SDTSB Finn Etal 2011

7/30/2019 SDTSB Finn Etal 2011

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Modeling soilfoundationstructure interaction

WD Liam Finn*,, Bishnu H Pandey and Carlos E Ventura

Department of Civil Engineering, University of British Columbia, Vancouver, Canada

SUMMARY

This paper offers a guided tour through the various ways, used in practice, of accounting for soilstructureinteraction in design and analysis, ranging from a complete analysis of the total combined system offoundation, soil and structure to approximate models of the system. The focus is on three types of structures:bridges on pile foundations, tall buildings with several levels of underground parking and large basementslabs with shallow embedment. The paper also reports on preliminary results from the study of seismicpressures against deep basement walls commissioned by the Structural Engineers Association of BritishColumbia. Copyright 2011 John Wiley & Sons, Ltd.

Received 13 October 2011; Accepted 26 October 2011

KEY WORDS: soil-structure interaction; base slab averaging; seismic earth pressures; basement walls

1. INTRODUCTION

This paper offers a guided tour through the various ways, used in practice, of accounting for

soilstructure interaction (SSI) in design and analysis, ranging from a complete analysis of the total

combined system of foundation, soil and structure to approximate models of the system. The focus

is on three types of structures: bridges on pile foundations, tall buildings with several levels of

underground parking and large basement slabs with shallow embedment. The paper also reports on

the preliminary results from the study of seismic pressures against deep basement walls commissioned

by the Structural Engineers Association of British Columbia (SEABC).

When analysis of the total soilstructure system is carried out, the effects of SSI are implicitly

included in the analysis and reflected in the results. No special consideration of SSI is required.

However, this type of analysis, although feasible, is rarely practical in practice because the structural

analysis programs used usually by structural engineers cannot handle the nonlinear soil continuum

directly. There are powerful commercial programs available that can do complete analyses, but the

learning curve is steep and long and the computational time is too long for the designers requirements

except for special projects. Therefore, it is necessary to uncouple the computational model of a

structure from the soil and to include SSI effects by appropriate springs and dashpots.

2. BRIDGE PIERS ON PILES

A three-span continuous box girder bridge structure shown in Figure 1 was chosen for a fundamental

study of SSI in pile foundations. A rigid base version of this bridge was used as an example in the

guide to the seismic design of bridges published by the American Association of State Highway and

*Correspondence to: WD Liam Finn, Department of Civil Engineering, University of British Columbia, Vancouver,Canada.E-mail: [email protected]

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 2011; 20: S47S62Published online 22 November 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/tal.735

Copyright 2011 John Wiley & Sons, Ltd.


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Transportation Officials (AASHTO, 1983). The sectional and physical properties of the superstructure

and piers were taken from the AASHTO guide.

Each pier is supported by a group of 16 (4 4) concrete piles. The diameter and length of each pile

are 0.36 m and 7.2 m, respectively. The piles are spaced at 0.90 m, center to center. The Youngs

modulus and mass density of the piles are E= 22000MPa and r = 2.6 Mg/m3, respectively. The soil

beneath the foundation is assumed to be a nonlinear hysteretic continuum with unit weight

g= 18kN/m3 and Poissons ratio n= 0.35. The low-strain shear modulus of the soil varies based on

the square root of the depth, with values of zero at the surface and 213 MPa 10 m deep. The variations

of shear moduli and damping ratios with shear strain are those recommended by Seed and Idriss (1970)

for sand. The surface soil layer overlies a hard stratum at 10 m. For the PILE-3D (Wu and Finn, 1997)

finite element mesh, the soil deposit was divided into 10 sublayers of varying thicknesses. Sublayer

thicknesses decrease toward the surface where soilpile interaction effects are stronger. Nine hundredbrick elements were used to model the soil around the piles, and 64 beam elements were used to model

the piles. The input acceleration record used in the study was the first 20 s of the NS component of the

free field accelerations recorded at CSMIP Station No. 89320 at Rio Dell, CA, during the April 25,

1992, Cape Mendocino Earthquake. The power spectral density of this acceleration record shows that

the predominant frequency of the record is 2.2 Hz.

2.1. Pile cap stiffness

The pile cap stiffness of the pile foundation shown in Figure 1 was determined for two different col-

umn/foundation stiffness ratios, 7% and 50%. A PILE-3D analysis was conducted first, and the

spatially varying time histories of modulus and damping were stored. Then, an associated program

PILIMP calculated the time histories of dynamic pile head impedances using the stored data. Thedynamic impedances were calculated at any desired frequency by applying a harmonic force of the

same frequency to the pile head and calculating the generalized forces for unit displacements. In this

paper, the focus is on the stiffness only because these are the parameters of primary interest for current

practice. However, the effects of damping are always included in the analyses.

The stiffness was calculated first without taking into account inertial interaction between the

superstructure and the pile foundation. This is the usual condition in which stiffness is estimated by

static loading tests, static analysis or elastic formulae. The stiffness was also calculated taking the

inertial effects of the superstructure into account. In the latter case, both kinematic and inertial interac-

tions were taken into account. Since the entire pile group was being analyzed, pilesoilpile interaction

was automatically taken into account under both linear and nonlinear conditions. Therefore, the usual

Figure 1. Three span bridge on pile foundation.

S48 WD LIAM FINN, B.H PANDEY AND C.E VENTURA

Copyright 2011 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 2011; 20: S47S62

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difficult problem of what interaction factors to use or what group factor to apply was avoided. The time

histories of lateral and cross-coupling kinematic stiffness are shown in Figure 2.

This stiffness, resulting from kinematic interaction only, was calculated for the predominant

frequency of the input motions, f= 2.2 Hz. It is clearly not an easy matter to select a single representative

stiffness to characterize the discrete single-valued springs often used in structural analysis programs to

represent the effects of the foundation. In the absence of a complete analysis, probably, a good approach

to including the effects of soil nonlinearity on stiffness is to get the vertical distribution of effectivemoduli by a SHAKE (Schnabel et al., 1972) analysis of the free field and calculate the stiffness at the

appropriate frequency using PILIMP with these moduli. The constant stiffness calculated in this way

is shown by the horizontal lines in Figure 2. However, this is kinematic stiffness. It is shown in the latter

part of this paper that inertial interaction by the superstructure may cause greater nonlinear behavior,

leading to substantially reduced stiffness. The SHAKE analysis cannot capture this effect.

2.2. Seismic response of code bridge to transverse earthquake loading

A three-dimensional space frame model of the bridge is shown in Figure 3.

At the abutments, the deck is free to translate in the longitudinal direction but restrained in the

transverse and vertical directions. Rotation of the deck is allowed about all three axes. The space frame

members were modeled using two eight-node three-dimensional beam elements with 12 degrees of

freedom, 6 degrees at each end. The bridge deck was modeled using 13 beam elements, and each pierwas modeled by 3 beam elements. The cap beam that connects the top of the adjacent piers was

modeled using a single-beam element. The sectional and physical properties of the deck and the piers

SHAKE: Lateral

(MN/m)

SHAKE: Cross-Coupling(MN/rad)

PILE-3D: Lateral

(MN/m)

PILE-3D: Cross-Coupling(MN/rad)

Time (s)4 8 16 200 12

0

0.2

0.4

0.6

0.8

1.0

1.2

Stiffness(x103)

Figure 2. Time histories of kinematic lateral and cross-coupling stiffness.

Figure 3. Computational model of the bridge.

MODELING SOILFOUNDATIONSTRUCTURE INTERACTION S49


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are those provided in the AASHTO guide (1983). The pier foundation was modeled using a set of

time-dependent nonlinear springs and dashpots that simulate exactly the time histories of stiffness

and damping from the PILE-3D analyses.

The response of the bridge structure was analyzed for different foundation conditions to study the influence

of various approximations to foundation stiffness and damping using the computer program BRIDGE-NL.

The free field acceleration was used as the input acceleration, and the peak acceleration was set to 0.5 g.

2.3. Foundation conditions for analyses

The seismic response of the bridge to transverse earthquake loading was analyzed for the four different

foundation conditions listed below:

1. Rigid foundation fixed base condition

2. Flexible foundation with elastic stiffness and damping

3. Flexible foundation with kinematic time-dependent stiffness and damping

4. Flexible foundation with stiffness and damping based on the SHAKE effective moduli

The fundamental transverse mode frequency of the computational model of the bridge structure with

afixed base was found to be 3.18 Hz. This is the frequency quoted in the AASHTO-83 guide. This

agreement in fundamental frequencies indicates an acceptable structural model. For this original case,

the lateral stiffness of the bridge pier is only 7% of the foundation stiffness. For this extremely lowstiffness ratio, the columns control the fundamental frequency of the bridge, and the influence of

the foundation is negligible. Results from analyses in which the column/foundation stiffness ratio

is 50% will be presented here. The stiffness ratio was raised by increasing the stiffness of the piers

only, with no changes to the superstructure. Normally, much stiffer piers would imply a heavier

superstructure and therefore higher inertial forces.

For a 50% stiffness ratio, thefixed base fundamental frequency of the bridge is 5.82 Hz. When the stiff-

ness associated with low-strain initial moduli was used, the fundamental frequency was 4.42 Hz, a 24%

reduction from thefixed base frequency. With kinematic strain-dependent stiffness, the frequency reached

a minimum value of 3.97 Hz during strong shaking, a 32% reduction from thefixed base frequency. When

the foundation stiffness was based on effective shear moduli from a SHAKE analysis of the free field, the

frequency was 4.18 Hz, a 28% change from the fixed base frequency. Figure 4 shows the variation with

time in fundamental transverse modal frequency for the different foundation conditions.

2.4. Inertial interaction of structure and pile

The time-dependent stiffness used in the analyses described above was computed without taking the

inertial interaction of superstructure and foundation into account. The primary effect of this interaction

is to increase the lateral pile displacements and cause greater strains in the soil. This in turn leads to

smaller moduli and increased damping. The preferred method of capturing the effect of superstructure

interaction is to consider the bridge structure and the foundation as a fully coupled system in the finite

element analysis. However, such fully coupled analysis is not possible with current commercial

Fixed Base Frequency = 5.82 Hz

Time (s)5 15 20100

Constant stiffness based on

the initial shear moduli

Constant stiffness

based on shear moduli

from SHAKE analysis

Variable stiffness based

on shear moduli from

PILE-3D analysis

Fixed Base Frequency = 5.82 Hz

3.5

4.0

4.5

5.0

5.5

FirstTransverseModeFrequency(Hz)

Figure 4. Time history of transverse modal frequencies for different foundation conditions.



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structural software. Even if it were, it would not be feasible in practice because it would require

enormous amounts of computational storage and time using the more sophisticated computer codes.

An approximate way of including the effects of superstructure interaction is to use the model shown

in Figure 5. In this model, the superstructure is represented by a single degree of freedom (SDOF)

system. The mass of the SDOF system is assumed to be the portion of the superstructure mass carried

by the foundation. The stiffness of the SDOF system is selected so that the system has the period of the

mode of interest of the fixed base bridge structure.This approximate approach is demonstrated by the analysis of the center pier at Bent 2. The

fundamental transverse mode frequency of the fixed base model was found earlier to be 5.82 Hz.

The static portion of the mass carried by the center pier is 370 Mg. The superstructure can be

represented by an SDOF system having a mass of 370 Mg at the same height as the pier top and

frequency of 5.82 Hz. The corresponding stiffness of the SDOF system is 495 MN/m.

A coupled soilpilestructure interaction analysis can be carried out using PILE-3D by incorporating the

SDOF model into thefinite element model of the pile foundation. The pile foundation stiffness derived from

this finite element model incorporates the effects of both inertial and kinematic interactions and is called

total stiffness. The time histories of stiffness with and without the superstructure are shown in Figure 6.

The reduction in lateral stiffness is greater throughout the shaking when the inertial interaction

was included. There is a similar reduction in the rotational and cross-coupling stiffness. When inertial

Figure 5. Pile foundation with superstructures.

Shear Moduli

from SHAKE

Analysis

PILE-3D:

Without Superstructure

Time (s)5 15 200 10

0

0.2

0.4

0.6

0.8

1.0

PILE-3D:

With Superstructure

SHAKE

LateralStiffness-MN/m(x103(

Figure 6. Effect of inertial interaction on lateral pile cap stiffness.



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interaction was included, the lateral stiffness reached a minimum of 188 MN/m, which is 22% of the

initial value. When the inertial interaction was not included, the minimum was 400 MN/m. Clearly,

in this case, inertial interaction has a major effect on foundation stiffness.

The results of the analyses for four different foundation conditions are summarized in the displace-

ment spectra for transverse vibrations of the bridge, shown in Figure 7. The displacement spectra clearly

show the importance of including inertial interaction when calculating foundation stiffness in this case.

The fixed base model for estimating response is inadequate. As the ratio of superstructural stiffness tofoundation stiffness is reduced, the effect of inertial interaction on system frequency is reduced and

kinematic stiffness becomes adequate. The fixed base model is adequate only for low stiffness ratios.

For the example bridge, when effective moduli from a SHAKE analysis of the free field are used in

an elastic analysis to obtain discrete foundation stiffness for each degree of freedom, the corresponding

system frequencies lead to acceleration and displacement responses very close to the responses from a

PILE-3D nonlinear analysis. This is true when the complete pile foundation is included in the analysis.

It may or may not be true if the effective moduli are used to get the stiffness of a single pile and the

stiffness of the pile group is developed from this with the help of empirical factors for group effects.

The results above suggest that kinematic stiffness may be obtained, taking nonlinear soil effects into

account, by an elastic structural program that can model the pile group foundation, if the effective

moduli from a SHAKE analysis are used. This needs to be verified by a few more case histories. A

more detailed discussion of SSI of pile foundation and a critical review of foundation springs used

in practice may be found in Finn (2004, 2005).

3. MODELS FOR TALL BUILDINGS

The presentation in this section is based on the paper by Naeimet al. (2008). The paper describes the

most reliable and effective way to develop reliable simplified computational models of structures that

incorporate SSI effects. Unfortunately, many analyses of the type used would be necessary to develop

a database that would be applicable to tall buildings in general. But valuable lessons can be learned

even from one well-conducted study of a single instrumented building.

The process of exploring what may be effective models of this structure starts with the construction

of the most accurate (MA) computational model compatible with the current structural software. Theresponse of this model to the Northridge Earthquake was evaluated to provide baseline response

data against which the performance of various simpler models could be checked. The MA model of

the 54-storey building is shown in Figure 8.

The action of the foundation soil against the basement walls was modeled by appropriate horizontal

springs and dashpots. The vertical and rocking stiffnesses of the base slab were modeled simul-

taneously by vertical springs with an appropriate distribution of stiffnesses. A detail of how these

springs and dashpots were determined is described in Naeim et al. (2008).

Response Spectra (5% Damping)

0

5

10

15

0 0.5 1 1.5 2Period (sec)

SpectralDisplaceme

nt(cm)

PILE-3D: Nonlinear Kinematic

PILE-3D with Shake Moduli and Damping

Rigid supports

PILE-3D Inertial + Kinematic Interaction

Figure 7. Spectral displacements of bridge for four different foundation conditions.



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The foundation input motion (FIM) to the base slab is the recorded motion of the slab. SHAKE

analysis of the free field was conducted using FIM as the input. This analysis provided

depth-dependent ground motion for application to the ends of springs acting on the basement walls.

The response of the MA structural model to the Northridge Earthquake was evaluated, and the

accelerations at different elevations in the building were compared with those recorded during the

earthquake. The MA model was tuned to give good agreement with the recorded accelerations. Many

different simplified soilstructure models were tested, but only three will be presented here to illustrate

how simpler models should be evaluated.

3.1. Approximate models

The simplest model (model 3c) is shown in Figure 9.The building was assumed to rest on a rigid base. There was no interaction between the soil and the

basement walls. The performance of this model was compared with that of the MA model in terms of

several different response parameters in Naeim et al. (2008), but owing to space limitations, the

Spring ends constrained to

the ground motion historyFoundation walls modeled with

the actual stiffness and strength

Figure 8. Most accurate model of a 54-storey building.

ug(z=0)

Figure 9. Simplest model of building with no soilstructure interaction.



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comparison was limited here to the interstorey drift ratios shown in Figure 10. For such a crude model,

the drift ratios were reasonably good except in the basement levels where the interstorey drift ratios

were overestimated and near the roof where the drift ratios were underestimated.

The next model (model 3b, Figure 11) rested on a rigid base, but some passive lateral restraint was

imposed on the basement walls by springs. Naiem et al. (2008) described this model as follows:

Neglect entirely soil flexibility at the level of the base slab (i.e. the base slab is fixed vertically and

horizontally), and simulate soil flexibility along the basement walls with horizontal springs with endsfixed to match the free field ground motion. Seismic demand consists only of horizontal motions

(equivalent free-field condition) at the base slab level and at the ends of foundation springs. This

simulates a condition commonly used in structural design offices.

The drift ratios of this model were compared with those of the MA model in Figure 12. Despite the

introduction of some restraint on the basement walls to model the effects of the soil, the drift ratios

predicted by this model compared very poorly with the ratios from the MA model.

The last model considered is model 3d shown in Figure 13. In this model, the structure was assumed

MA

3c

Story Drift Ratio (x10-3)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-3

2

7

12

17

22

27

32

37

42

47

52

Story

Figure 10. Drift ratios for models MA and 3c. MA, most accurate.

Figure 11. Model 3b.



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to be on a rigid base at the ground surface and the structures below that were ignored. According to

Naeim et al. (2008), seismic demand consists only of horizontal motions (equivalent free-field

condition) applied at ground level.

The response of this model to the Northridge Earthquakecompared surprisingly well with the MA model as shown in Figure 14, although the drift ratios were

overestimated by model 3d at the ground level and underestimated near the roof.

This study explores the effectiveness of simplified models of the tall buildings commonly used in

practice by comparing the response of each model with the response of MA model. The MA was

carefully calibrated using data recorded on the structure during Northridge Earthquake. Two models

commonly used in practice, models 3c and 3d, performed reasonably well.

The immediate effect of choosing a simpler model is to alter the dynamic characteristics of the

computational model such as periods and mode shapes. The effects of these changes are never

explored on a job-to-job basis. Therefore, studies such as that of Naeimet al. (2008) are crucial in pro-

viding some reliability covered for simpler models. However, many more studies on different building

Story Drift Ratio (x10-3)

0 1.0 1.5 2.5 3.0-3

2

7

12

17

22

27

32

37

42

47

52

Story

0.5 2.0

Figure 12. Drift ratios for models MA and 3b. MA, most accurate.

Figure 13. Model 3d.



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Figure 15 depicts the design lateral earth seismic pressure distribution for the basement wall for a

friction angle of 33 and PGA = 0.24 g. The required moment resistance of the wall along its height

is shown on the right in Figure 15. In this design, no overstrength or ductility factor is applied to

the seismic pressures on the wall. The wall has uniform properties of I= 0.0013m4, A =0.25m2 and

E= 2.74107 kN/m2.

Ground motions for the analyses were selected from the Pacific Earthquake Engineering and

Research Center (PEER, 2011) strong ground motion database. Based on the results of de-aggregationof the Uniform Hazard Spectrum (UHS), Site Class C for Vancouver (NRCC, 2005) candidate input

motions were selected in the magnitude range M=6.57.5 and the distance range 1030 km using

the program Design Ground Motion Library (PEER, 2011). Table 1 shows the list of three ground

motions selected for this initial part of the study.

The selected ground motions are spectrally matched to UHS for Vancouver in the period range of

0.021.7 s using the computer program SeismoMatch (2011).

The time history of resultant force against the wall due to the 1979 Imperial Valley Earthquake

is shown in Figure 16. More recent results from nine different earthquakes show that the total

MononobeOkabe force is in the range of10% to 2% of the maximum dynamic force.

The dynamic pressure distribution at the moment of maximum force is very different from the

distribution assumed for the MO force in the current design as shown in Figure 17. This is due to

the very different displacement patterns of the wall in the dynamic analysis compared with that

assumed for development of the active MO force.

Envelopes of moments and shears are shown in Figure 18. Yielding occurs where the seismic

moment envelope touches the yield moment frame.

Average drift ratios for three ground motions used in analysis are shown in Figure 19. The definition

of drift ratio is also illustrated in the figure. Acceptable drift ratios have not been presented for

basement walls, and discussions with structural engineers on the issue were inconclusive.

Figure 15. Distribution of the design lateral pressure along the height of the wall based on the currentpractice for a seismic event with PGA = 0.24 g and a backfill soil with friction angle of 33; the figure

on the right shows the moment resistance distribution along the height of the wall.

Table 1. List of selected ground motions.

Ground motion Record no. Event Year Station Magnitude

G1 162 Imperial Valley 1979 Calexico Fire 6.53G2 987 Northridge 1994 LA-Centinela 6.69G3 778 Loma Prieta 1989 Hollister 6.93



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Figure 16. Time history of maximum force against the wall compared with MO seismic forces for

1/475 and 1/2475 rates of exceedance. MO, MononobeOkabe.

Mononobe- Okabe

Figure 17. Pressure distribution at time of maximum force on the wall compared with linear

MononobeOkabe maximum pressure. MO, MononobeOkabe.

Figure 18. Envelopes of positive and negative bending moments and shears (yield limits for moments

and shear are shown by the black frames.)

Figure 19. Average drift ratios for three earthquakes over the depth of the wall.



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The definition of drift ratio given above is identical to the definition of hinge rotation given by the

Task Committee on Blast Resistant Design (TCBRG, 1997). This committee related hinge rotation to

structural performance. They specified two performance categories that may apply to basement walls:

low and medium response categories. The low response category is defined as follows: . . . localized

building/component damage. Building can be used; however repairs are required to restore integrity of

structural envelope. Total cost of repairs is moderate. The medium response category is defined as

follows:. . . widespread building/component damage. Building cannot be used until repaired. Total

cost of repairs is significant. The hinge rotations (and hence the drift ratios) associated with these

two response states are 2% and 4%, respectively. According to these criteria, only the response of

the top basement wall needs careful consideration.

5. BASE SLAB AVERAGING

It appears to be generally accepted that large foundation slabs reduce the free field ground motions for

period up to 0.5 s. FEMA-440 (ATC, 2005) has developed reduction factors for spectral values due to

the action of foundation slabs as shown in Figure 20 for slab foundation with shallow embedment. We

have examined 98 case histories of free field and slab motions, and 68 pair of these motion pairs of free

field and slab motions showed a reduction in slab motions from free field motions. Typically, examples

are shown in Figures 21 and 22. However, in 30 cases, we found that the slab motions are greater thanthe free field as shown in Figures 23 and 24. Poland et al. (2000) also found that there were cases of

motion amplified instead of reduced. The fact that the 30% of cases we investigated showed significant

increases in slab motion suggests that caution is warranted in relying on a reduction. It is interesting to

note that a recent series of centrifuge tests on a structure resting on a foundation slab consistently

showed an increase in slab motion over the free field (Rayhani and Nagger, 2008). In this test, the

foundation was on soft clay. Analysis of the test using the computer program FLAC 3D and Mohr

Column failure criterion confirmed the increase in slab motion.

6. CONCLUDING REMARKS

The coupled analysis of structures and foundations is not a feasible option in engineering practice atpresent because of practical difficulties with the analysis. Therefore, the analysis was conducted on

simpler structural models with add-ons, usually linear or nonlinear springs, to simulate SSI effects.

The uncertainties inherent in these uncoupled systems needs to be more fully documented. The

sensitivity of response to spring characteristics is especially important.

0 0.2 0.4 0.6 0.8 1 1.2Period (s)

0.4

0.5

0.6

0.7

0.8

0.9

1

Foundation/free

-fieldRRS

fromb

aseslabaveraging(RRSbsa

)

Simplified Modelb

e= 6 5 f t

be

= 1 30 ft

be

= 2 00 ft

be

= 3 30 ft

Figure 20. Spectral reduction from base slab averaging (RRSbsa) as a function of period in FEMA-440.



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Naeim et al. (2008) have used the recorded response of a tall building to evaluate the reliabil-

ity of simpler structural models used in practice in which soilstructural interaction effects are

simulated by single-valued springs and dashpots. They found that some models were not reliable

and should not be used, whereas other models gave various levels of satisfactory performances. A

database on the performance of simple models for different building configurations and heights

and for various levels of shaking is essential for providing a reliable basis for selection of simpler

computational models.

The behavior of basement walls during earthquakes and the seismic pressures for which they should

be designed are important aspects of SSI in tall buildings. A major study of this problem is being

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.5 1 1.5 2

T (s)

PSA(

g)

Free Field

Basement

Figure 21. Spectral accelerations at the site of Pomona two-storey commercial building in the 1990

Upland Earthquake (EW direction).

0

0.1

0.2

0.30.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

T (s)

PSA(

g)

Free FieldBasement

Figure 22. Spectral accelerations at the site of Rancho Cucamonga four-storey Justice Centre building

in the 1990 Upland Earthquake (EW direction).

Figure 23. Spectral accelerations at the site of El Centro Imperial County Service building in the 1979

Imperial Valley Earthquake (NS direction).



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conducted at the University of British Columbia at the request of SEABC. In exploring the capacity of

the walls to absorb seismic demand, the flexibility and yield moments of the wall structure are taken

into account. Early results suggest the behavior of the top basement is critical. This basement is higher

than the other basements (4 m versus 3 m in BC) and is not as restrained at the top as the lowerbasements are. Typically, the drift ratio in the top basement is more than twice the drift ratios in

the lower basements. There is, at present, no performance criteria for basement walls. In the study,

the standard adopted for blast loading would suggest that the behavior of a wall designed for a

PGA= 0.24 g would potentially show unsatisfactory performance only in the top basement when

subjected to PGA = 0.46 g.

A major study of the effects of shallow foundation slabs with shallow embedment on free field

motions was conducted involving 98 pairs of free field and slab motions. Sixty-eight pairs show that

the motions of the slabs were smaller than the free field motions in the period range below 0.5 s.

But in 30 cases, the motions of the slabs were greater than the free field motions. These findings

confirm earlier findings of Poland et al. (2000) who also showed many of the slab motions were

amplified. These findings raised some concerns about the FEMA-440 recommendations for universal

reduction in slab motions from free field values. So far, no clear reason for the different slab behaviorin the amplified cases has been advanced.

ACKNOWLEDGMENTS

The study is financially supported by a grant for SSI studies from the Canadian Seismic Research

Network. The section on seismic pressure against basement walls is a part of an ongoing study for

the SEABC.

REFERENCES

AASHTO. 1983. Guide specifications for seismic design of highway bridges. American Association of State Highway and

Transportation Officials, Washington, DC, USA.

Ahmadnia, A, Taiebat, M, Finn, WDL, Ventura, C, 2011. Seismic evaluation of existing basement walls. Proceedings of the Third

International Conference on Computational Methods in Structural Dynamics & Earthquake Engineering. Corfu, Greece.ATC. 2005. Improvement of nonlinear static seismic analysis procedures. Rep. No. FEMA-440, Washington, DC.

Finn WDL. 2004. Characterizing pile foundations for evaluation of performance based seismic design of critical lifeline

structures. Invited keynote lecture, 13th WCEE, Vancouver, BC, Canada.

Finn WDL. 2005. A study of piles during earthquakes: issues of design and analysis. Bulletin of Earthquake Engineering 3

141-234.

Mononobe N. Matsuo H. 1929. On determination of earth pressure during earthquakes. Proceedings of the World Engineering

Congress. Tokyo, 9, 275.

Naeim F, Tileylioglu S, Alimoradi A, Stewart AP. 2008. Impact of foundation modeling on the accuracy of response history analysis

of a tall building. SMIP08 Seminar Proceedings. (http://www.consrv.ca.gov/cgs/smip/docs/seminar/SMIP08/Documents/

Z4_Paper_NaeimStewart.pdf)

NRCC. 2005. National Building Code of Canada. National Research Council of Canada. Canadian Commission on Building and

Fire Codes, Ottawa, Canada.

Figure 24. Spectral accelerations at the site of Sylmar six-storey County Hospital building in the 1994

Northridge Earthquake (EW direction).



DOI: 10.1002/tal
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