seismic protection of structures with base isolation

Concrete Solutions 09 Paper 7a-3

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Seismic Protection of Structures with Modern Base Isolation Technologies

Luis Andrade1 and John Tuxworth2 1Senior Structural Engineer, Green Leaf Engineers

2Director, Green Leaf Engineers Synopsis: Increased resistance to earthquake forces is not always a desirable solution for buildings which house contents that are irreplaceable or simply more valuable than the actual primary structure (eg museums, data storage centres, etc). Base isolation can be employed to minimize inter-story drifts and floor accelerations via specially designed interfaces at the structural base, or at higher levels of the superstructure. This paper presents the design comparison of two isolation systems (lead-rubber bearings, and friction pendulum bearings) for a five-story reinforced concrete framed building. The response of the base-case, fixed-structure, and isolated systems is compared for dynamic analysis to actual historical records for five significant seismic events. Keywords: bearing, concrete, damping, dissipation, drift, isolation, inter-storey, lead-rubber, pendulum, seismic. 1. Introduction Conventionally, seismic design of building structures is based on the concept of increasing resistance against earthquake forces by employing the use of shear walls, braced frames, or moment-resistant frames. For stiff buildings these traditional methods often result in high floor accelerations, and large inter-story drifts for flexible buildings. With both scenarios building contents and nonstructural components may suffer significant damage during a major event, even if the structure itself remains basically intact. Obviously this is an undesirable outcome for buildings which house contents that are irreplaceable, or simply more costly and valuable than the actual primary structure (eg museums, data storage centers, etc).

The concept of base isolation is increasingly being adopted in order to minimize inter-story drift and floor accelerations. In this instance the control of structural forces and motion is exercised through specially designed interfaces at the structural base — or potentially at a higher level of the superstructure — thus filtering out the actions transmitted from the ground. The effect of base isolation is to essentially uncouple the building from the ground.

This paper presents the design comparison of two isolation systems — Friction Pendulum System (FPS) and Lead-Plug Bearings (LPB) — for a five-story reinforced concrete framed building. The response of the fixed-base structure is compared to base-isolated cases for five different historical time-history records for significant earthquake events.

2. Base Isolation Systems There are two common categories of large-displacement base (or seismic) isolation hardware: Sliding Bearings and Elastomeric Bearings. This paper considers Friction Pendulum Systems (FPS) and Lead-Plug-Bearings (LPB), which belong to the first and second categories respectively.

2.1 Friction Pendulum System (FPS) A FPS is comprised of a stainless steel concave surface, an articulated sliding element, and cover plate. The slider is finished with a self-lubricating composite liner (e.g. Teflon). During an earthquake, the articulated slider within the bearing, travels along the concave surface, causing the supported structure to move with gentle pendulum motions as illustrated in Figure 1(a) and 1(b). Movement of the slider


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generates a dynamic frictional force that provides the required damping to absorb the earthquake energy. Friction at the interface is dependent on the contact between the Teflon-coated slider and the stainless steel surface, which increases with pressure. Values of the friction coefficient ranging between 3% to 10% are considered reasonable for a FPS to be effective, Wang (1). The isolator period is a function of the radius of curvature (R) of the concave surface. The natural period is independent of the mass of the supported structure, and is determined from the pendulum equation:

gRT /2π= (1)

where g is the acceleration due to gravity.

The horizontal stiffness (KH) of the system, which provides the restoring capability, is provided by:

RWk H /= (2)

where W is the weight of the structure.

The movement of the slider generates a dynamic friction force that provides the required damping for absorbing earthquake energy. The base shear V, transmitted to the structure as the bearing slides to a distance (D), away from the neutral position, includes the restoring forces and the friction forces as can be seen on the following equation, where μ is the friction coefficient:

DRWWV += μ (3)

The characterised constant (Q) of the isolation system is the maximum frictional force, which is defined as:

WQ μ= (4)

The effective stiffness (keff) of the isolation system is a function of the estimated largest bearing displacement (D), for a given value of μ and R, and is determined by:

RW

DWDVk eff +==

μ/ (5)

A typical hysteresis loop of a FPS can be idealized as shown in Figure 1(c).

(a)

(b)

(c)

Figure 1. Motion in a FPS (a) initial condition, (b) displaced condition at maximum displacement, (c) Idealized Hysteresis Loop of a FPS

The dissipated energy (area inside the hysteretic loop) for one cycle of sliding, with amplitude (D), can be estimated as:

WDE D μ4= (6)

Thus the damping of the system can be estimated as:

keff 1

kH Q

Displacement

Force Vmax

1

Dmax


3

μμ

ππβ

+==

RDDkE

eff

D

/2

4 2 (7)

2.2 Lead-Plug Bearings (LPB) The elastomeric LPB which are generally used for base isolation of structures consist of two steel fixing plates located at the top and bottom of the bearing, several alternating layers of rubber and steel shims, and a central lead core as shown in Figure 2(a). The elastomeric material provides the isolation component with lateral flexibility; the lead core provides energy dissipation (or damping), while the internal steel shims enhance the vertical load capacity whilst minimizing bulging. All elements contribute to the lateral stiffness. The steel shims, together with the top and bottom steel fixing plates, also confine plastic deformation of the central lead core. The rubber layers deform laterally during seismic excitation of the structure, allowing the structure to translate horizontally, and the bearing to absorb energy when the lead core yields. The nonlinear behavior of a LPB isolator can be effectively idealized in terms of a bilinear force-deflection curve, with constant values throughout multiple cycles of loading as shown on Figure 2(b).

(a) (b)

Figure 2. LPB isolator (a) components, (b) Idealized Hysteresis Loop of a LPB

The natural period of the isolated LPB system is provided by:

gkWTeff

π2= (8)

The characterised strength (Q) is effectively equal to the yield force (Fy,) of the lead plug. The yield stress of the lead plug is usually taken as being around 10MPa. The effective stiffness (keff ) of the LPB, at a horizontal displacement (D) being larger than the yield displacement (Dy) may be defined in terms of the post-elastic stiffness (kd,) and characteristic strength (Q), with the following equation:

DQkk deff /+= (9)

As a rule of thumb for LPB isolators, the initial stiffness (ki) is usually taken as 10 x kd , Naeim et al (2). The energy dissipated for one cycle of sliding, with amplitude (D) can be estimated as:

)(4 yD DDQE −= (10)

Following on from this assumption, it has been shown by Naeim et al (2) that the effective percentage of critical damping provided by the isolator can be obtained from:

keff 1

kd

Force

Vmax

ki

1

Displacement

Q Dmax

Dy


4

DQDkkQDQ

DkE

i

I

eff

D

)(9/(2

4 2 +−

==ππ

β (11)

3. Model-building Configuration

A reinforced concrete moment-resisting frame was adopted as the structural system for the analysis building. Figure 3 (a) and 3(b) show the structural configuration of the building in plan.

(a) (b)

Figure 3. Structural configuration plans (a) 1st to 3rd floors. (b) 4th and 5th floors.

Self weight of the structure was based on a concrete density (γ ) = 24 kN/m3. Super-dead loads of 1 kN/m2 was also applied to represent floor finishes, and 140 mm thick, 2.5-m high hollow masonry partitions with a density of (γ ) = 15 kN/m3 were considered to contribute as a line-load along beams of 4.9 kN/m. The imposed (live) load applied in each floor was taken as 2 kN/m2. Story heights were taken as 3 m. The Universal Building Code was considered in relation to seismic classification and variables, so as to enable consistency of symbols and nomenclature throughout the paper. Most international standards including AS 1170.4:2007 are either based on, or align significantly with, UBC 1997(3). It was assumed that the building ‘model’ was located in a Seismic Zone 4 of source Type A, and rests on a soil profile Type C.

4. Design Parameters According to Mayes et al (4), an effective seismic isolation system should have the following characteristics: • sufficient horizontal flexibility to increase the structural period and accommodate spectral demands of

the installation (except for very soft soil sites), • sufficient energy dissipation capacity to limit displacement to a practical level, • adequate rigidity to enable the building structure to behave similarly to a fixed base building under

general service loadings. As recommended by both Naeim et al (2) and Mayes et al (4), a target period (T) of 2.2 seconds was adopted for the isolated structure — approximately 3 times the fixed-base fundamental period (TF ) of 0.7 seconds. Following UBC 1997, the target design displacement can be calculated as:


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D

VDD B

TCgD

)4/( 2π= (12)

where CVD is a seismic coefficient, and BD is a damping coefficient which is a function of the effective damping β. From UBC 1997 Table 16-R, CVD = 0.56. An affective damping of 15% was assumed for both LPB and FPS — to be confirmed at the end of the design. From Equation 12, the design displacement = 220 mm. The effective stiffness for both bearing types was calculated following the formulas presented previously. Properties including damping, hardness, modulus of rigidity, modulus of elasticity and poisons ratio (for LPB), and friction coefficient (for FPS) were adopted from manufacturer’s data. As the performance of LPB isolators is weight dependant, three different sizes were incorporated in the model. The positions nominated in Figure 5 were adopted to promote an economical design. Final design parameters and details for each isolator type are provided following. Detailed design calculations have been omitted for clarity, however iterative calculation is required to ascertain effective stiffness and effective damping as both are typically displacement dependent. Figures 4(a) & 4(b) display cross-sectional details for isolator characteristics summarised in Tables 1 and 2 respectively.

(a) (b)

Figure 4. Geometrical characteristics of Base Isolators (a) FPS. (b) LPB Type A

Table 1. Design Parameters of FPS isolators.

Symbol Value Nomenclature T (sec) 2.2 (Design Period) β (%) 15 (Effective damping)

BD 1.38 (Damping factor) DD (mm) 220 (Design displacement Eq. 12) R (mm) 1200 (radius of curvature, calculated from Eq. 1)

μ 0.057 (friction coefficient)

RI 2.0 (Force reduction factor, UBC 1997 Table A-16-E, Concrete special moment resisting frame)

W (kN) 7318 (Total weight of the building) Keff (kN/m) 7961 (Total effective stiffness Eq. 5) kH (kN/m) 6085 (Non-linear stiffness Eq. 2 )

ki (kN/m) 310330 (Elastic stiffness, taken as 51kH)

Q (kN) 416 (Frictional force Eq. 4) Dy (m) 1.4 (Yield displacement calculated as Q / ( ki- kH ) β (%) 14.9 (Check of assumed effective damping Eq. 7)

R=1200mm


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Table 2. Design Parameters of LPB isolators. Parameter Value Nomenclature

T (sec) 2.2 (Design period) β (%) 15 (Effective damping)

BD 1.38 (Damping factor) DD (mm) 220 (Design displacement Eq. 12) G (MPa) 0.45 (Shear modulus) T (sec) 2.2 (Design period)

Isolator Nomenclature Parameter Type A Type B Type C Wi (kN) 1030 740 510 (Axial load on isolator)

Keff (kN/m) 840 604 416 (Effective stiffness calculated from Eq. 8) ED (kN-m) 38.9 28.0 19.3 (Global energy dissipated per cycle, calculated from Eq. 11)

Q (kN) 43.9 31.5 21.7 (Short term yield force, calculated form Eq. 10) Kd (kN/m) 642 461 318 (Inelastic stiffness, calculated form Eq.9) Ki (kN/m) 6422 4614 3180 (Elastic stiffness, taken as 10kd)

Kd / Ki 0.10 0.10 0.10 (Stiffness ratio) Dy (mm) 7.6 7.6 7.6 (Yield displacement, calculated as Q/9 kd) Fy (kN) 48.8 35.0 24.1 (Yield Force calculated as kiDy)

Figure 5. Location of LPB isolators Type A, B and C.

5. Modal Analysis SAP2000 structural analysis software is capable of Time History Analysis, including Multiple Base Excitiation. SAP2000 facilitates the dynamic modeling of base isolators as link elements, which can be assigned various stiffness properties. This stiffness values for both FPS and LPB isolators were calculated as detailed in previous sections of this paper. Calculations associated with the following summary and totaling some one-hundred pages have been excluded from the paper. Table 3 provides the fundamental period for the three cases studied: structure with fixed base; with FPS isolators; and with LPB isolators, as derived from an SAP2000 modal analysis. It can be seen that the periods obtained for both types of isolator are close to the target period (T = 2.2 sec) recommended by Naeim et al (2) and Mayes et al (4). Figure 6 shows the shape of the first mode of vibration for the 3 models. In addition to influencing fundamental period Figure 6 shows the isolators’ influence on modal shape.

Table 3. Fundamental Periods Model Fundamental Period, T (sec)

Fixed Base 0.73

LPB 2.23

FPS 2.05


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(a) (b) (c)

Figure 6. First mode of vibration for (a) fixed base building, (b) FPS isolated building and (c) LPB isolated building.

6. Time History Analysis A nonlinear analysis was carried out in SAP2000 in order to test the response of the structural systems, and to validate isolator functionality. The models were subjected to the following historical seismic time-history records:

• 1940 Imperial Valley Earthquake, El Centro Record (Richter Scale 7.1), • 1979 Imperial Valley Earthquake, El Centro Record, Array #5 (Richter Scale 6.4), • 1989 Loma Prieta Earthquake, Los Gatos Record (Richter Scale 7.1), • 1994 Northridge Earthquake, Newhall Record (Richter Scale 6.6), • 1995 Aigion Earthquake, Greece (Richter Scale approx. 5)

A seismologist is of invaluable assistance when selecting applicable time-histories, however guidance for selecting scaling records can be gleaned from codes, Kelly (5). The events chosen for consideration in this paper represent several of the major earthquakes in recorded history, with the 1995 Aigion Earthquake in Greece being of similar magnitude to the Newcastle earthquake of 1989 (Richter Scale 5.6) Figure 7 shows maximum response values for each of the earthquake records for roof acceleration, elastic base shear, inter-storey drift, and isolator displacements. Maximum roof acceleration is dominated by the 1989 Loma Prieta earthquake record which yields a value of about 36 m/sec2 for the fixed base structure, while for the isolated structures is in the order of 8.5 m/sec2 (76% reduction) (see Figure 7(a)). Maximum elastic base shears are dominated also by the 1989 Loma Prieta earthquake. An elastic base shear of approximately 120%W (where W is the building’s weight) for the fixed base building is reduced to 35%W (68% reduction) and 45%W (63% reduction) for LPB and FPS isolators respectively (see Figure 7(b)). Maximum Inter-storey drifts for fixed base and isolator cases are again generated by the 1989 Loma Prieta Earthquake, with values of about 129mm for the fixed base structure and 25mm (81% reduction) and 35mm (73% reduction) for LPB and FPS respectively (see Figure (c)). The drift ratio derived for Level-1 of the fixed base structure is 4.3%, about twice the maximum limit of 2% imposed by the UBC 1997. The FPS isolated structure displays a value of 1.15% which is well under the limit. Figure 7(d) shows maximum isolator displacements in the order of 473mm and 469mm. It can be seen in Figure 7(e) that these values are round 215% of the isolator design displacement of 220 mm, indicating that both isolator systems would fail during the 1989 Loma Prieta Earthquake and 1994 Northridge Earthquake.


8

0

5

10

15

20

25

30

35

40

1940 El Centro

1979 El Centro

1989 Loma Prieta

1994 Northridge

1995 Aigion

Acc

eler

atio

n (m

/sec

/sec

)

Earthquake Record

Roof Acceleration

LBSFPSFixed Base

050

100150200250300350400450500

1940 El Centro

1979 El Centro

1989 Loma Prieta

1994 Northridge

1995 Aigion

Isol

ator

Dis

plac

emen

t (m

m)

Earthquake Record

Isolator Displacement

LRBFPS

0

20

40

60

80

100

120

140

1940 El Centro

1979 El Centro

1989 Loma Prieta

1994 Northridge

1995 Aigion

Drif

t (m

m)

Earthquake Record

1st Floor Inter - Story Drift

LRB

FPS

Fixed Base

0%

50%

100%

150%

200%

250%

1940 El Centro

1979 El Centro

1989 Loma Prieta

1994 Northridge

1995 Aigion

Earthquake Record

Time History Displacement / Design Value

LRBFPS

0

20

40

60

80

100

120

140

1940 El Centro

1979 El Centro

1989 Loma Prieta

1994 Northridge

1995 Aigion

V / W

(%

)

Earthquake Record

Elastic Base Shear

LRBFPSFixed Base

Force-Displacement hysteresis loops for the FPS and LPB isolator (Type A), as subjected to the 1989 Loma Prieta earthquake record, are provided in Figures 8(a) and 8(b). These curves follow the mathematical models presented in section 2 of this paper. Elastic and post-elastic stiffness can be obtained as the slopes of the first two initial segments.

(a) (b)

(c) (d)

(e)

Figure 7. Comparison of Response to the 5 earthquake records (a) roof acceleration, (b) elastic base shear (c) 1st floor inter-story drift, (d) isolator displacement, (e) time history displacement /

design value utilization ratio.


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The energy dissipated by each isolator is provided by the area inside each loop cycle. Effective damping can be calculated using Equations 7 or 11 and compared with the assumed design value. Note that there is seemingly an anomaly present in Figure 8 (a), as maximum ‘-ve’ deflection for the FPS isolator corresponds to a reduction in elastic base shear. This anomaly was evident only for the Loma Prieta earthquake, and further study is required to ascertain why this issue occurred.

(a) (b)

Figure 8. 1989 Loma Prieta Earthquake Record. Force-displacement hysteresis loops for (a) FPS isolator (b) LPB isolator Type A.

-40.0

-20.0

0.0

20.0

40.0

0 5 10 15 20 25 30Acc

eler

atio

n (m

/sec

/sec

)

Time (sec)

Lead Plug Bearing Friction Pendulum System Fixed Base

-9000

-4500

0

4500

9000

0 5 10 15 20 25 30

Bas

e She

ar (k

N)

Time (sec)

Lead Plug Bearing Friction Pendulum System Fixed Base

-500

-250

0

250

500

0 5 10 15 20 25 30

Isol

ator

Dis

plac

emen

t (m

m)

Time (sec)

Lead Plug Bearing Friction Pendulum System

Figure 9. Time-history results for 1989 Loma Prieta earthquake record. (a) Roof acceleration, (b)

elastic base shear, (c) isolator displacement.


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Finally, time-history results for the Loma Prieta earthquake record are shown in Figure 9. It can be noticed from Figures 9(a) and 9(b) how the response in time of the isolated system is significantly less than the fixed base structure, specially between the first 10 to 15 seconds of the seismic excitation. Figure 9(c) compares the two types of isolators’ lateral displacements, which appears to be less for the FPS.

7. Conclusions & Recommendations

It can be seen that resultant accelerations, elastic base shears and inter-storey drifts were all effectively reduced by the adoption of Lead-Plug and Friction-Pendulum isolator systems, resulting in significant improvement in modeled building performance, and a very likely minimisation of post-event losses. For the ground conditions and sway-frame structural system adopted, LPB & FPS base isolation would be excellent options to reduce structural and non-structural damage, and to protect building contents. Both the LPB and FP systems provided a comparative reduction in roof level accelerations (up to 76%); however the LPB provided the best reduction in elastic base shear, and inter-storey drift (at first floor). For the adopted bearing characteristics, the FPS provided greatest control of isolator displacement — a significant serviceability constraint with respect to boundary conditions.

Response of the isolated structural framing systems was dominated by the time-history record of the 1989 Loma Prieta Earthquake. The second highest intensity experienced by the test structure was due to 1994 Northbridge earthquake. The isolator design displacement (being a function of the nominated isolator characteristics) of both systems was exceeded by these earthquakes, indicating alternate properties/sizes would be required to accommodate higher intensity events.

Further work is recommended to establish applicability of these base-isolation systems for the common braced-frame structural framing paradigm, and also to confirm suitability (or lack thereof) for high-rise construction, and or use on deep alluvial soil strata as evident in Australian centers such as Newcastle.

8. References

1. Wang, Yen-Po, “Fundamentals of Seismic Base Isolation”, International Training programs for Seismic Design of Building Structures.

2. Naeim, F. & Kelly, J. M., “Design of Seismic Isolated Structures: From Theory to Practice”, John Wiley & Sons, Inc. 1999.

3. International Conference of Building Officials, ICBO (1997), “Earthquake Regulations for Seismic-Isolated Structures”, Uniform Building Code, Appendix Chapter 16, Whittier, CA.

4. Mayes, R. & Naeim, F., “Design of Structures with Seismic Isolation”, Earthquake Engineering Handbook, University of Hawaii, CRC Press, 2003.

5. Kelly, T. E., “Base Isolation of Structures Design Guidelines”, Holmes Consulting Group Ltd, July 2001.

seismic protection of structures with base isolation

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