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Soil Dynamics and Earthquake Engineering 29 (2009) 1249–1261

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Soil Dynamics and Earthquake Engineering

0267-72

doi:10.1

� Corr

E-m

(M.H. E

journal homepage: www.elsevier.com/locate/soildyn

Seismic performance of three-dimensional frame structures withunderground stories

H. El Ganainy, M.H. El Naggar �

Department of Civil and Environmental Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9

a r t i c l e i n f o

Article history:

Received 27 September 2008

Accepted 18 February 2009

Keywords:

Soil–structure interaction (SSI)

Performance-based design (PBD)

Seismic design of buildings

Underground stories

Uniform hazard spectrum (UHS)

Ground response analysis

61/$ - see front matter & 2009 Elsevier Ltd. A

016/j.soildyn.2009.02.003

esponding author. Tel.: +1519 6614219; fax:

ail addresses: [email protected] (H. El Gana

l Naggar).

a b s t r a c t

This paper investigates the seismic performance of moment-resisting frame steel buildings with

multiple underground stories resting on shallow foundations. A parametric study that involved

evaluating the nonlinear seismic response of five, ten and fifteen story moment-resisting frame steel

buildings resting on flexible ground surface, and buildings having one, three and five underground

stories was performed. The buildings were assumed to be founded on shallow foundations. Two site

conditions were considered: soil class C and soil class E, corresponding to firm and soft soil deposits,

respectively. Vancouver seismic hazard has been considered for this study. Synthetic earthquake records

compatible with Vancouver uniform hazard spectrum (UHS), as specified by the National Building Code

of Canada (NBCC) 2005, have been used as input motion. It was found that soil–structure interaction

(SSI) can greatly affect the seismic performance of buildings in terms of the seismic storey shear and

moment demand, and the deformations of their structural components. Although most building codes

postulate that SSI effects generally decrease the force demand on buildings, but increase the

deformation demand, it was found that, for some of the cases considered, SSI effects increased both

the force and deformation demand on the buildings. The SSI effects generally depend on the stiffness of

the foundation and the number of underground stories. SSI effects are significant for soft soil conditions

and negligible for stiff soil conditions. It was also found that SSI effects are significant for buildings

resting on flexible ground surface with no underground stories, and gradually decrease with the

increase of the number of underground stories.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The current state-of-practice for seismic design of buildingswith multiple underground stories involves approximate ap-proaches that primarily differ according to the designer’s judg-ment and experience. This is a consequence of lack of relevantrecommendations in building codes. Most building codes treatlow and medium rise regular buildings with multi-level under-ground stories with the same recommendations used for build-ings with surface foundations.

In general, buildings with multiple underground stories aredesigned by cropping the superstructure and analyzing it as afixed base structure founded on the ground surface. On the otherhand, the substructure is designed for the seismic base shear andmoment demand resulting from the superstructure in addition tothe seismic earth pressure acting on the basement walls, due tothe oscillating mass of side soil. Even though this two step

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approach is common in practice, it might differ in detailsdepending on the procedure used in the seismic analysis of thebuilding.

It is important to incorporate the underground stories, base-ment walls, foundation soil and side soil explicitly in themathematical model of the structure to be able to assess theeffect of the underground part of the building adequately on itsseismic performance. This is also essential since the current trendof using performance-based design approaches in lieu of tradi-tional force-based design approaches in the seismic design ofbuildings dictate that soil–structure interaction (SSI) analysisbecomes an integral part of methods used in the seismicevaluation of buildings. Perhaps the most popular approach inmodeling the nonlinear response of the foundation soil and sidesoil is the Beam-on-a-Nonlinear Winkler Foundation (BNWF)approach due to its merit of simplicity in defining the parametersinvolved in the model.

The main objective of this paper is to better understand theseismic performance of three-dimensional (3D) frame structureswith multiple underground stories. To achieve this objective,nonlinear direct integration time–history analyses for 3D moment-resisting frame steel structures with above-ground stories ranging

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H. El Ganainy, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 29 (2009) 1249–12611250

from five to fifteen stories, and underground stories ranging fromzero (i.e. no basement) to five underground stories wereperformed. The nonlinear structural analysis programPerform-3D [1] was chosen for this research since it is dedicatedmainly for the performance assessment of 3D structures in thecontext of performance-based design (PBD). Its material librarycontains a wide variety of structural components formulatedto account for both geometric and material nonlinearity instructures.

Fig. 1. Plan of the repetitive story of the buildings.

Fig. 2. Lateral resisting system f

2. Description of model buildings

2.1. Description of model geometry and structural system

The models adopted herein are 4�5 bays moment-resistingframe steel buildings, having a constant bay width of 7.2 m andconstant story height of 3.6 m. Fig. 1 shows the plan of therepetitive story of the buildings. The lateral resisting system of thebuilding constituted four perimeter frames along the periphery ofthe building where the girders were rigidly connected to thecolumns, except where the girders were connected to the weakside of the columns. Fig. 2 shows the layout of the lateral resistingsystem of a typical model building. On the other hand, the innerframes work mainly as the gravity load carrying system wheregirders were pin-connected to the columns.

The parametric study involves evaluating the seismic perfor-mance of five, ten and fifteen story buildings with three under-ground stories. The buildings were assumed to be resting onshallow foundations. To further explore the effect of the numberof underground stories on the seismic performance of buildings,the ten story building was analyzed for zero (i.e. no basement),one and five underground stories.

The thickness of the reinforced concrete basement walls wasassumed 0.25 m considering that they will resist the lateral earthpressure only. Their reinforcement ratio was 0.25%, in accordancewith the specifications of FEMA 310 [2] document. Although theywere not designed to be part of the lateral resisting system of thebuilding, they were included in its structural model since theyshould affect its seismic response due to their large mass andin-plane bending stiffness.

On the other hand, the thickness of the slabs was taken as0.25 m to be consistent with approximately 1/30 of the slab span

or a typical model building.

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Table 1Unit weights and distributed loads used in defining the gravity loads acting on the

buildings.

Unit weights of materials (kN/m3)

Unit weight of steel 77

Unit weight of concrete 25

Equivalent uniformly distributed load (kPa)

Nonstructural components 1.1

Live load 2.4

Table 2Soil properties assigned for soil class C and soil class E.

Soil class C Soil class E

Shear wave velocity, Vs (m/s) 560 150

Dry unit weight, gdry (kN/m3) 21.00 18.00

Angle of internal friction, f1 40 30

Wall–soil friction angle, d1 25 20

Material damping ratio, e 0.05 0.05

Poisson ratio, n 0.35 0.35

Table 3Parameter used in calculating the seismic loads on the buildings using the NBCC

2005 equivalent static force procedure considering the Vancouver seismic zone.

Elastic design response spectrum parameters (g)

Peak ground acceleration (PGA) 0.5

Sa (0.2) 1.00

Sa (0.5) 0.68

Sa (1.0) 0.34

Sa (2.0) 0.18

H. El Ganainy, M.H. El Naggar / Soil Dynamics and Earthquake Engineering 29 (2009) 1249–1261 1251

as specified by FEMA 310 [2] document. The slabs wererepresented in the structural model of the building using itsweight in the gravity load case and as concentrated masses at thecenter of gravity of each floor for the seismic analysis. In addition,all the nodes lying in the plane of each floor were assigned a rigiddiaphragm constraint. However, the slabs were not modeledexplicitly and consequently their bending stiffness was neglected.This is consistent with the assumption that the moment-resistingframes form the lateral resisting system of the building.

Equivalent static force procedure parameters

Importance factor, IE 1.0

Higher mode factor, Mv 1.0

Ductility-related force modification factor, Rd 5.0

Overstrength-related force modification factor, Ro 1.5

2.2. Gravity loads

The gravity loads assigned to the buildings were the ownweight of structural components, including the steel girders andcolumns and the reinforced concrete slabs and basement walls.It also included the weight of the nonstructural components(e.g. cladding, partitions, floor finishing, etc.) in addition to thelive load assigned to the slabs.

Since the slabs were not modeled explicitly, their weight andthe live load they carry were included in the structural model bydistributing its reaction on the supporting girders. Table 1 lists theunit weights and distributed loads used in defining the gravityloads acting on the buildings.

3. Materials strengths and moduli

3.1. Steel and concrete

The steel members of the building and the reinforcing steel ofthe basement walls were assumed to be of the same grade. Thesteel yield strength was taken as 482,633 kPa, with an elasticmodulus of 199,948 MPa. The steel hardens to 689,476 kPa at astrain of 0.1, corresponding to a post-yield strain hardening ratioof 1.1%. The steel Poisson’s ratio was taken as 0.3. The concrete ofthe basement walls had f 0c ¼ 82,737 kPa, elastic modulus ¼ 37,232MPa and Poisson’s ratio ¼ 0.25.

3.2. Foundation and side soil

The buildings site was assumed to have a 30-m-thick deposit ofhomogeneous soil underlain by the bedrock. Therefore, theaverage properties in the top 30 m were used for calculating thefoundation and side soil mechanical properties in accordance withthe National Building Code of Canada (NBCC) 2005 specifications.Two scenarios were assumed for the soil deposit used in thecurrent study, namely: soil class C corresponding to ‘‘very densesoil and soft rock’’; and soil class E corresponding to ‘‘soft soil’’ inaccordance with the site classification of the NBCC 2005. Table 2lists the properties assigned for these two soil classes in thecurrent study from the ranges specified by NBCC 2005, Das [3,4]and FEMA 356 [5] document.

4. Preliminary analysis of the buildings

The five, ten and fifteen story buildings were designed usingthe structural analysis program ETABS [6] assuming fixed basecondition at the ground surface. This step provided preliminarysections for the structural members of the buildings, which wouldbe augmented by the underground stories, foundation soil andside soil for further seismic analysis. Although the columnsections should increase below the ground level in considerationof the added gravity loads from the underground stories, theywere not changed since the seismic performance of the buildingsrather than its seismic design is the objective of this study.

The steel design feature included in ETABS was utilized toperform the seismic design of the buildings. The seismic loadswere calculated using the equivalent static force procedure asspecified by the NBCC 2005 for a building in Vancouver. Table 3lists the parameters used in calculating the seismic loads actingon the buildings. The structural members of the buildings weredesigned according to the loading cases and guidelines specifiedby the NBCC 2005, the Canadian Standards Association (CSA) andthe Canadian Institute of Steel Construction (CISC). Table 4 liststhe preliminary sections for the girders and columns of thebuildings as obtained from the ETABS analysis and design stage.

5. Intended behavior and performance levels

The seismic performance of the model buildings was examinedwith an emphasis on the effect of underground stories, foundationsoil and side soil on the building performance. To achieve this goalthe nonlinear structural analysis program Perform-3D [1] is used.

5.1. Intended behavior of structural components

The perimeter frames were considered the primary structuralcomponent and comprise the lateral resisting system of thebuildings. Therefore, the perimeter frames are intended to

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experience inelastic behavior in flexure but to remain essentiallyelastic in axial and shear deformations. The connection panelzones between the girders and columns of the perimeter framesare also considered primary structural components, as they affectthe performance level of the building, and are intended toexperience inelastic behavior in shear. However, the interiorgirders and columns that comprise the gravity load carryingsystem are intended to behave elastically in flexure, axial andshear deformations, since they are considered secondary structur-al components. These designations are in accordance with theguidelines given by ASCE 41 [7] in classifying the structuralcomponents of buildings in the context of the PBD principles.

The basement walls of the building contribute to its lateralresistance because of their orientation within the structuralsystem. Therefore, they also can be considered as primarystructural components and hence are intended to experiencenonlinear behavior in in-plane bending. However, they shouldremain essentially elastic in shear, since shear failure in reinforcedconcrete is a brittle mode of failure. This renders inelastic shearbehavior in structural members an undesired target performance.Finally, the slabs are intended to behave elastically and, as statedbefore, were not included in the structural model.

To achieve these intended behaviors, the perimeter girders andcolumns and the connection panel zones are modeled usinginelastic frame and connection panel zone elements, respectively.They are assigned deformation-controlled force–deformationactions in bending and shear, respectively, in accordance withASCE 41 [7] guidelines for structural steel components. Theinterior girders and columns are assigned force-controlledforce–deformation actions in flexure, axial and shear deforma-tions (i.e. the components’ strengths are assigned to the elasticstructural members without defining the associated plasticdeformations) as well as axial and shear modes of deformationin perimeter girders and columns. The components’ strengths canbe calculated in accordance with the established principles ofmechanics (e.g. Load and Resistance Factor Design (LRFD)specifications for structural steel design considering a strengthreduction factor equals to unity). Perform-3D calculates thecomponents’ strength from the geometric properties of members’cross section (e.g. section modulus) and the associated mechan-ical properties of the cross section’s material (e.g. yield strength ofsteel).

Table 4Preliminary sections for girders and columns of the model buildings as obtained

from ETABS.

5 story building 10 story building 15 story building

Perimeter girders W 27�146 W 27�94 W 27�146

E–W interior girders W 18�106 W 18�97 W 18�106

N–S interior girders W 24�104 W 24�104 W 24�104

Perimeter columns W 14�90 W 14�145 W 14�233

Interior columns W 14�90 W 14�132 W 14�193

Table 5Deformation capacities for inelastic structural components of buildings corresponding

Immediate occupancy

Plastic rotation angle (radians)

Perimeter girders 1yy

Perimeter columns 1yy

Angular plastic shear deformation (radians)

Connection panel zones 0.01–0.00015d

On the other hand, the basement walls are modeled usinginelastic fiber wall elements that could experience nonlinearbehavior in in-plane bending, including: concrete fibers crackingand crushing; and steel fibers yielding. However, they wereassigned an elastic shear material to behave essentially elastic inshear.

5.2. Definition of performance levels

To assess the performance of buildings, ASCE 41 [7] defines theacceptance criteria of the structural components of the building interms of strength demand capacity ratios or deformation demandcapacity ratios, depending on the force–deformation actions of thestructural components whether they are force-controlled ordeformation-controlled, respectively.

Perform-3D automatically calculates the strength and defor-mation demand on the structural components of the buildingthroughout the analysis steps. However, ASCE 41 [7] givesdeformation capacities for the inelastic components correspond-ing to the three target performance levels for structural compo-nents, namely: immediate occupancy (IO), life safety (LS)and collapse prevention (CP). It defines the deformationcapacities as multiple of the yield deformations of the compo-nents. Table 5 gives the deformation capacities of the inelasticstructural components encounter in the model buildings corre-sponding to the IO, LS and CP performance levels and inaccordance with ASCE 41 [7] specifications. Deformation capa-cities for perimeter girders and columns are expressed as multi-ples of the chord rotation (yy) at yield. The deformation capacitiesfor the connection panel zones (assuming an improvedWUF-bolted web connection for the moment connectionsbetween girders and columns) are expressed as functions of thegirders’ depth (d). It should be noted that these deformationcapacities are plastic rotations and angular shear deformations,which dictates adding the yield deformations to them in order toget the total deformation capacities.

ASCE 41 [7] specifies that the strength capacity of structuralcomponents should be assigned different values corresponding tothe considered performance level. In the current study, compo-nents that have force-controlled force–deformation actions arerequired to remain elastic. Therefore, for the performance levelsIO, LS and CP, the strength capacities were taken equal to thenominal capacities of the components.

To reduce the volume of analysis output results, Perform-3Dgroups demand capacity ratios of similar components together todistill the results down to few ‘‘Limit States’’ that can be easilyused in assessing the performance of buildings. Each limit stategroups similar demand capacity ratios (e.g. end rotation ofperimeter girders) at a certain performance level (e.g. LSperformance level). It then calculates the maximum demandcapacity ratio, within each time step, for all the components in thelimit state. Perform-3D defines this maximum demand capacityratio as the ‘‘Usage Ratio’’ of the limit state at this time step. The

to IO, LS and CP performance levels.

Life safety Collapse prevention

6yy 8yy

6yy 8yy

0.0139–0.0002d 0.021–0.0003d

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Table 6Shallow foundations’ properties used with the model buildings.

Soil class C Soil class E


performance of the building can be thus assessed by ensuring thatthe usage ratios of the target performance level of the componentshave not exceeded unity throughout the seismic event.

Perimeter footings

Plan dimensions (m) 1.7�1.7 3.1�3.1

Depth of foundation (m) 1.5 2.0

Ultimate bearing capacity, qu (kPa) 4206.63 1235.54

Soil passive resistance along footing front face (kPa) 20.00 15.00

Foundation vertical stiffness, kv (kN/m3) 18,48,932.57 57,725.55

Foundation horizontal stiffness, KH (kN/m) 7,255,630.5 6,99,894.48

Interior footings

Plan dimensions (m) 2.1�2.1 4.0� 4.0

Depth of foundation (m) 1.5 2.0

Ultimate bearing capacity, qu (kPa) 4594.07 1359.5

Soil passive resistance along footing front face (kPa) 20.00 15.00

Foundation vertical stiffness, kv (kN/m3) 13,99,578.64 41,870.41

Foundation horizontal stiffness, KH (kN/m) 8,015,932.36 801,808.65

6. Foundation system

The foundation system of the buildings comprises shallowspread footings. For the ease of modeling, it was assumed thatthey are square in plan, and concentric with the supportedcolumns. Two footing models were considered for each building:one for the interior columns and one for the perimeter columns,due to the substantial difference between the vertical load actingon them. The strip footings beneath the basement walls and thesemelles and straps connecting the footings were neglected in thisstudy.

The side soil is assumed to be homogeneous throughout theembedment depth of the building. It is assumed that it possessesthe same mechanical and physical properties of the foundationsoil.

The foundation and side soil were assumed to experiencenonlinear behavior under seismic shaking. Therefore, they weremodeled using the Beam-on-a-Nonlinear Winkler Foundationapproach that is capable of simulating the important aspects ofthe nonlinear behavior of the foundation and side soil.

6.1. Shallow foundations

The model buildings encountered in this study involved a widerange of footing vertical dead loads corresponding to differentscenarios considered. In addition, two soil classes were consideredin this study: soil class C corresponding to ‘‘very dense soil andsoft rock’’ and soil class E corresponding to ‘‘soft soil’’. This widerange of variable parameters makes the task of sizing the footingscumbersome. Using a constant value for the vertical bearingcapacity safety factor would result in a wide range of footing plandimensions, and consequently different foundations’ bearingcapacities and stiffness. This would complicate the comparisonof the seismic performance of consistent buildings (e.g. ten storybuildings with zero, one, three and five underground stories).Therefore, a variable vertical bearing capacity safety factor wasused when sizing the foundations, since it is neither the seismicdesign of the footings that is being investigated in this researchnor the evaluation of the code recommendations for the seismicdesign of shallow foundations is to be done.

For each soil class, two model footings were used: perimetercolumns footings and interior columns footings. These footingswere sized so that the vertical bearing capacity safety factorranged from 7.0 for five story buildings to 2.0 for fifteen storybuildings. The bearing capacities of the foundations are calculatedusing Terzaghi’s standard bearing capacity formula for squarefootings. The soil passive resistance along the front face of thefooting is taken according to the presumptive values recom-mended by FEMA 356 [5] document for different soil types.However, the side friction along the footing side–soil interface isneglected.

The vertical and horizontal elastic stiffness of the foundationsis calculated using the frequency-independent formulas givenby FEMA 356 [5] document. To account for the cyclic natureof the seismic load on the footings, the unload–reload stiffness ofthe footing was used in lieu of the initial elastic stiffness.Allotey and El Naggar [8] recommend using an effective shearmodulus of 0.8 of the elastic shear modulus of the soil incalculating the vertical stiffness of the foundation. Therefore,the elastic shear modulus, Go, of the soil was calculated fromits shear wave velocity and mass density, then an effective

shear modulus, G ¼ 0.8Go, was used in calculating thevertical and horizontal stiffness of the footings. Table 6 liststhe shallow foundations’ properties used with the modelbuildings.

El Ganainy [9] has shown that based on the BNWF approach,the cyclic rocking, vertical and horizontal responses of shallowfoundations can be modeled effectively using an assemblage of acurvature hinge (or a moment–rotation hinge), shear hingeconnected in series with an elastic frame member attached tothe bottom end of ground story columns. El Ganainy [9] hasderived three bounding surfaces to couple the responses of thesehinges to be able to model the complete 3D response of shallowfoundations. To account for the ‘‘Soil Squeeze Out’’ phenomenon[9] observed in the cyclic rocking response of shallow foundation,El Ganainy [9] has shown that assigning an appropriate energydegradation factor to the curvature hinge would result inadjusting the material damping from the cyclic moment–rotationresponse of the footings and yield hysteretic moment–rotationloops consistent with the S-shape loops observed from experi-mental results.

This modeling approach was adopted herein in modeling theshallow foundations of the model buildings encounter in thisstudy. Bilinear approximations for the moment–rotation relationand the horizontal force–shear displacement relation wereassigned to the curvature and shear hinges, respectively [9].The geometric and mechanical properties of the curvature hinge,shear hinge and the elastic frame member were calculated,utilizing the mechanical properties of the specified soil classes,using the procedure outlined in El Ganainy [9].

To account for the soil squeeze out phenomenon, energydegradation factors were assigned to the curvature hinges at0.55 and 0.8 for soil classes C and E, respectively. These valuesprovided good fit with the experimental results obtained fromTRISEE experiment for the high density (HD) and low density (LD)tests, respectively [9], noting that soil classes C and E areapproximately consistent with the relative densities of 85% and45% of the HD and LD tests [9]. Hence, the corresponding energydegradation factors values were used herein.

A P–MB–ML bounding surface was assigned for the curvaturehinge to account for the interaction between the vertical androcking responses of the footing [9]. El-Tawil and Deierlein’sbounding surface [10,11], which is built-in Perform-3D, was usedin this regard. The fitting exponent m that controls the shape ofthe P–M bounding surface was assigned a value of 2 and theexponent n that controls the shape of the bounding surface in theMB–ML plane was assigned a value of 1.8 [9].

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A VB–VL bounding surface was assigned for the shear hinge toaccount for the interaction between the horizontal responsesof the footing along its width and length. The elliptical equation ofthis bounding surface is built-in Perform-3D and was used in thisregard [9]. Finally, the radiation damping through the foundationsoil was neglected. This is considered an acceptable approxima-tion, since the hysteretic damping is more important in the case ofseismic loading.

6.2. Side soil

The effect of side soil on the seismic performance of buildingswith underground stories can be grouped into three aspects:

(1)
Side soil serves as a flexible support to the building in lateraldeformation. In the static case, it acts on the basement wallswith a lateral pressure corresponding to the active earthpressure. Under seismic shaking, as the building oscillatesback and forth towards and away from the side soil, itresponds like horizontal elastic springs. As the intensity of theseismic shaking increases, the side soil could experience anonlinear behavior, in which it cannot provide a lateralpressure on the basement walls more than its passiveresistance, Pp, while the building is swaying towards thebackfill. Also, it cannot provide a lateral pressure less than itsactive resistance, Pa, while the building is swaying away fromthe backfill. In some types of soils, especially cohesive soil,gapping could occur between the basement walls and thebackfill as a result of the building oscillation. In this case, thelateral pressure of the backfill on the basement walls drops tozero. This nonlinear behavior can result in hysteretic for-ce–deformation actions in the side soil where the resultinghysteretic damping provides an additional source for dissipat-ing the earthquake energy. Fig. 3 shows the backbone curvefor the hysteretic lateral pressure–lateral deflection relation ofthe side soil.
(2)
Under severe seismic shaking, where the backfill experiencesnonlinear response, the wedge of the soil behind the base-ment walls could fail and begin oscillating with the building,either in-phase or out-of-phase. This oscillating mass of soilcould affect the seismic response of the building by altering itseffective oscillating mass. However, this oscillating soil masscould be neglected in comparison to the mass of the structuralcomponents and basement walls of the building, withoutaffecting the seismic response of the building significantly.
(3)
Side soil dissipates the earthquake energy through radiationdamping. This additional damping can affect the seismicresponse of the building, since it increases its effectivedamping ratio. However, this effect would be most significantfor stiff structures, such as shear wall and braced frame
Fig. 3. Backbone curve of the hysteretic lateral pressure–

structures. For flexible structures, such as moment-resistingframe structures, the effect of the radiation damping would beminimal and can be neglected.

In the current study, the elastic stiffness and nonlinear behaviorof side soil were modeled. However, the oscillating mass of theside soil and the radiation damping effects were neglected.

Currently, there are no nonlinear bar elements in Perform-3Dcapable of modeling the nonlinear backbone curve of the side soilas shown in Fig. 3. Therefore, approximating assumptions wereintroduced in order to make use of the available nonlinear barelements in Perform-3D to model the nonlinear response of theside soil adequately.

The approximation done herein can be better understood if thelateral pressure–lateral deflection relation of the side soil isrepresented into two distinct parts as follows (with reference toFig. 4):

(1)
Under static loading condition, the side soil acts on thebasement walls with a static pressure corresponding to theactive earth pressure.
(2)
As the building oscillates, the side soil acts like horizontalnonlinear springs, where their ultimate compression capa-cities are Pp�Pa. However, they possess no tension capacity.
It should be noted that the soil considered in this study iscohesionless and should not experience gapping (i.e. the mini-mum earth pressure cannot drop below the active value). Thus,this approach is considered to be adequate in representing thebackbone curve for the lateral pressure–lateral deflection relationof the side soil.

Briaud and Kim [12] have recommended a set of static P�y

curves for sand and clay to be used within a beam–columnmethod for the design of tieback walls. They validated the curvesby comparing their predictions with the measured behavior offour-full scale tieback walls in sand and in clay. The P�y curvesrecommended by Briaud and Kim [12] for sand are used herein inmodeling the backbone curve of the hysteretic lateral pressur-e–lateral deflection relation of the side soil.

The active, Pa, and passive, Pp, earth pressures and thecorresponding wall deflections ya and ya, respectively, arecalculated for sand as follows:

Pa ¼ KagZ cosðdÞ (1)

Pp ¼ KpgZ cosðdÞ (2)

ya ¼ 1:3 mm (3)

yp ¼ 13 mm (4)

lateral deflection relation for the side soil.

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Fig. 4. Approximate representation of the lateral pressure–lateral deflection relation for the side soil.


where

Ka ¼cos2ðfÞ

cosðdÞ 1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisinðfþ dÞ sinðfÞ

p= cosðdÞ

� �h i2

Kp ¼cos2ðfÞ

cosðdÞ 1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisinðfþ dÞ sinðfÞ

p= cosðdÞ

� �h i2

g is the unit weight of the soil, Z is the depth at which the lateralearth pressure is calculated, f is the angle of internal friction ofthe soil, and d is the wall–soil friction angle.

Using Eqs. (1)–(4) and the soil properties for site class C andsite class E listed in Table 2, the backbone curves for the hystereticlateral pressure–lateral deflection relation of the side soil werecalculated at selected depths.

The backbone curve for the side soil can be adequatelymodeled using the horizontal nonlinear springs and static activeearth pressure distributed over the basement walls’ area. Thus,nonlinear inelastic horizontal bar elements distributed horizon-tally and vertically over the surface area of the basement wallswere used to model the nonlinear behavior of the side soil. Thebar elements were equally spaced vertically at 1.2 m andhorizontally at 7.2 m (i.e. the bar elements were distributed alongthe underground perimeter columns, so that one bar is located ateach story level and two intermediate bars are equally spacedwithin each story). The backbone curve for each bar element wascalculated using its corresponding depth. The minimum activeearth pressure acting on the basement walls was represented bystatic concentrated loads acting at the bar elements’ locations.These loads were calculated as the value of the active earthpressure at the bar level multiplied by the horizontal and verticalspacing of the bar elements.

7. Earthquake loads

The model buildings are assumed to be located in theVancouver area. Thus, earthquake records compatible with the

design response spectrum of the Vancouver area, specified by theNBCC 2005, were used.

7.1. Uniform hazard spectra (UHS) and compatible

earthquake records

The NBCC 2005 has introduced uniform hazard spectra thathave a constant probability of exceedance of 2% in 50 years as afunction of spectral period. These spectra are based on aprobabilistic seismic hazard assessment for different zones acrossCanada [13]. The UHS eliminate the need to use standard spectralshapes scaled to the peak ground acceleration, thus providing amore site-specific description of the earthquake spectrum andensuring a uniform hazard level to be achieved for all spectralperiods [13].

The UHS can be considered as a composite of all earthquakeevents that contribute most strongly to the hazard at the specifiedprobability level. In general, the dominant contributor to theshort-period ground-motion hazard comes from small-to-moder-ate earthquakes at close distances, whereas larger earthquakes atgreater distance contribute most strongly to the long-periodground-motion hazard [14].

The artificial ground-motion time histories compatiblewith the 2% in 50 year UHS of the NBCC 2005 for theVancouver area suggested by Atkinson and Beresnev [14] wereused as input motion. They proposed an event of M6.5 at adistance of 30 km to represent the short-period hazard and anevent of M7.2 at a distance of 70 km to represent the long-periodhazard. In addition, an earthquake of M8.5 for the Cascadia eventscaled by a factor of 2.2 is used to simulate a great earthquake onthe Cascadia subduction zone. Therefore, three earthquakerecords are required to cover the entire hazard represented bythe NBCC 2005 UHS for the Vancouver area. Figs. 5–7 show thethree artificial acceleration records used in the dynamic analysisof the buildings. Each building was analyzed for each of thesethree records.

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Fig. 5. Acceleration record for M6.5 at a distance of 30 km event.

Fig. 6. Acceleration record for M7.2 at a distance of 70 km event.

Fig. 7. Acceleration record for M8.5 Cascadia event scaled by a factor of 2.2.


7.2. Ground response analysis

The UHS given by the NBCC 2005 are defined with reference tosite class C that is defined as ‘‘very dense soil and soft rock’’. Thus,the compatible records can be considered bedrock motions.

In general, the characteristics of the bedrock motion can beamplified or attenuated while propagating from the bedrocktowards the ground surface. This alteration depends mainly on thefrequency content of the bedrock motion and the properties of thesoil deposit. Firm soil deposits, such as site class C, will probablynot alter the characteristics of the bedrock motion since they canbe considered part of the bedrock. Therefore, all buildings foundedon site class C can be analyzed for the bedrock motions shown inFigs. 5–7, whether they are surface building or have multipleunderground stories.

On the other hand, a soft soil deposit as site class E wouldprobably alter the characteristics of the bedrock motion, byamplification or attenuation. Thus, the ground motions shown inFigs. 5–7 were propagated within a 30-m-thick deposit of soil siteclass E (Table 2), performing nonlinear free-field site responseanalyses using the one-dimensional (1D) site response analysisprogram DEEPSOIL [15]. The G/Gmax modulus reduction curve andthe equivalent damping ratio versus shear strain relationship forsand given by Seed and Idriss [16] were assigned to the soildeposit [17].

Three ground response analyses were conducted, one for eachof the three ground motions as input bedrock motion and theresponse of the soil deposit was evaluated. The ground motionwas calculated at four foundation levels corresponding tobuildings having five, three and one underground stories andat the ground surface for buildings with surface foundations.Figs. 8–10 show the results of the ground response analyses interms of the acceleration time histories of the three bedrock

motions at the considered foundation levels. In general, theresults show attenuation for the three bedrock motions, which ismost pronounced for M6.5 at a distance of 30 km event.

8. Nonlinear dynamic analysis

Nonlinear dynamic analyses were performed to assess theseismic performance of the model buildings. A series of nonlineardirect integration time–history analyses were conducted using thenonlinear structural analysis software Perform-3D [1].

The seismic responses of five, ten and fifteen story buildingswith underground stories ranging from zero (i.e. founded on theground surface) to five underground stories were investigated.The response of the buildings was evaluated in terms of: (1) themagnitudes and distribution of the envelope of the story shearand moment demand on the buildings throughout each seismicevent; (2) the maximum usage ratio of the limit states definingthe performance level of the primary structural components ofthe building. The performance of the following structuralcomponents has been investigated: (1) perimeter columns’ endrotation; (2) perimeter girders’ end rotation; (3) connection panelzones’ shear deformation, in terms of three performance levels,namely: immediate occupancy, life safety and collapse prevention,as specified by the ASCE 41 [7] standard.

8.1. Nonlinear direct integration time–history analysis

Perform-3D utilizes step-by-step integration through timeusing the constant average acceleration (CAA) method (alsoknown as the trapezoidal rule or the Newmark b ¼ 1

4 method) tocalculate the seismic response of buildings.

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Fig. 8. Ground response analysis results for M6.5 at a distance of 30 km event.

Fig. 9. Ground response analysis results for M7.2 at a distance of 70 km event.


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Fig. 10. Ground response analysis results for M8.5 Cascadia event scaled by a factor of 2.2.


The input ground motions resulting from the ground responseanalyses and the corresponding bedrock motions were used inthe analysis of the buildings. The earthquake direction was setto the W–E direction for all buildings. The ground motions weregiven in 0.01 s time steps. Therefore, the integration time step forthe analysis was taken 0.01 s in order to accurately capture theinput ground motions. Also, it is sufficiently small to capturethe structure response, since it is considerably smaller thanthe recommended practical value of 1

12 of the structure period [18]that ranges around 3.0 s for all model buildings encountered inthis study.

There are two sources of damping in nonlinear structures: (1)for a structure that is essentially elastic, the earthquake energy isdissipated through viscous damping; (2) after the structure yields,hysteretic damping resulting from the inelastic behavior of thestructural components would add to the total dissipated energy.Modeling the structural elements of the building using inelasticcomponents inherently accounts for this source of damping [18].To simulate viscous damping in buildings, either the modaldamping or Rayleigh damping can be used.

Rayleigh damping calculates the damping matrix of thestructure using a combination of the mass matrix and the initialelastic stiffness matrix of the structure, multiplied by scalingfactors, a and b, for the mass and stiffness matrices, respectively.The Rayleigh damping is widely used in linear structural analysis.However, it can lead to unrealistic large damping values innonlinear analysis. The Rayleigh damping matrix is calculatedonce at the beginning of the analysis using the initial elasticstiffness matrix of the structure and is used throughout theanalysis. However, as the intensity of the seismic shakingincreases and the structure experiences nonlinear behavior inthe form of plastic hinging, the structure would soften and itsstiffness would decrease and become much less than the elasticvalue used initially in calculating the damping matrix. Hence, the

Rayleigh damping could overestimate the viscous damping innonlinear structures [18]. Using the modal damping couldalleviate this defect.

In the modal damping approach, the damping matrix iscalculated for linear analysis using the elastic mode shapes andperiods of the structure utilizing the specified damping ratio. Thisdamping matrix is kept constant throughout the analysis steps.For nonlinear analysis, the deformed shape for the nonlinearstructure generally contains contributions from the elastic modeshapes. However, the effective periods of vibration for theseshapes are not the linear periods. Consequently, the mode shapesare still damped, but since the effective period may have changedafter yielding of structural components (probably increased)while the damping matrix is unchanged, the amount of damping,expressed as a proportion of critical damping, generally changes[18]. A shortcoming of using modal damping in nonlinear analysisis that only the calculated elastic mode shapes are damped.However, the higher modes are undamped.

To provide reasonable damping values, avoiding the pitfalls ofboth methods, a combination of modal damping and a small valueof the Beta-K Rayleigh damping (with no Alpha-M damping) couldbe used. This is to insure that the Beta-K part will serve indamping the higher modes of vibration, and the modal dampingserves in damping the lower modes (i.e. elastic modes). For thecurrent study, the damping ratio was assigned to the modelbuildings as a combination of 3% modal damping in addition to0.1% Beta-K Rayleigh damping, and six modes of vibration werecalculated for the buildings.

The analyses involved a gravity load case followed by a seriesof independent dynamic analyses, each having the gravity loadcase as the preceding case. The self weight of the structure and theactive earth pressure acting on the basement walls were appliedin the gravity load case. The p–d effects were considered for all thevertical components of the building. The elastic frame members

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used within the assemblage utilized in modeling the shallowfoundations’ response were not assigned p–d effects to eliminateany additional artificial moments on the footings that could resultfrom the self weight of the structure.

Fig. 12. Story shear demand on five story buildings—M8.5 Cascadia event scaled

by a factor of 2.2 (soil class E).

9. Results and discussion

Because of the extensive amount of results obtained from theparametric study, only some representative results are presentedhere. The complete set of results can be found in El Ganainy [9].The results are presented in the form of graphs comparingresponse quantities for each of the five, ten and fifteen storybuildings with these conditions: fixed base, flexible foundation(i.e. zero underground stories) and having one, three or fiveunderground stories. The response quantities presented include:(1) the envelope of the story shear and moment demand on thebuildings throughout the earthquake events; (2) the maximumusage ratio of the limit states defining the performance level ofthe structural components of the building.

9.1. Story shear and moment demand

Figs. 11 and 12 show the envelope of story shear demand onfive story buildings for the M8.5 Cascadia event scaled by a factorof 2.2 for soil classes C and E, respectively, while Figs. 13 and 14show the envelope of moment demand for the same conditions.The figures show that the SSI decreased the base shear andmoment demands on buildings founded on stiff soil, but increasedthe base story shear and moment demand on buildings foundedon soft soil conditions. For example, it increased by about 10–25%of the fixed base buildings values for buildings founded on soilclass E. This shows that the common assumption that SSI has afavorable effect by decreasing the seismic forces postulated byalmost all the design code does not always hold. The figures alsoshow that the behavior of buildings with underground stories iscloser to that of fixed base, i.e., as the number of undergroundstories increased, the SSI effects decreased. This could beattributed to the rigidity of the basement walls together withthe rigid diaphragm action of the underground stories’ slabs

Fig. 11. Story shear demand on five story buildings—M8.5 Cascadia event scaled

by a factor of 2.2 (soil class C).

Fig. 13. Story moment demand on five story buildings—M8.5 Cascadia event

scaled by a factor of 2.2 (soil class C).

rendering the embedded part of the building essentially a rigidbox, hence fixing the structure. These fixing effects wouldprobably increase with the number of the underground stories.The results for the 10 and 15 story buildings (found in El Ganainy[9]) show that the SSI effects are less pronounced for buildingswith longer period.

Inspecting the whole set of graphs for the envelope of storyshear and moment demand on the buildings found in El Ganainy[9], the following observations are made:

(1)
For buildings with underground stories or flexible foundationsfounded on soil class C, the envelope of the story shear and

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Fig. 14. Story moment demand on five story buildings—M8.5 Cascadia event

scaled by a factor of 2.2 (soil class E).

Fig. 15. Usage ratio of limit states for five story buildings—M8.5 Cascadia event

scaled by a factor of 2.2 (soil class C).


moment demand almost has not changed, either in magnitudeor in shape of distribution, compared to the fixed basebuildings case. The minimal SSI effect in this case is attributedto the high soil stiffness and hence minimal change in thedynamic characteristics of the soil–structure system.

(2)
The effects of the SSI on the seismic loads are pronounced forbuildings founded on soil class E for all seismic eventsconsidered. The envelopes of story shear and moment demandfor buildings with underground stories or flexible foundationshave changed in magnitude compared to the case of buildingswith fixed base condition. The magnitudes of base shear andmoment have mostly increased, especially at the base wherethe increase generally ranged from about 10% to 25% of thefixed base values.
Fig. 16. Usage ratio of limit states for five story buildings—M8.5 Cascadia event

scaled by a factor of 2.2 (soil class E).

9.2. Usage ratio of the limit states

Figs. 15 and 16 show the maximum usage ratio of the limitstates for five story buildings for the M8.5 Cascadia event scaledby a factor of 2.2 for soil classes C and E, respectively. Fig. 15 showsthat for soil class C, the deformations of the structural compo-nents of buildings with flexible foundations or undergroundstories are slightly different from those of buildings with fixedbase conditions. On the other hand, Fig. 16 shows that for the soilclass E, the deformations of the structural components ofbuildings with flexible foundations or underground stories aresubstantially different (larger) from those of buildings with fixedbase conditions. However, as the number of underground storiesincreased, the deformation of the structural components gradu-ally decreased approaching the fixed buildings values. Similarobservations can be made from the rest of figures found in ElGanainy [9], for ten and fifteen story buildings and differentseismic events. In general, the SSI effects are less pronounced asthe period of the building increased. Comparing the deformationsof the structural components of buildings founded on soil class Eto that of the corresponding buildings founded on soil class C, it isnoted that the deformation level generally increases for the soilclass E case. The increase ranges from about 50% to about 300%

especially for the connection panel zones’ shear deformationsperformance levels. This observation clearly demonstrates that SSIeffects on the seismic performance of buildings increase as thesoil stiffness decreases.

10. Summary and conclusions

The seismic performance of buildings with multiple under-ground stories was investigated. Five, ten and fifteen story 3Dmoment-resisting frame steel buildings with underground storiesranging from zero to five underground stories have beenexamined. The buildings were assumed to be founded on shallowfoundations. Two site conditions were considered: soil class C andsoil class E, corresponding to firm and soft soil deposits,

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respectively. Vancouver seismic area has been considered for thisstudy. Synthetic earthquake records compatible with the Vancou-ver UHS, as specified by the NBCC 2005, have been used as inputmotion. For buildings founded on site class C, the bedrock motionshave been utilized in the seismic analyses of the buildings.However, for buildings founded on site class E, ground responseanalyses have been performed to evaluate the characteristics ofthe ground motion within the soil profile at each of the desiredfoundation levels for the considered buildings.

The building foundations were modeled using an assemblageof a curvature hinge, shear hinge connected in series with anelastic frame member attached to the bottom end of the groundstory columns. El Ganainy [9] has shown that this approach can beused in modeling the 3D cyclic rocking, vertical and horizontalresponses of shallow foundations effectively. The behavior of theside soil has been modeled using an approximate method:nonlinear bar elements were used to model its flexibility andultimate horizontal capacity and static earth pressure was appliedto the basement walls in order to simulate the effect of the initialactive earth pressure prior to the seismic event.

The dynamic analysis was conducted using the nonlinearstructural analysis software Perform-3D. The results indicate thatthe SSI can considerably affect the seismic response of surfacebuildings as well as buildings with underground stories foundedon soft soil conditions. In general, the results showed that SSIeffects are important for buildings founded on soft groundconditions. However, for firm ground conditions its effects canbe neglected.

The results showed that the SSI effects increased the base shearand moment demand on buildings founded on soft soil. This iscontrary to the common assumption that SSI effect on seismicforces is always favorable, postulated by almost all the designcodes. It is clearly demonstrated that the base shear and momentdemand on short-period buildings could increase by up to 25% ofthe fixed base buildings values.

The deformations of the structural components of the build-ings have also been affected by the SSI. The deformations ofbuildings with flexible bases have shown a considerable increasethat ranged from 50% to about 300% compared to the fixed base

case for buildings founded on soil class E. This would in turnincrease the lateral deflection of the whole building. Thus, SSI canhave a detrimental effect on the performance of buildings.

References

[1] Computers and Structures Inc. (CSI). Perform-3D—A computer program fornonlinear analysis and performance assessment of 3D structures. 2007: 4.0.3.

[2] American Society of Civil Engineers (ASCE). FEMA 310-handbook for theseismic evaluation of buildings: a prestandard. Washington, DC: FederalEmergency Management Agency; 1998.

[3] Das BM. Principles of foundation engineering. Toronto, Ontario, Canada:Thomson; 2007.

[4] Das BM. Fundamentals of geotechnical engineering. Pacific Grove, CA: Brooks/Cole; 1999.

[5] American Society of Civil Engineers (ASCE). FEMA 356—Prestandard andcommentary for the seismic rehabilitation of buildings. Washington, DC:Federal Emergency Management Agency; 2000.

[6] Computers and Structures Inc. (CSI). ETABS—an integrated building designsoftware; 2008 9.2.0.

[7] American Society of Civil Engineers. ASCE 41—seismic rehabilitation ofexisting buildings. American Society of Civil Engineers; 2006; ASCE/SEI 41-06.

[8] Allotey N, El Naggar MH. Analytical moment–rotation curves for rigidfoundations based on a Winkler model. Soil Dyn Earthquake Eng2003;23:367–81.

[9] El Ganainy HM. Seismic performance of buildings with multiple undergroundstories. M.E.Sc. thesis, University of Western Ontario, London, Ontario, Canada2008.

[10] El-Tawil S, Deierlein GG. Nonlinear analysis of mixed steel–concrete frames. I:element formulation. J Struct Eng 2001;127:647–55.

[11] El-Tawil S, Deierlein GG. Nonlinear analysis of mixed steel–concrete frames.II: implementation and verification. J Struct Eng 2001;127:656–65.

[12] Briaud J, Kim N. Beam–column method for tieback walls. J GeotechGeoenviron Eng 1998;124:67–79.

[13] Adams J, Atkinson G. Development of seismic hazard maps for the proposed2005 edition of the national building code of Canada. Can J Civ Eng 2003;30:255–71.

[14] Atkinson GM, Beresnev IA. Compatible ground-motion time histories for newnational seismic hazard maps. Can J Civ Eng 1998;25:305–18.

[15] Hashash Y, Park D, Tsai CC. DEEPSOIL—a computer program for one-dimensional site response analysis. University of Illinois at Urbana-Cham-paign; 2005: 2.6.

[16] Seed HB, Idriss IM. Soil moduli and damping factors for dynamic responseanalysis. Berkeley, California: Earthquake Engineering Research Center,University of California; 1970: UCB/EERC-70/10.

[17] Hashash Y, Park D, Tsai CC. DEEPSOIL—tutorial and user manual. University ofIllinois at Urbana-Champaign; 2005; 2.6.

[18] Computers and Structures Inc. (CSI). Perform-3D—user manuals. 2007: 4.0.3.

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