Nonlinear Amplification

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Vol.11, No.4 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION December, 2012

Earthq Eng & Eng Vib(2012) 11: 541-551 DOI: 10.1007/s11803-012-0140-2

Effect of nonlinear soil-structure interaction on seismic response of

low-rise SMRF buildings

Prishati Raychowdhuryand Poonam Singh

Indian Institute of Technology, Kanpur, India

Abstract: The nonlinear behavior of a soil-foundation system may alter the seismic response of a structure by providingadditional flexibility to the system and dissipating hysteretic energy at the soil-foundation interface. However, the current

design practice is still reluctant to consider the nonlinearity of the soil-foundation system, primarily due to lack of reliable

modeling techniques. This study is motivated towards evaluating the effect of nonlinear soil-structure interaction (SSI) on

the seismic responses of low-rise steel moment resisting frame (SMRF) structures. In order to achieve this, a Winkler-

based approach is adopted, where the soil beneath the foundation is assumed to be a system of closely-spaced, independent,

nonlinear spring elements. Static pushover analysis and nonlinear dynamic analyses are performed on a 3-story SMRF

building and the performance of the structure is evaluated through a variety of force and displacement demand parameters. It

is observed that incorporation of nonlinear SSI leads to an increase in story displacement demand and a signi ficant reduction

in base moment, base shear and inter-story drift demands, indicating the importance of its consideration towards achieving

an economic, yet safe seismic design.

Keywords: soil-structure interaction; Winkler modeling; nonlinear analysis; seismic response; low-rise steel momentresisting frame

Correspondence to: Prishati Raychowdhury, Indian Institute of

Technology, Kanpur, IndiaTel: +91 512 259 6692; Fax: +91 512 259 7395

E-mail: [email protected] Professor; Former Graduate Student

Received January 2, 2012; AcceptedSeptember 20, 2012

1 Introduction

Nonlinear behavior of a soil-foundation interface

due to mobilization of ultimate capacity and consequent

energy dissipation during an intense seismic event

may alter the response of a structure in several ways.

Foundation movement can increase the period of the

structure by introducing additional flexibility, material

nonlinearity and hysteretic energy dissipation at the

soil-foundation interface may reduce the force demand

to the structure, foundation deformations may alter

the characteristics of input ground motion, and so on.

However, todate, the current design practice is reluctant

to account for the nonlinear soil-structure interaction

(SSI), for two principal reasons: (a) in anticipation

that consideration of SSI leads to more conservative

design, and (b) absence of reliable nonlinear modeling

techniques.

In the last few decades, a number of analytical and

experimental studies have been conducted to understand

the effect of SSI on the seismic behavior of structures

(Chopra and Yim (1985); Yim and Chopra (1985);

Xiong et al. (1993, 1998); Nakaki and Hart (1987);Gazetas and Mylonakis (2001); Stewart et al. (2003);

Dutta et al. (2004); Allotey and Naggar (2007); Harden

and Hutchinson (2009); Raychowdhury and Hutchinson

(2009, 2010, 2011); Gajan et al. (2010); Figini et al.

(2012) and so on). These studies have indicated that

the nonlinear soil-foundation behavior under intense

earthquake loading has a considerable effect on the

response of structure-foundation system (Fig. 1).

Design and rehabilitation provisions (e.g., ATC-40,

1996; NEHRP, 2003; FEMA 356, 2000; ASCE-7, 2005)

have traditionally focused on simplified pseudo-static

force-based or pushover type procedures, where thesoil-foundation interface is characterized in terms of

modified stiffness and damping characteristics. However,

the above-mentioned approaches cannot capture the

complex behavior of nonlinear soil-foundation-structure

systems, such as hysteretic and radiation damping, gap

formation in the soil-foundation interface and estimation

of transient and permanent settlement, and sliding and

rotational deformations of the foundation.

In this study, the seismic response of a ductile

steel moment resisting frame (SMRF) building has

been evaluated considering nonlinear soil-foundation

interface behavior using a Beam-on-Nonlinear-

Winkler-Foundation (BNWF) approach, where the

soil-foundation interface is assumed to be a system of

closely-spaced, independent, inelastic spring elements.


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542 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol.11

The effect of nonlinear SSI on the structural response

is studied in terms of base moment, base shear, story

displacement, and interstory drift angle. Nonlinear timehistory analysis is carried out along with static pushover

analysis and eigenvalue analysis. The analysis is

conducted using finite element models in the framework

of Open System for Earthquake Engineering Simulation

(OpenSees, 2008). The details of the modeling technique,

soil and structural properties considered, and analysis

procedures adopted are discussed below.

2 Selection of structure and soil properties

A 3-story, 4-bay steel moment resisting frame(SMRF) building adopted from Gupta and Krawinkler

(2000) is considered for the present study. The building

was designed based on weak-beam strong-column

mechanism, with a floor area of 36:6 36:6m and four

bays at an interval of 9.15 m in each direction (Fig.

2). The section properties and geometric details of the

structure have been taken from Gupta and Krawinkler

(2000). The columns of the building are assumed to be

supported on a mat foundation resting on dense silty

sand of the Los Angeles area (site class-D, NEHRP);

with the following soil properties: cohesion: 70 kPa,

unit weight: 20 kN/m3, shear modulus: 5.83 MPa and

Poissons ratio: 0.4. The effective shear modulus is

obtained by reducing the maximum shear modulus

corresponding to small strain values by 50% to representthe high strain modulus during significant earthquake

loadings. The foundation was designed in such a way

that it has a bearing capacity three times the vertical load

coming to it (i.e., a static vertical factor of safety of 3).

Further details of the structure and soil properties and

analysis procedure can be found in Singh (2011).

3 Numerical modeling of SSI

In this study, the soil-foundation interface is modeled

using a Beam-on-Nonlinear-Winkler-Foundation(BNWF) concept, where the soil-foundation interface is

assumed as an assembly of closely spaced, independent

nonlinear spring elements. Each spring consists of

different elements such as: drag and closure spring,

dashpot, near-field plastic spring, and a far-field elastic

spring (Fig. 3). These elements together are responsible

for capturing several salient features of a foundation-soil

interface, such as transient and permanent deformations,

gap formation between foundation and surrounding soil,

radiation and hysteretic damping of the adjacent soil,

strength and stiffness degradation, and so on. Vertical

springs (q-z elements) distributed along the length of

the footing are intended to capture the rocking, uplift

and settlement, while horizontal springs (t-x and p-x

elements) are intended to capture the sliding and passive

resistance of the footing, respectively. The constitutive

relations used for the q-z,p-xand t-xmechanistic springs

are represented by nonlinear backbone curves that were

originally developed by Boulanger (2000), based on

an earlier work of Boulanger et al. (1999); and later

calibrated and validated by Raychowdhury (2008) for

more appropriate utilization towards shallow foundation

behavior modeling. Each spring material model consistsof an initial elastic portion followed by a smooth

inelastic curve (as shown in Fig. 4). In the elastic portion

of a q-zmaterial, the instantaneous load q is assumed

to be linearly proportional with the instantaneous

High forcescause shearwall damage

Foundation yield-ing and rocking

protects shear wall

Large displacementscause frame damage

,large,small

Small displace-ment protectframe from

damage

(a) Stiff and strong (b) Flexible and weak

Fig. 1 Effect of foundation flexibility on a typical structure (after ATC 40, 1996)

[email protected]

3 @ 3.96 m

Fig. 2 SMRF structure considered in the study (adopted from

Gupta and Krawinkler (2000))

4 bays @ 9.15 m


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No.4 Prishati Raychowdhuryet al.: Effect of nonlinear soil-structure interaction on seismic response of low-rise SMRF buildings 543

displacementz:

q = kinz (1)

where kin is the initial elastic (tangent) stiffness. The

range of the elastic region is defined by the following

relation:

q0= C

rq

ult(2)

where q0is the load at the yield point, C

ris a parameter

controlling the range of the elastic portion, and qult

is the

ultimate load. In the nonlinear (post-yield) portion, the

backbone curve is described by

q q q qcz

cz z z

n

= +

ult ult p p( )0

50

50 0

(3)

where z50

is the displacement at which 50% of the

ultimate load is mobilized, zp

o is the displacement atthe yield point, zp is the displacement at any point in

the post-yield region, and c and n are the constitutive

parameters controlling the shape of the post-yield portion

of the backbone curve. The expressions governing both

p-xand t-xelements are similar to Eqs. (1) to (3), with

variations in the constants n, c, and Cr, controlling the

general shape of the curve. Furthermore, it may be noted

that q-zmaterial has a reduced capacity in the tension

side (Fig. 4(a)), which allows the footing to uplift

without losing contact with the soil beneath it during a

rocking movement. On the other hand, the p-xmaterial

is characterized by a pinched hysteretic behavior (Fig.

4(b)), whereas the t-xmaterial is characterized by a large

initial stiffness and a broad hysteresis (Fig. 4(c)).

It is evident from Eqs. (1) to (3) that the shape of

spring backbone curves, which is basically a controlling

factor for the SSI behavior, is mainly dependant on

two physical parameters related to soil characteristics;

namely, capacity (qult

), and initial elastic stiffness (kin).

The capacity and elastic stiffness of each spring is

obtained by distributing the global footing capacity and

stiffness utilizinga proper tributary area of each spring.

The footing capacity is derived using the general bearingcapacity equation from Terzaghi (1943) with shape,

depth and inclination factors after Meyerhof (1963) as

shown in Eqs. (4) to (7).

Fig. 3 Numerical modeling of nonlinear SSI: BNWF approach

Near-structureplastic response

Far-structure elasticresponse

PlasticDamper

Drag Closure

Elastic

Zero length

G.S.

q-zelements

NodesElastic beam-column

elements p-xelementsG.S.

t-xelements

Fig. 4 Material models for soil-foundation interface elements: (a) q-zelement; (b)p-xelement and (c) t-xelement

1.0

0.5

0

-0.5

Normalizedload,q/quit

-8 0 8 16

Vertical displacement (mm)

(a)

1.0

0.5

0

-0.5

-1.0

Normalizedload,p/puit

-16 -8 0 8 16

Horizontal displacement (mm)

(b)

1.0

0.5

0

-0.5

-1.0

Normalizedload,t/tuit

-16 -8 0 8 16Horizontal displacement (mm)

(c)


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qult

=cNcF

csF

cdF

ci+D

fN

qF

qsF

qdF

qi+0.5BN

F

sF

dF

i

(4)

where qult

is the ultimate vertical bearing capacity per

unit area of footing, c the cohesion, the unit weight

of soil, Df the depth of embedment, and B the width

of footing. Bearing capacity factors, Nc, N

q and N

are

calculated after Meyerhof (1963):

Nq = +tan ( )tan2

452

e (5)

N Nc q= ( ) cot1 (6)

N Nq = ( ) tan( . )1 1 4 (7)

For the p-x material, the ultimate lateral loadcapacity is determined as the total passive resisting

force acting on the front side of the embedded footing.

For homogeneous backfill against the footing, the

passive resisting force can be calculated using a linearly

varying pressure distribution resulting in the following

expression:

p D Kult f 2

p= 0 5. (8)

where pult

= passive earth pressure per unit length of

footing, and Kp = passive earth pressure coefficient.

For the t-xmaterial, the lateral load capacity is the totalsliding (frictional) resistance, which can be defined as

the shear strength between the soil and the footing as:

t W A cult g b= +tan (9)where t

ult = frictional resistance per unit area of

foundation, Wg= vertical force acting at the base of the

foundation, = angle of friction between the foundation

and soil (typically varying from 1/3to 2/3 ) andAb=

the area of the base of footing in contact with the soil

(=L B).

The initial elastic stiffness (vertical and lateral) ofthe footing are derived from Gazetas (1991) as follows:

kGL

v

B

Lv =

+

10 73 1 54 0 75. . ( ) . (10)

kGL

v

B

Lh =

+

22 2 5 0 85. ( ) . (11)

where kvand k

hare the vertical and lateral initial elastic

stiffness of the footing, respectively; G is the shear

modulus of soil; is the Poissons ratio of soil; and B

andLare the footing width and length, respectively.Theinstantaneous tangent stiffness k

p, which describes

the load-displacement relation within the post-yield

or nonlinear region of the backbone curves, may be

expressed as:

k n q qcz

cz z z

n

np ult=

+

+( )( )

( )

050

50 0

1 (12)

Note that Eq. (12) was obtained by rearranging Eq.

(3). Also, note that the shape and instantaneous tangent

stiffness of the nonlinear portion of the backbone curve

is a function of the parameters cand n, which are derived

by calibrating against a set of shallow footing tests on

different types of soil. It is evident from the preceding

equations that the spring responses are primarily

dependent on basic strength and stiffness parameters of

soil such as cohesion (c), friction angle (), unit weight

(), shear modulus (G) and Poissonsratio ()of soil.

The BNWF model has shown good predictivecapability in capturing the key features of a shallow

foundation behavior. Figure 5 shows a sample result

showing the BNWF model performance in predicting

experimentally observed behavior of a strip footing of

size 2.8m 0.65m (prototype scale) resting on dry dense

sand with a relative density of 80%, and a vertical factor

of safety of 5.2 carried out at the centrifuge facility at the

University of California. Note that the BNWF model can

reliably predict the following behavior of a seismically

loaded footing: (a) peak moment, (b) peak shear, (c)

initial and post-yield stiffness of moment-rotation and

shear-sliding responses, (d) transient and permanentsliding, settlement and rotation, and (e) overall shape

of the moment-rotation and shear-sliding loops. More

comparison results can be found in Raychowdhury

(2008), Raychowdhury and Hutchinson (2009), and

Gajan et al. (2008, 2010).

In order to investigate the effect of foundation

nonlinearity efficiently, in addition to the nonlinear

base condition (i.e., BNWF model), two additional

base conditions are considered: (1) fixed base, where

the movement of the foundation is neglected indicating

absolutely no SSI, and (2) linear base condition, where

the force-deformation behavior of the interface springsare assumed to be linear elastic with initial stiffness the

same as that considered in the nonlinear base condition.

The initial elastic stiffness and vertical capacity of the

soil springs are calculated based on Gazetas (1991) and

Terzaghi (1943), respectively. Springs are distributed at

a spacing of 1% of the footing length at the end region

and 2% of the footing length at the mid region. The end

region is defined as a high stiffness region extending

10% of the footing length from each end of the footing;

while the mid region is the less stiff middle portion. This

variation in the stiffness distribution is provided based

on the recommendations of ATC-40 (1996) and Harden

and Hutchinson (2009) in order to achieve desirable

rocking stiffness of the foundation.


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4 Eigenvalue analysis

In order to understand the effect of SSI on the eigen

properties of the structure, eigenvalue analysis is carried

out for the fixed base, linear base and nonlinear base

structure. The results are compared and tabulated inTable 1. It has been found that the fundamental period

of the fixed base structure (i.e., ignoring the SSI effects)

is obtained as 1.03 s, which is in accordance with the

period obtained by Gupta and Krawinkler (2000).

However, when the base flexibility is introduced, the

fundamental period is increased to 1.37 s, indicating a

significant period elongation (about 33%) due to the SSI

effects. Further, the period elongation obtained using

methods outlined in NEHRP (2003) gives very close

results (Table 1), indicating that inelastic behavior of

foundations does not significantly affect the fundamental

period and the first mode shapes of a structure.

5 Pushover analysis

Following eigenvalue analysis, static pushover

analysis is conducted on the building with three different

base conditions: fixed, linear and nonlinear. Figure 6

shows the pushover curves for different base conditions.It is observed that for linear modeling of the soil-

foundation interface, the global response of the system

only slightly varies from that of a fixed base case, with

almost no change in the shape of the curve (depicting

a typical elastic-plastic behavior common for a steel

building). However, when the soil springs are modeled

as nonlinear, the curve becomes much softer, resulting

in lower yield force and higher yield displacement

demands, which may be associated with yielding of

the soil beneath the foundation. Table 2 provides the

numerical values of the displacements and forces

corresponding to the first yield point for these three

400

200

0

-200

-400

Moment(

kN.m)

-0.08 -0.04 0 0.04 0.08

Rotation (rad)

20

0

-20

-40

-60

-80

-100

Settlement(mm)

80

40

0

-40

-80

Shearforce(kN)

20

0

-20

-40

-60

-80

-100

Settlement(mm)

Experiment

BNWF simulation

-20 0 20 40 60

Sliding (mm)

Fig. 5 Predictive capability of BNWF model: Comparison of load-deformation behavior of a footing for BNWF simulation and

SSG02_03 centrifuge test carried out by Gajan (2006)

Table 1 Eigenvalue analysis results

Fundamental

period from

Gupta and

Krawinkler

(2000)

Fundamental

period from

present study

(Fixed base case)

Fundamental

period from

present study

(Linear base case)

Fundamental

period from

present study

(Nonlinear base

case)

Period elongation

( T T/ )

from present study

Period elongation

( T T/ )

using NEHRP

provisions

1.03 s 1.03 s 1.37 s 1.37 s 1.34 1.33

Table 2 Pushover analysis results

Base condition Yield displacement (m) Yield force (MN)

Fixed base

Linear base

Nonlinear base

0.19

0.25

0.28

4.53

4.28

2.86


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cases. It can be observed that the yield displacement

increases about 32% from fixed base to linear base

case, whereas it increases about 47% for the nonlinear

base. The yield force, on the other hand, decreases only

slightly (about 5.5%) from the fixed base to linear base,

but significantly (about 37%) when base nonlinearity is

introduced. This significant difference in the force and

displacement demands for the nonlinear base condition

may be due to the capacity mobilization and yielding

of the soil-foundation interface spring elements. Sincepushover analysis is a well-accepted and widely-used

method for assessing the seismic demand of structures,

these observations provide a crucial indication that

nonlinear SSI may significantly alter the seismic demand

of a structure.

6 Nonlinear dynamic analysis

In this section, nonlinear dynamic analysis is

carried out using 60 ground motions (SAC motions

from Somerville et al., 1997). These ground motionsare divided into three sets (each set having 20 motions),

representing the probabilities of exceedance of 50%,

10% and 2% in 50 years; with return periods of 72

years, 475 years, and 2,475 years, respectively. Table 3

provides the details of the ground motions used in this

study. Figure 7 shows the acceleration response spectra

of the motions, where spectra for individual motions are

shown with light grey lines and the median and 84th

percentile curves are shown with darker and thicker

lines. A 2% Rayleigh damping is used for the dynamic

analysis. In this paper, the three sets of ground motions

are denoted as 50/50, 10/50 and 2/50, respectively, forbrevity. See Somerville et al. (1997) for further details

regarding these motions.

Since the geometry and material properties of the

moment frame is taken from Gupta and Krawinkler

(2000), the structural response is first compared with

that of the above-mentioned study in order to check the

validity and reliability of the current fixed-base model.

Figure 8 shows a comparison of frame responses from

the present study (fixed base case) with that from Gupta

and Krawinkler (2000). The observation indicates that

the results are comparable for all floor levels and all

ground motions, ensuring the reliability of the structural

model.

However, to predict the seismic responses of the

frame in a more accurate way, seismic SSI effects must

be taken into account. The following paragraphs provide

results showing the effect of considering both linear

and nonlinear SSI effects. Figures 9 through 13 provide

the statistical results of various force and displacement

demands obtained from the nonlinear dynamic analysisconsidering fixed, linear and nonlinear base conditions

using the aforementioned 60 ground motions. The

maximum absolute value of each response parameter

(such as moment, shear, story displacement, and story

drift angle) is considered as the respective demand

value.

Figure 9 demonstrates the median values of story

displacements for three sets of ground motions and three

base conditions. Note that story displacement increases

up to 40% from fixed base to linear base, and up to

about 2.5 times from fixed base to nonlinear base. This

increase in story displacement in flexible bases (bothlinear and nonlinear) is caused by the overall reduction

in the global stiffness resulting from the induced

foundation movements. Further, this trend is consistent

for all ground motions and all floor levels. These results

indicate that lack of proper consideration of SSI will

lead to an underestimation of the story displacement

demands, and may crucially affect several design

decisions.

Although the absolute displacements at story levels

are greater in the case of flexible-base conditions (both

linear and nonlinear), the relative displacements show a

decreasing trend when base nonlinearity is introduced,as indicated in Fig. 10. The statistical values of the

story drift angle (story drift divided by story height),

presented in Fig. 10 indicate that the relative story drift,

which is generally known as the inter-story drift ratio,

only slightly alters when the base condition is changed

from fixed to elastic SSI, but reduces significantly (as

much as one-third) when nonlinear SSI is incorporated.

Since the story drift demand can be related to the global

demands, such as root drift and spectral displacement,

as well as to the element level force and displacement

demands, it can be considered as an important parameter

to assess the performance of a structure (Gupta andKrawinkler, 2000). Current design provisions (such as

NEHRP, 2003) provide indicative values for acceptable

story drifts at various performance levels, making these

parameters crucial from a performance-based design

Fig. 6 Global pushover curves for different base conditions

5

4

3

2

1

0

Baseshear(MN)

Fixed base

Linear base

Nonlinear base

0 0.2 0.4 0.6 0.8

Roof displacement (m)


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Fig. 7 Acceleration response spectra of the ground motions considered in the study with hazard levels: (a) 50% in 50 years;

(b) 10% in 50 years and (c) 2% in 50 years

4

3

2

1

00.01 0.1 1 10

Period (s)

(a)

Spectralacceleration(g)

5

4

3

2

1

00.01 0.1 1 10

Period (s)

(b)

Spectralacceleration(g)

10

8

6

4

2

00.01 0.1 1 10

Period (s)

(c)

Spectralacceleration(g) Individual ground motion

Median

84th percentile

Table 3 Details of selected ground motions (adopted from Somerville et al.(1997))

Hazard Level SAC Record Earthquake Distance Duration PGA PGV PGDName Magnitude (km) (s) (cm/s2) (cm/s) (cm)LA41 Coyote Lake, 1979 5.7 8.8 39.38 578.34 69.51 11.06LA42 Coyote Lake, 1979 5.7 8.8 39.38 326.81 26.72 6.68

LA43 Imperial Valley, 1979 6.5 1.2 39.08 140.67 42.43 22.97LA44 Imperial Valley, 1979 6.5 1.2 39.08 109.45 22.57 14.27LA45 Kern, 1952 7.7 107 78.60 141.49 24.74 14.15LA46 Kern, 1952 7.7 107 78.60 156.02 24.24 14.98LA47 Landers, 1992 7.3 64 79.98 331.22 40.85 33.44LA48 Landers, 1992 7.3 64 79.98 301.74 25.02 12.58LA49 Morgan Hill, 1984 6.2 15 59.98 312.41 26.94 6.87LA50 Morgan Hill, 1984 6.2 15 59.98 535.88 22.81 5.74LA51 Park field, 1966, Cholame 5W 6.1 3.7 43.92 765.65 42.58 6.53LA52 Park field, 1966, Cholame 5W 6.1 3.7 43.92 619.36 36.87 5.36LA53 Park field, 1966, Cholame 8W 6.1 8 26.14 680.01 31.21 6.34LA54 Park field, 1966, Cholame 8W 6.1 8 26.14 775.05 32.08 9.07LA55 North Palm Springs, 1986 6 9.6 59.98 507.58 36.72 7.19LA56 North Palm Springs, 1986 6 9.6 59.98 371.66 25.42 5.85LA57 San Fernando, 1971 6.5 1 79.46 248.14 21.67 12.84LA58 San Fernando, 1971 6.5 1 79.46 226.54 27.05 17.73LA59 Whittier, 1987 6 17 39.98 753.70 98.54 12.66

LA60 Whittier, 1987 6 17 39.98 469.07 60.02 7.89LA01 Imperial Valley, 1940, El Centro 6.9 10 39.38 452.03 62.39 27.68LA02 Imperial Valley, 1940, El Centro 6.9 10 39.38 662.88 59.89 14.29LA03 Imperial Valley, 1979, Array #05 6.5 4.1 39.38 386.04 83.00 33.42LA04 Imperial Valley, 1979, Array #05 6.5 4.1 39.38 478.65 77.11 48.20LA05 Imperial Valley, 1979, Array #06 6.5 1.2 39.08 295.69 89.20 48.29LA06 Imperial Valley, 1979, Array #06 6.5 1.2 39.08 230.08 47.44 30.00LA07 Landers, 1992, Barstow 7.3 36 79.98 412.98 66.07 33.25LA08 Landers, 1992, Barstow 7.3 36 79.98 417.49 65.68 39.50LA09 Landers, 1992, Yermo 7.3 25 79.98 509.70 91.32 56.25LA10 Landers, 1992, Yermo 7.3 25 79.98 353.35 60.36 46.45LA11 Loma Prieta, 1989, Gilroy 7 12 39.98 652.49 79.09 28.16LA12 Loma Prieta, 1989, Gilroy 7 12 39.98 950.93 56.04 16.50LA13 Northridge, 1994, Newhall 6.7 6.7 59.98 664.93 95.55 19.82LA14 Northridge, 1994, Newhall 6.7 6.7 59.98 644.49 80.96 35.58LA15 Northridge, 1994, Rinaldi RS 6.7 7.5 14.945 523.30 98.57 18.01LA16 Northridge, 1994, Rinaldi RS 6.7 7.5 14.945 568.58 100.60 26.38LA17 Northridge, 1994, Sylmar 6.7 6.4 59.98 558.43 80.17 17.37

LA18 Northridge, 1994, Sylmar 6.7 6.4 59.98 801.44 118.93 26.87LA19 North Palm Springs, 1986 6 6.7 59.98 999.43 68.27 15.64LA20 North Palm Springs, 1986 6 6.7 59.98 967.61 103.83 25.57LA21 1995 Kobe 6.9 3.4 59.98 1258.00 142.70 37.81LA22 1995 Kobe 6.9 3.4 59.98 902.75 123.16 34.22LA23 1989 Loma Prieta 7 3.5 24.99 409.95 73.75 23.07LA24 1989 Loma Prieta 7 3.5 24.99 463.76 136.88 58.85LA25 1994 Northridge 6.7 7.5 14.945 851.62 160.42 29.31LA26 1994 Northridge 6.7 7.5 14.945 925.29 163.72 42.93LA27 1994 Northridge 6.7 6.4 59.98 908.70 130.46 28.27LA28 1994 Northridge 6.7 6.4 59.98 1304.10 193.52 43.72LA29 1974 Tabas 7.4 1.2 49.98 793.45 71.20 34.58LA30 1974 Tabas 7.4 1.2 49.98 972.58 138.68 93.43LA31 Elysian Park (simulated) 7.1 17.5 29.99 1271.20 119.97 36.17LA32 Elysian Park (simulated) 7.1 17.5 29.99 1163.50 141.12 45.80LA33 Elysian Park (simulated) 7.1 10.7 29.99 767.26 111.03 50.61LA34 Elysian Park (simulated) 7.1 10.7 29.99 667.59 108.44 50.12

LA35 Elysian Park (simulated) 7.1 11.2 29.99 973.16 222.78 89.88LA36 Elysian Park (simulated) 7.1 11.2 29.99 1079.30 245.41 82.94LA37 Palos Verdes (simulated) 7.1 1.5 59.98 697.84 177.47 77.38LA38 Palos Verdes (simulated) 7.1 1.5 59.98 761.31 194.07 92.56LA39 Palos Verdes (simulated) 7.1 1.5 59.98 490.58 85.50 22.64LA40 Palos Verdes (simulated) 7.1 1.5 59.98 613.28 169.30 67.84

50%in50years

10%in50years

2%in50years


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perspective. Therefore, according to the findings of this

study, the individual structural members are likely to be

over-conservatively designed if the inelastic behavior of

foundations is ignored.

In addition to the displacement demands, the effects

of the SSI on the force demands of the structure are

also investigated. Figures 11(a) and (b) provide the

normalized base moment demand and normalized baseshear demand, respectively, plotted against the spectral

acceleration corresponding to the fundamental period of

the building. Note that both moment and shear demands

significantly reduce when nonlinearity of soil-foundation

interface is considered, whereas linear modeling

of SSI does not give significantly different results

when compared to a fixed base case. This qualitative

observation is systematically quantified by showing the

statistical values of these demands. Figures 12(a) and

(b) summarize the median and 84th percentile values,

respectively, of the maximum absolute base moment

demand normalized by the same demand parametercorresponding to the fixed base case. It can be observed

that when linear SSI is considered, the base moment is

reduced up to 30% of the fixed base moment, whereas

consideration of nonlinear SSI leads to a reduction

of up to 60% of the fixed base moment. A consistent

observation is obtained for each set of ground motions

for median as well as 84th percentile values. A similar

trend is observed for the normalized base shear demand,

as indicated in Fig. 13. It can be observed that the base

shear reduces up to 10% of the fixed base shear for the

linear elastic base condition, whereas the reduction is as

much as 60% when nonlinearity at the base is considered.These observations indicate that nonlinear modeling of

SSI may lead to a significant reduction in the structural

force demand, mostly due to mobilization of the bearing

capacity and energy dissipation of the underlying soil.

7 Summary and conclusions

This study focuses on the effect of foundation

nonlinearity on various force and displacement demands

of a structure. A medium height SMRF building adopted

from Gupta and Krawinkler (2000) has been usedfor this purpose. The nonlinear behavior of the soil-

foundation interface is modeled using a Winkler-based

model concept. Static pushover analyses and nonlinear

dynamic analyses are carried out using SAC ground

Fig. 8 Comparison of responses from present study (fixed-base case) with Gupta and Krawinkler (2000)

4

3

2

1

0

Floorlevel Gupta and Krawinkler, 2000 (50/50 Median)

Gupta and Krawinkler, 2000 (10/50 Median)Gupta and Krawinkler, 2000 (2/50 Median)Present study, fixed base case (50/50 Median)Present study, fixed base case (10/50 Median)Present study, fixed base case (2/50 Median)

0 0.02 0.04 0.06 0.08 0.10 0.12

Story drift angle

Fig. 9 Median values of total story displacement

4

3

2

Floorlevel

50/50 Median (Fixed base)50/50 Median (Linear base)50/50 Median (Nonlinear base)10/50 Median (Fixed base)10/50 Median (Linear base)10/50 Median (Nonlinear base)2/50 Median (Fixed base)2/50 Median (Linear base)2/50 Median (Nonlinear base)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Story displacement (m)


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Fig. 11 Seismic force demands of the building: (a) normalized base moment demand and (b) normalizedbase shear demand (W=

weight of the building,L=length of the footing)

3

2

1

0 0 2 4 6 8 10

Sa(T

1) (m/s2)

(a)

Fixed baseLinear baseNonlinear baseN

ormalizedmomentdemand

(Mmax

/WL)

3

2

1

00 2 4 6 8 10

Sa(T

1) (m/s2)

(b)

Fixed baseLinear baseNonlinear base

Normalizedsheardemand

(Vmax/W)

Fig. 10 Statistical values of inter-story drift demands for ground motions: (a)50% in 50 years; (b) 10% in 50 years and (c) 2% in

50 years hazard levels

4

3

2

1

Floorlevel

0 0.02 0.04 0.06 0.08 0.10 0.12

Story drift angle

(a)

Median

84th percentile

Median

84th percentile

Median

84th percentile

(Fixed base)

(Fixed base)

(Linear base)

(Linear base)

(Nonlinear base)

(Nonlinear base)

4

3

2

1

Floorlevel

0 0.02 0.04 0.06 0.08 0.10 0.12

Story drift angle

(b)

4

3

2

1

Floorlevel

0 0.02 0.04 0.06 0.08 0.10 0.12

Story drift angle

(c)


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motions for three different hazard levels provided

by Somerville et al. (1997). The following specific

conclusions are made from the present study:

(1) Pushover analysis results indicate that with

incorporation of SSI, the global force demand of a

structure reduces about 5.5%, while the roof displacement

demand increases about 32%. However, this alteration is

more significant (as much as 37% reduction in forcedemand and 47% increase in displacement demand)

when the inelastic behavior of the soil-foundation

interface is taken into account.

(2) The dynamic time history analysis indicates that

the story displacement demands significantly increase

when base nonlinearity is taken into account. However,

the inter-story drift angle values are observed to

consistently decrease for nonlinear SSI cases, indicating

lower design requirements for individual structural

members upon consideration of nonlinear SSI.

(3) The global force demands such as base moment

and base shear of the columns are reduced to as much as60% with incorporation of nonlinear SSI, indicating that

ignoring nonlinear SSI may lead to an over-conservative

estimation of the structural forces.

Finally, it may be concluded from this study that

nonlinear behavior of the soil-foundation interface may

play a crucial role in altering the seismic demands of a

structure, indicating the necessity for incorporation of

inelastic foundation behavior in modern design codes to

accomplish more economic, yet safe structural design in

a performance-based design framework.

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