 | 0.282 | 0.076 | 2.242 | 0.774 |

**Table 9.**Average of maximum * response values for the records NR1.1-5, NR1.1-7 and AW1.1-1 (Table 7).

Story | Input Direction | Drift Angle (%) | Shear Force/Supported Weight | Absolute Acceleration/Input Acceleration | |||
---|---|---|---|---|---|---|---|

Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | ||

Ground | x | - | 128.0 ** | - | 0.095 | 1 | 0.763 |

y | - | 132.0 ** | - | 0.105 | 1 | 1.035 | |

x + y | - | 168.5 ** | - | 0.126 | 1 | 0.947 | |

1 | x | 0.772 | 0.308 | 0.379 | 0.103 | 1.215 | 0.568 |

y | 0.903 | 0.381 | 0.387 | 0.115 | 1.073 | 0.731 | |

x + y | 1.066 | 0.434 | 0.457 | 0.133 | 1.199 | 0.621 | |

2 | x | 1.139 | 0.307 | 0.415 | 0.103 | 1.539 | 0.470 |

y | 1.656 | 0.433 | 0.453 | 0.115 | 1.636 | 0.497 | |

x + y | 1.919 | 0.475 | 0.516 | 0.141 | 1.633 | 0.502 | |

3 | x | 1.095 | 0.255 | 0.465 | 0.103 | 1.826 | 0.438 |

y | 1.726 | 0.384 | 0.520 | 0.115 | 2.152 | 0.480 | |

x + y | 2.018 | 0.415 | 0.591 | 0.133 | 2.210 | 0.509 | |

4 | x | 0.960 | 0.204 | 0.513 | 0.104 | 2.012 | 0.497 |

y | 1.541 | 0.310 | 0.580 | 0.116 | 2.586 | 0.523 | |

x + y | 1.803 | 0.335 | 0.660 | 0.134 | 2.658 | 0.542 | |

5 | x | 0.659 | 0.131 | 0.564 | 0.106 | 2.330 | 0.562 |

y | 1.118 | 0.213 | 0.631 | 0.118 | 2.992 | 0.582 | |

x + y | 1.311 | 0.227 | 0.716 | 0.135 | 3.082 | 0.578 | |

6 | x | 0.356 | 0.068 | 0.630 | 0.115 | 2.733 | 0.604 |

y | 0.668 | 0.125 | 0.708 | 0.126 | 3.433 | 0.631 | |

x + y | 0.786 | 0.130 | 0.797 | 0.145 | 3.463 | 0.625 |

Input | Maximum * Drift Angle (%) | Maximum * Shear Force/Supported Weight | Maximum * Accel./Input Acceleration | E_{ζ}/E_{I} (Struct. Damp.) | E_{HD}/E_{I} (Dampers) | E_{HI}/E_{I} (Isolators) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Code | Period (s) | Direction | Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | Fixed-Base | Base Isolation | Base Isolation | ||

NR0.9-3 | 0.9 | x | 0.388 | 0.108 | 0.151 | 0.042 | 2.79 | 0.771 | 0.196 | 0.551 | 0.247 |

y | 0.293 | 0.169 | 0.099 | 0.057 | 1.707 | 0.886 | 0.176 | 0.507 | 0.312 | ||

x + y | 0.400 | 0.168 | 0.156 | 0.058 | 2.281 | 0.723 | 0.177 | 0.508 | 0.313 | ||

NR0.9-6 | 0.9 | x | 0.363 | 0.108 | 0.148 | 0.044 | 2.493 | 0.716 | 0.151 | 0.557 | 0.292 |

y | 0.416 | 0.137 | 0.133 | 0.049 | 2.457 | 0.799 | 0.165 | 0.509 | 0.326 | ||

x + y | 0.388 | 0.151 | 0.164 | 0.061 | 2.394 | 0.812 | 0.148 | 0.525 | 0.327 | ||

AW0.9-1 | 0.9 | x | 0.271 | 0.113 | 0.101 | 0.041 | 1.996 | 0.799 | 0.165 | 0.565 | 0.262 |

y | 0.296 | 0.157 | 0.114 | 0.050 | 1.813 | 0.809 | 0.192 | 0.519 | 0.285 | ||

x + y | 0.421 | 0.184 | 0.148 | 0.059 | 2.052 | 0.788 | 0.167 | 0.552 | 0.276 | ||

NR1.1-5 | 1.1 | x | 0.689 | 0.191 | 0.317 | 0.083 | 2.531 | 0.656 | 0.145 | 0.532 | 0.322 |

y | 1.299 | 0.308 | 0.391 | 0.104 | 3.422 | 0.66 | 0.156 | 0.491 | 0.351 | ||

x + y | 1.460 | 0.294 | 0.410 | 0.117 | 3.652 | 0.665 | 0.151 | 0.532 | 0.316 | ||

NR1.1-7 | 1.1 | x | 1.028 | 0.265 | 0.444 | 0.123 | 3.212 | 0.628 | 0.154 | 0.531 | 0.314 |

y | 1.451 | 0.359 | 0.432 | 0.131 | 4.032 | 0.740 | 0.190 | 0.489 | 0.315 | ||

x + y | 1.632 | 0.332 | 0.444 | 0.154 | 4.166 | 0.782 | 0.176 | 0.527 | 0.297 | ||

AW1.1-1 | 1.1 | x | 0.716 | 0.174 | 0.301 | 0.079 | 2.457 | 0.528 | 0.138 | 0.533 | 0.328 |

y | 0.980 | 0.359 | 0.294 | 0.080 | 2.843 | 0.492 | 0.144 | 0.488 | 0.366 | ||

x + y | 1.280 | 0.282 | 0.410 | 0.106 | 2.571 | 0.428 | 0.137 | 0.519 | 0.342 |

**Table 11.**Maximum * response values for the bearings No. 29 (NRB **), 32 (LRB ***), 24 (LRB **) and 17 (LRB **).

Input | Axial Force (kN) | Torsion Angle (rad) | Drift Displacement (mm) | |||||
---|---|---|---|---|---|---|---|---|

Code | Period (s) | Input Direction | No. 32 | No. 24 | No. 29 | No. 17 | ||

NR0.9-3 | 0.9 | x | 338.1 | 266.5 | 12.7 | 409 | 0.00129 | 44 |

y | 467.8 | 921.5 | 430.3 | 789.1 | 0.00176 | 104 | ||

Combination | 577.2 | 1001.5 | 434.1 | 911.8 | 0.00180 | 105 | ||

x + y | 645.5 | 1010.9 | 424.7 | 713.9 | 0.00175 | 103 | ||

NR0.9-6 | 0.9 | x | 361.2 | 284.4 | 13.8 | 408.2 | 0.00129 | 46 |

y | 370.2 | 738 | 342.3 | 630.7 | 0.00143 | 76 | ||

Combination | 517.2 | 823.3 | 346.4 | 753.2 | 0.00143 | 77 | ||

x + y | 681.8 | 935.1 | 294.6 | 527.3 | 0.00127 | 89 | ||

AW0.9-1 | 0.9 | x | 398.6 | 315.7 | 10.5 | 343.9 | 0.00136 | 42 |

y | 246.5 | 484.8 | 226.9 | 415 | 0.00164 | 76 | ||

Combination | 472.6 | 579.5 | 230.1 | 539.0 | 0.00164 | 77 | ||

x + y | 298.4 | 397.5 | 218.3 | 567.1 | 0.00161 | 86 | ||

NR1.1-5 | 1.1 | x | 594 | 466.9 | 22.3 | 717.4 | 0.00229 | 186 |

y | 839.7 | 1669.2 | 772.3 | 1435.4 | 0.00321 | 255 | ||

Combination | 1028.6 | 1809.3 | 779.0 | 1650.6 | 0.00320 | 261 | ||

x + y | 1188.6 | 1849.8 | 695.9 | 1367.8 | 0.00290 | 272 | ||

NR1.1-7 | 1.1 | x | 712.7 | 564.7 | 24.4 | 959.2 | 0.00317 | 329 |

y | 967.5 | 1938.1 | 882.6 | 1661.5 | 0.00375 | 355 | ||

Combination | 1201.7 | 2107.5 | 889.9 | 1949.3 | 0.00375 | 369 | ||

x + y | 1013.6 | 1971.3 | 918.5 | 2368.8 | 0.00391 | 491 | ||

AW1.1-1 | 1.1 | x | 606.9 | 477.3 | 15.6 | 543 | 0.00208 | 163 |

y | 499.7 | 990.7 | 458.5 | 849 | 0.00258 | 182 | ||

Combination | 786.1 | 1133.9 | 463.2 | 1011.9 | 0.00258 | 189 | ||

x + y | 624 | 1052 | 449.2 | 1309.5 | 0.00237 | 247 | ||

D + 0.5 L | - | - | 2755.4 | 2565 | 4349 | 3730 | - | - |

Input | Base Shear Force/Building Weight | Shear Strain (%) | |||||
---|---|---|---|---|---|---|---|

Code | Period (s) | Direction | Fixed-Base without SSI | Base Isolation with SSI-a/SSI-b | Base Isolation without SSI | Base Isolation with SSI-a/SSI-b | Base Isolation without SSI |

NR0.9-3 | 0.9 | x | 0.148 | 0.041/0.042 | 0.041 | 23.40/23.63 | 22.28 |

y | 0.097 | 0.044/0.060 | 0.056 | 63.68/58.95 | 50.18 | ||

NR0.9-6 | 0.9 | x | 0.145 | 0.043/0.044 | 0.043 | 23.63/23.18 | 23.18 |

y | 0.131 | 0.032/0.048 | 0.048 | 37.80/37.78 | 37.80 | ||

AW0.9-1 | 0.9 | x | 0.099 | 0.044/0.042 | 0.041 | 22.50/22.50 | 20.93 |

y | 0.112 | 0.035/0.048 | 0.049 | 37.35/37.35 | 37.35 | ||

NR1.1-5 | 1.1 | x | 0.311 | 0.085/0.086 | 0.081 | 94.28/94.50 | 92.93 |

y | 0.384 | 0.097/0.100 | 0.102 | 126.76/126.38 | 127.53 | ||

NR1.1-7 | 1.1 | x | 0.436 | 0.123/0.120 | 0.121 | 164.93/164.70 | 164.25 |

y | 0.423 | 0.134/0.126 | 0.128 | 177.53/177.53 | 177.75 | ||

AW1.1-1 | 1.1 | x | 0.295 | 0.079/0.081 | 0.078 | 83.70/83.70 | 81.45 |

y | 0.290 | 0.072/0.080 | 0.079 | 88.43/88.65 | 90.90 |

**Table 13.**Maximum * base shear coefficient and shear strain in the rubber for modified parameters of the isolators.

Input | Base Shear Force/Building Weight | Shear Strain (%) | ||||
---|---|---|---|---|---|---|

Code | Period (s) | Direction | Lower Bounds | Upper Bounds | Lower Bounds | Upper Bounds |

NR0.9-3 | 0.9 | x | 0.037 | 0.052 | 23.95 | 17.01 |

y | 0.049 | 0.074 | 59.81 | 38.42 | ||

NR0.9-6 | 0.9 | x | 0.039 | 0.059 | 25.41 | 20.42 |

y | 0.043 | 0.058 | 40.47 | 24.08 | ||

AW0.9-1 | 0.9 | x | 0.036 | 0.055 | 23.07 | 18.80 |

y | 0.044 | 0.065 | 40.81 | 28.22 | ||

NR1.1-5 | 1.1 | x | 0.069 | 0.114 | 96.97 | 71.95 |

y | 0.078 | 0.149 | 117.49 | 113.48 | ||

NR1.1-7 | 1.1 | x | 0.109 | 0.159 | 188.27 | 117.88 |

y | 0.118 | 0.162 | 209.78 | 126.85 | ||

AW1.1-1 | 1.1 | x | 0.067 | 0.109 | 85.76 | 65.52 |

y | 0.067 | 0.108 | 94.80 | 73.10 |

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## Share and Cite

**MDPI and ACS Style**

Almansa, F.L.; Weng, D.; Li, T.; Alfarah, B.
Suitability of Seismic Isolation for Buildings Founded on Soft Soil. Case Study of a RC Building in Shanghai. *Buildings* **2020**, *10*, 241.
https://doi.org/10.3390/buildings10120241

**AMA Style**

Almansa FL, Weng D, Li T, Alfarah B.
Suitability of Seismic Isolation for Buildings Founded on Soft Soil. Case Study of a RC Building in Shanghai. *Buildings*. 2020; 10(12):241.
https://doi.org/10.3390/buildings10120241

**Chicago/Turabian Style**

Almansa, Francisco López, Dagen Weng, Tao Li, and Bashar Alfarah.
2020. "Suitability of Seismic Isolation for Buildings Founded on Soft Soil. Case Study of a RC Building in Shanghai" *Buildings* 10, no. 12: 241.
https://doi.org/10.3390/buildings10120241