ORI GIN AL PA PER

On the resonance effect by dynamic soil–structureinteraction: a revelation study

Hamza Gullu • Murat Pala

Received: 27 May 2013 / Accepted: 7 January 2014� Springer Science+Business Media Dordrecht 2014

Abstract The present study makes an attempt to investigate the soil–structure resonance

effects on a structure based on dynamic soil–structure interaction (SSI) methodology by

direct method configuration using 2D finite element method (FEM). The investigation has

been focused on the numerical application for the four soil–structure models particularly

adjusted to be in resonance. These models have been established by single homogenous

soil layers with alternating thicknesses of 0, 25, 50, 75 m and shear wave velocities of 300,

600, 900 m/s-a midrise reinforced concrete structure with a six-story and a three-bay that

rests on the ground surface with the corresponding width of 1,400 m. The substructure has

been modeled by plane strain. A common strong ground motion record, 1940 El Centro

Earthquake, has been used as the dynamic excitation of time history analysis, and the

amplitudes, shear forces and moments affecting on the structure have been computed under

resonance. The applicability and accuracy of the FEM modeling to the fundamental period

of soils have been confirmed by the site response analysis of SHAKE. The results indicate

that the resonance effect on the structure becomes prominent by soil amplification with the

increased soil layer thickness. Even though the soil layer has good engineering charac-

teristics, the ground story of the structure under resonance is found to suffer from the larger

soil layer thicknesses. The rate of increment in shear forces is more pronounced on

midstory of the structure, which may contribute to the explanation of the heavily damage

on the midrise buildings subjected to earthquake. Presumably, the estimated moment ratios

could represent the factor of safeties that are excessively high due to the resonance con-

dition. The findings obtained in this study clearly demonstrate the importance of the

resonance effect of SSI on the structure and can be beneficial for gaining an insight into

code provisions against resonance.

H. Gullu (&)Department of Civil Engineering, University of Gaziantep, 27310 Gaziantep, Turkeye-mail: hgullu@gantep.edu.tr

M. PalaDepartment of Civil Engineering, Adıyaman University, 02040 Adıyaman, Turkey

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Nat HazardsDOI 10.1007/s11069-014-1039-1

Keywords Resonance � Soil–structure interaction � Finite element method �Site response analysis

1 Introduction

Resonance effect is an important subject in earthquake engineering practice. It is the result

of making the frequency of super structure to the frequency of supporting soil closer

(Takewaki 1988). This fact has been experienced in the several past earthquakes where

tuning of the natural period of a building structure with that of a surface ground caused

significant response amplifications on the buildings and resulted significant damage (The

earthquakes of 1970 Gediz, 1985 Mexico City, 1998 Adana-Ceyhan, etc.). Soil–structure

interaction (SSI) is a major topic that deals with the resonance phenomenon in detail. It

refers to the relationship between the characteristics of both the structure and the soil

stratum and is usually represented by modifying the dynamic properties of the structure.

This interaction causes energy dissipation and changes the natural modes of vibration of

the structure such as natural frequencies and the corresponding mode shapes (Wolf 1985;

Veletsos and Prasad 1989; Wenk et al. 1998).

It is increasingly desired to take into account the soil effects on the design of structures

particularly those located in active seismic zones. In recent years, numerous researchers

have performed studies on the effects of SSI on the dynamic seismic response of buildings

(Wolf and Song 2002; Aviles and Perez-Rocha 2003; Khalil et al. 2007). The analysis and

design process for dynamic loading generally assumes structures to be fixed at their bases.

However, supporting soil medium actually allows a movement to some extent due to

flexibility. This may reduce the overall stiffness of the structural system and may increase

the natural periods of the system. Considerable change in spectral acceleration with natural

period can be observed from the response spectrum curve. Such change in natural period

may considerably alter the seismic response of any structure (Stewart et al. 1999; Dutta and

Roy 2002; Dutta et al. 2004). Aviles and Perez-Rocha (1997) noted that SSI may be very

important for medium- and long-period structures when the predominant site periods are

large. Despite this dynamic SSI effects should be taken into account for stiff and/or heavy

structures supported on a relatively soft soil. These are generally small and may be

neglected for soft and/or light structures founded on stiff soils. In general, the natural

frequency of a soil–structure system due to SSI effects is obtained lower than the frequency

of the structure itself. In addition, radiation damping increases the total damping of a soil–

structure system comparing with the damping of the structure itself (Kramer 1996). Based

on the latest study of Khalil et al. (2007), it is apparently inferred that SSI effects directly

alter the resonance characteristics of the soil–structure system. Although many works have

been attempted about the SSI effects on soil and structures, there is limited number of work

that particularly involved the resonance effects from resonance models (Dutta et al. 2004).

Moreover, there is a lack of resonance study for models in resonance that systematically

examine the effects of soil layer thickness on the dynamic response of plane frame

structures under strong ground motion.

The aim of this work is to gain some insights into the reasons for earthquake damage to

engineered buildings due to the resonance effect on the basis of dynamic SSI methodology.

Investigation was carried out using some hypothetical SSI models which were adjusted so

the soil and structure were in resonance. The soil layer thickness in these models was

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varied; however, a constant structure (a midrise building) resting on soil surface was used

throughout the study. The reason for choosing the midrise building is that majority of them

in previous severe earthquakes did not demonstrate good performance (Celebi 2000;

Sancio et al. 2002; Ulusay et al. 2004). Direct method configuration was used for the SSI

analysis. The SSI model was constructed by 2D finite element method with rectangular

meshes employing a common method of SAP2000. Site response analysis of soil layers to

the interaction from FEM modeling was carried out by the method of SHAKE. This study

is believed to contribute to engineers in practice when designing structures against

resonance.

2 A review on resonance effects from past earthquakes

The fundamental periods of structures can be crudely estimated from a rule of thumb

method in which the fundamental period of N-story building is approximately N/10 s

(Kramer 1996). They may range from about 0.05 s for a well-anchored piece of equipment,

0.1 s for a one story simple bent or frame, 0.5 s for a low structure up to about four stories

and between 1 and 2 s for a tall building from 10 to 20 stories (Arnold and Reitherman

1982). The fundamental periods of soils usually have values varying from 0.1 s (rock, stiff

or dense soils) to 1 s (soft or loose soils) (ICBO 1994). If the two fundamental periods are

matched each other, there is a high probability for the building will approach a state of

partial resonance (quasi-resonance). Experiences from historical earthquakes reflect that

long-period seismic waves from large-magnitude earthquake events can be amplified by

some four- to sixfolds due to resonance with flexible soil layers (Lam et al. 2001; Chandler

et al. 2002). The amplified motion may be subjected to further resonance with flexible tall

buildings where torsional inertia generated by dynamic coupling can create significant

horizontal rotation and result in a significant increase in the drift demand on individual

lateral load resisting elements. This torsional coupling effect of resonance is particularly

apparent in structures that respond elastically to an earthquake prior to initiation of damage

(Balendra et al. 2005).

The 1970 Turkish Gediz Earthquake demolished the paint workshop building of the

Tofas-Fiat automobile factory in Bursa, located 135 km away from the epicenter, while no

other building in Bursa was damaged. The main reason for the demolished structure was

found that the predominant periods of the structure and underlying soil were approximately

equal around a value of 1.2 s (Tezcan et al. 2002). Gullu (2001) obtained GIS-based

microzonation maps with respect to soil amplification and fundamental periods for the

town of Dinar comparing with the damages due to 1995 Dinar Earthquake. From the

fundamental period versus damage models, it is concluded that there is a likely resonance

effect which resulted in medium-heavy damage or collapse of the 3- to 4-story masonry

and reinforced concrete buildings which are overlaid by the soils with the predominant

periods of 0.3–0.5 s. In addition, 5- to 6-story reinforced concrete buildings over the sites

with the fundamental periods of 0.5–0.7 s may be damaged also by the resonance of soil–

structure. Similar results supporting the resonance effect in the damage during 1995 Dinar

Earthquake can be seen in Ansal et al. (2001). An investigation of 1998 Adana-Ceyhan

Earthquake indicates that one of the main causes of collapses or severe damage on the

midrise buildings (7–10 stories) in Ceyhan is double resonance. Because the spectrum of

recorded strong ground motion in Ceyhan has a predominant period frequency about

1.5 Hz (0.67 s), and predominant frequency of site conditions depicted by alluvial media is

found similar to the ones of structures and strong motion (Celebi 2000). A damage survey

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conducted in Ceyhan found a strong correlation between the frequencies of site and

damaged buildings (Wenk et al. 1998). A recent study supports the previous ones such that

the resonance effect from the soil–structure or the ground motion soil–structure has been

important in the damage observed in Ceyhan (Yalcınkaya and Alptekin 2005).

1999 Kocaeli and Duzce Earthquakes attacked a densely populated area, Marmara

Region, in Turkey and severely shaked the region resulting devastating damages to

building and structures. Investigations on the localization of observed settlements around

buildings, the relative infrequency of observations of liquefaction in open fields and the

higher rate of severe ground failure for taller buildings indicate that ground strains asso-

ciated with soil–structure interaction may have contributed to the triggering and severity of

ground failure during the 1999 Kocaeli Earthquake (Sancio et al. 2002). Some previous

studies demonstrate a possible resonance effect on the damage of Fatih Mosque (Istanbul)

during the 1999 Kocaeli Earthquake. The predominant period of the structure (2.4 Hz NS–

2.5 Hz EW) was estimated as falling into the predominant period of seismic loading

(Beyen 2007). A seismic amplification study was conducted for the town of Avcılar

(Istanbul), located at about 120 km west from the epicenter of the 1999 Kocaeli Earth-

quake, using the NS component of this earthquake recorded at Izmit Meteorological

Station. It is found that the buildings at Avcılar, with the natural periods of vibration close

to anyone of 0.70, 1 and 1.60 s, are expected to experience relatively heavier damage due

to resonance effects as well as soil amplification (Tezcan et al. 2002). The resonance effect

can also be considered one of the contributing factors to the damage of some buildings in

Cay-Eber Earthquake of February 3, 2002. Fundamental periods of response spectra of the

strong ground motion recorded at Afyon station are found to be very close to the natural

period of tall structures which were collapsed or heavily damaged (Ulusay et al. 2004)

The 1985 Mexico City earthquake is one of the instructive earthquakes where the

resonance is well defined in many damaged buildings. The greatest damage occurred in the

Lake Zone underlain by soft soil (38–50 m depth) where the characteristics of site periods

were estimated from 1.9 to 2.8 s. Buildings less than five stories and modern buildings

greater than 30 stories were exposed to slight damage within this area. However, most of

the buildings in range from 5 to 20 stories, those fundamental periods were nearly equal to

or somewhat less than the characteristics site period, either were collapsed or badly

damaged. The possible reason for the damage was the double resonance (Kramer 1996).

It is shown from the past events that tuning of the natural period of a building structure

with that of a surface soil causes significant amplifications that result in the increasing of

inertial forces acting on the structure with a considerable damage. So, it is very important

to check the interactions between the vibration periods (or frequencies) of structures and

the supporting soil in order to determine how close they are to resonance.

3 Methodology of SSI analysis

SSI can significantly change the free-field ground motion at the foundation level and the

dynamic properties of the structure, while local site conditions may produce large

amplifications and important spatial variations in seismic ground motion (Veletsos and

Prasad 1989). In a dynamic SSI analysis, a bounded structure (which may be linear or

nonlinear), consisting of the actual structure and an adjacent irregular soil if present, will

interact with the unbounded (infinite or semi-infinite) soil which is assumed to be linear

elastic (Fig. 1). In SSI problems, the ability to predict the coupled response of the soil and

structure has great significance. Hence, SSI-related problems need a combination of soil

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and structure models. Although structure models have a good basis in the literature, soil

models include complicated analysis due to their unbounded nature. In fact, the major

difficulty in modeling the soil region can be attributed to the characteristics of wave

propagation through the soil medium. Because soil has very complex characteristics due to

the heterogeneous, anisotropic and nonlinear natures in force versus displacement.

Moreover, the presence of fluctuations in water table further adds to its complexity (Dutta

and Roy 2002). Therefore, one of the most important objectives in a SSI study is to build

up reliable and easily implemented models (Wolf and Song 2002). The various rigorous

numerical methods developed for the analysis of dynamic SSI can be classified into two

main groups: the direct method and the substructure method. The direct method is applied

in this paper due to its simple implementation of SSI approach in a single by Eq. 1:

½M�f€ug þ ½K��fug ¼ �½M�f€uffðtÞg ð1Þ

where f€uffðtÞg is the specified free-field accelerations at the boundary nodal points, [M] is

the mass matrix, [K*] is the complex stiffness matrix and {u}is the vector of unknown

nodal point displacements (Kramer 1996).

In order to estimate SSI by the direct method, a finite bounded soil zone adjacent to the

structure (near-field) and the structure itself may be modeled using the finite element

method and the seismic free-field motion is applied at a fictitious interface enclosing the

soil–structure system. The effect of the surrounding unbounded soil (far-field) is approx-

imately analyzed by imposing transmitting boundaries along the fictitious (near-field/far-

field) interface (Zhang et al. 1999; Halabian and El Naggar 2002; Wegner et al. 2005). A

lot of transmitting boundaries have been developed to satisfy the radiation condition such

as a viscous boundary (Lysmer and Kuhlemeyer 1969), a superposition boundary (Smith

1974) and others (Liao and Wong 1984). The soil with the superstructure is modeled up to

the artificial boundary (Fig. 2), and the response of the soil and structure is determined

simultaneously by analyzing the idealized soil–structure system in a single step (Jaya and

Meher Prasad 2002). The artificial boundary (Fig. 2) is obtained by modifying the viscous

boundary (Lysmer and Kuhlemeyer 1969) to all degrees of freedom of the boundary nodes

for elastic wave propagation in semi-infinite medium. It is assumed that the wave energy

arrives at the boundary with equal probability from all directions. In order to get a proper

accuracy and reduce the effects of reflected waves by the transmitting boundary, it is

necessary to consider a large amount of soil around the structure when the direct method is

employed. In this way, the radiation condition is taken into account for an unbounded

medium. Thus, modeling of a significant part of the soil is an essential point in the direct

method. The distance between the artificial soil boundary and the building is usually

several times of the width of the structure. Applying a finite element mesh, the total

number of nodes in the unbounded soil medium will dominate to those of the soil–structure

system. Therefore, the direct method is usually used to study two-dimensional models

(Wegner et al. 2005). The mass matrix [Mb] of the bounded medium with degrees of

freedom on the boundary can be obtained as in structural dynamics:

½SbðxÞ� ¼ ½Kb� � x2½Mb� ð2Þ

where [Kb] and [Sb(x)] are the static-stiffness and dynamic-stiffness matrices of the

bounded medium, respectively (Halabian and El Naggar 2002).

FEM is usually applied for SSI problems because of its accuracy and convenient

standard algorithms in the public domain (Wegner et al. 2005). Even if care must be taken

about the possibilities of inaccuracy arising out of numerical limitations while interpreting

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the results, it is the most powerful and versatile tool for solving SSI problems. The main

advantage of the FEM is that it can easily be employed for incorporating the effect of

material nonlinearity, nonhomogeneity and anisotropy of the supporting soil medium as

well as the geometry (Dutta and Roy 2002; Pitilakis et al. 2007). Even though the method

is able to treat soil domains of arbitrary layer geometry and to accommodate material

nonlinearity, anisotropy and inhomogeneity, it does not satisfy the radiation-toward-infi-

nity condition at the boundaries, a phenomenon inherent in SSI. Special boundary con-

ditions, as mentioned in the direct method, have to be developed to simulate the unbounded

nature of the soil medium. The FEM can be applied efficiently to geometries requiring

transmitting boundaries (Pitilakis et al. 2007). There are some finite element codes,

FLUSH (Lysmer et al. 1975), SASSI (Ostadan et al. 2000) and SAP2000, which are

designed specifically to perform SSI analyses incorporating an equivalent linear visco-

elastic model for the soil behavior. In this paper, SAP2000 was employed for the dynamic

Fig. 1 Problem definition of dynamic SSI (Wolf and Song 2002)

Fig. 2 Direct method configuration (Jaya and Meher Prasad 2002)

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response of SSI by the FEM. The application of SAP2000 is extremely advantageous

because this numerical method significantly reduces the computational effort and makes

the solution of problem simpler.

4 Numerical application

In this study, 2D soil–structure models were adopted to account the resonance effect on the

response of reinforced concrete (RC) structure subjected to earthquake. The main reason

for the usage of 2D modeling is that 3D modeling deals with very complex motion

equations that produce a computationally intensive task and make the solution of SSI

problems more difficult even if it appears to be more reliable (Zhang et al. 1999). The

resonance effect from dynamic SSI was investigated concerning the four model cases

(Fig. 3) which were adjusted so the soil and the structure were in resonance. This allows us

to find out the resonance effects in the structure. Alternating soil layer thicknesses (SLT)

with 0 m (case 1), 25 m (case 2), 50 m (case 3) and 75 m (case 4) were assigned over the

bedrock. However, dynamic properties of the soil layers in shear wave velocity (Vs) were

determined by trial-and-error method where it was aimed to get shear wave values pro-

ducing the fundamental periods of soils close to the ones of the structure in order to have

the cases concerned in the resonance. Estimation of Vs is described in the paragraphs later.

In all cases, the structure was considered to rest on the ground surface. Here, it should be

noted that the bedrock in the SSI methodology of this study is considered to have relatively

high rigidity characteristics that define its shear wave velocity to become much greater than

the one of the soil layers.

A RC structure that is 18 m in height (H) with a 6-story (i.e., midrise building) and 9 m

in width (B) with a 3-bay was used for the models given in the cases by Fig. 3. The model

cases might give some insights for the reasons of the damage on those buildings. The story

heights and bay intervals of 3 m were taken to be constant in the frame. The structure has a

flexible shallow foundation that consists of a RC mat footing with 1 m depth. The sections

of structural elements were rectangular, and their dimensions were kept constant for all

stories. The cross sections of columns and beams were taken to be 400 9 400 mm and

200 9 600 mm, respectively. They were constant through the story height. The RC

structure was considered to be homogenous, isotropic and linear elastic with Young’s

modulus (modulus of elasticity) E = 28 GPa, Poisson’s ratio m = 0.20 and mass density

q = 24 kN/m3. The damping ratio of the structure was taken to be 8 %. Since plane strain

elements were employed in the ground, mass and stiffness of the structure were defined as

the quantities per unit length with respect to the out-of-plane direction.

For analyze purpose of the soil layers, isotropic, homogeneous and linear stress–strain

conditions were assumed. The damping ratio of 8 % was also used for the soil considering

the contribution of radiation and material damping for a mat footing feasible range of

footing size, by following the guideline prescribed in the literature (Gazetas 1991). Pois-

son’s ratio equal to 0.3 was selected, and the mass density of the soil layers taken into

account was 18 kN/m3. Some of the characteristics of soils and structure are summarized

in Table 1.

Following the suggestions of surveyed methodologies, while solving the SSI problem,

the side nodes of the discretized finite elements in the boundary are considered to be

connected with dashpots allowing only the horizontal movements and the bottom nodes are

considered to be pin support. The middle node at the base of the foundation is kept fixed in

order to prevent rigid body translation in the horizontal direction. The established SSI

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model for this study was given in Fig. 4. In this SSI model, FEM was employed to

formulate the mass and stiffness matrices for the structural frames. Consistent mass matrix

was used to develop the formulation as accurate as possible. The soil layer under the

structure was modeled with maximum 7872 solid elements. The viscous boundary was

obtained by using link elements. Each element has four nodes with three degrees of

freedom in each node. The Lysmer and Waas transmitting boundary that is intended to

absorb the body surface waves on the lateral infinite boundary was used in the model

(Lysmer and Waas 1972). The Lysmer–Wass transmitting boundaries that consist of dash

pots were specified at the vertical edges of the finite element mesh to model radiation

damping and the artificial boundaries of the soil. The maximum dimension of the mesh of

solid elements was chosen from the literature (Lysmer et al. 1975). In order to increase the

accuracy of results as noticed by Wegner et al. (2005), a soil medium of 1,400 m in length

around the structure was taken into account. As mentioned above, SLT over the bedrock

was changed from zero to 75 m as the four cases of SSI model.

In the dynamic analysis of soil–structure models, one of the most common strong

ground motion records for dynamics research, the 1940 El Centro Earthquake, with a time

step of 0.02 s was used. The NS component of this earthquake ground motion that has

maximum amplitude of 0.319 g was selected as the excitation (Fig. 5).

By taking the characteristics of the structure, soil layers and FEM mesh employed above

into consideration, a trial-and-error method via FEM was performed to determine Vs of

SLT for the study cases (Fig. 3) such that the soil layers and structure are to be resonance.

Fig. 3 Cases in resonance considered in the study. The height and width of structures are 18 and 9 m whichare constant in all cases. The estimated shear wave velocities are 300 m/s (SLT = 25 m), 600 m/s(SLT = 50 m) and 900 m/s (SLT = 75 m). SLT soil layer thickness

Table 1 Some characteristics ofsoil and structure

Property Soil Structure

Poisson’s ratio 0.30 0.20

Unit weight (kN/m3) 18 24

Damping ratio (%) 8 8

Elasticity modulus (GPa) – 28

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Vs of soil layers were estimated as 300, 600 and 900 m/s, respectively, for 25, 50 and 75 m.

Consequently, four resonance cases have been defined to examine the resonance effect on

the structure. In the case 1, the structure in the SSI model was solved for fixed base

condition (or cantilever); thus, it does not need to calculate Vs of soil. Following the Vs

estimations, the fundamental periods of the soil layers that represent to these estimated Vs

values have been also computed by FEM and obtained as 0.334 s (SLT = 25 m), 0.335 s

(SLT = 50 m) and 0.331 s (SLT = 75 m) for the soil layer thicknesses. Moreover, fun-

damental period of the employed structure that has H/B = 2 was computed for all soil

layers using FEM and estimated to be 0.333 s. The computation results of the study cases

are presented in Table 2 for VS of soil layers, in Table 3 for the fundamental periods of soil

and structure to be in resonance.

The applicability and accuracy of the numerical analysis of FEM for estimating the

fundamental periods of the soil layers have been verified with the computations of fun-

damental periods from the most common evaluation formula given by Eq. 3 and from the

site response analysis performed by SHAKE code (Schnabel et al. 1972) in both. Con-

sidering the shear waves traveling vertically upward through a single soil layer of thickness

Fig. 4 Finite element mesh and boundary conditions for the soil and structure in SAP 2000

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SLT above bedrock, the fundamental period of horizontal vibration of the ground is given

by

T ¼ 4SLT

ð2n� 1ÞVs

ð3Þ

where n is an integer, 1, 2, 3,…, representing the various modes of vibration (Tezcan et al.

2002). The fundamental period of soil or characteristic site period depends on the thickness

and shear wave velocity of soil and provides a very useful indication of the period of

vibration at which the most significant amplification can be expected (Kramer 1996). For

Fig. 5 El Centro earthquake, May 1940, record used in the study (NS component, PGA = 0.32 g)

Table 2 Computed Vs of soillayers for the study cases, whichare to be in resonance, usingFEM from SSI model (the struc-ture rests on the ground surface)

Study case Depth of bedrock or soillayer thickness (SLT) (m)

Estimated Vs (m/s)

Case 1 0 (fixed or cantilever) –

Case 2 25 300

Case 3 50 600

Case 4 75 900

Table 3 Computed fundamentalperiods of soils and structure,which are to be in resonance,using FEM from SSI model

Study case Fundamental period (s) by FEM

Soil Structure (H/B = 2,H = 18 m, B = 9 m)

Case 1 (Fixed orcantilever)

(Fixed or cantilever)

Case 2 0.334 0.333

Case 3 0.335 0.333

Case 4 0.331 0.333

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the first mode of vibration using Eq. 3, the fundamental periods of all layers (SLT 25, 50

and 75 m) were evaluated as 0.333 s.

SHAKE performs one-dimensional shear wave propagation analysis and computes the

response in a homogeneous and viscoelastic soil layers of infinite horizontal extent sub-

jected to vertically traveling shear waves. The nonlinear soil behavior is accounted by the

use of equivalent linear soil properties using an iterative procedure to obtain the values for

modulus and damping compatible with the strains developed in each layer. In this work,

the variation in dynamic shear modulus and damping ratio of the soil layers with respect to

the shear strain was established from the past studies (Seed and Idriss 1970; Vucetic and

Dobry 1991). The effective strain ratio was taken to be equal to 0.65. Using the employed

strong ground motion record (Fig. 5) as the input ground surface motion (i.e., object

motion), the wave propagation analysis by SHAKE was conducted for the soil profiles of

SLT = 25, 50 and 75 m, and a hypothetical record at the bedrock was obtained first. Next,

this hypothetical record as the bedrock input motion (i.e., object motion) was transferred to

the ground surface, and the free surface motion was computed on the ground surface as a

site response to the structure. Fast Fourier Transform algorithm was utilized to analyze the

earthquake record. The hypothetical bedrock motions for all soil layers were obtained as

same with each other (Fig. 6). As for the hypothetical ground surface motion, it was

calculated to be exactly equal to the real motion given in Fig. 5 for all soil layers.

Accordingly, the spectral amplitudes and amplifications for the soil layers due to site

response analysis were also estimated as same with each other on the ground surface. The

computed absolute spectral acceleration, spectral velocity and spectral displacement for the

bedrock and free ground surface are shown in Fig. 7. As seen from Fig. 7, that the surface

ground motion has greater amplitudes than the bedrock motion due to local site effects.

These amplitudes are more prominent up to the vibrations of 1-s period. This may be

attributed to the rigidity characteristics of soil. The amplifications seem more prominent at

the accelerations as compared to ones of velocity and displacement likely due to earth-

quake nature of response. Subsequent to the analysis by the SHAKE, the fundamental

periods of soil layers were determined using spectral amplitude ratios of the absolute

accelerations based on the study of Borcherd (1970), in which the spectral amplitude ratio

is calculated by the ratio of Fourier amplitude spectrum of a soil site to the one of a nearby

hard-rock site (reference site). Since this method is mostly offered when the distance

between the two sites is much smaller than their epicenter distances, it could be accurately

applied for this study. The estimated spectral amplification using spectral ratios of the

absolute acceleration for the soil layers is presented in Fig. 8. It is clearly appeared from

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0 2 4 6 8 10

Time (sec)

Bed

rock

Acc

eler

atio

n (g

)

Fig. 6 The estimatedhypothetical bedrock motion bySHAKE for the soil layers of 25,50 and 75 m (it was obtained assame with each other for all thelayers)

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the Fig. 8 that the fundamental periods of the soil layers are nearly equal to 0.3 s. This

period is very close to the fundamental period of the midrise buildings and may be

beneficial for explanation of the reasons to the damage on the midrise buildings in the

earthquakes.

The evaluated fundamental periods from both the Eq. 3 and the SHAKE (site response

analysis) demonstrate that they are nearly equal to the ones obtained from the FEM. This

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Period (sec)

Abs

olut

e A

ccel

erat

ion

(g)

BedrockSurface

0

10

20

30

40

50

60

70

80

0.01 0.1 1 10

0.01 0.1 1 10

Period (sec)

Rel

ativ

e V

eloc

ity (

cm/s

ec)

0

5

10

15

20

25

1010.1

Period (sec)

Rel

ativ

e D

ispl

acem

ent (

cm)

Fig. 7 Spectral amplitudes forthe soil layers of 25, 50 and 75 m

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relatively confirms the results of FEM in the adopted SSI model. It is realized from the

fundamental periods that SSI models for all study cases are in resonance, and the resonance

effect on the structures could be studied based on the parameters such as displacement,

velocity, acceleration, shear force and moment capacity of the structure. Consequently, the

particular role of resonance effect on the structural damage from the soil–structure inter-

action could be attempted and properly discussed.

5 Results and discussions

Time history analysis of dynamic soil–structure models for the study cases in resonance

was performed, and influence of the resonance on the RC structure for the alternating SLT

was investigated. For the case of SLT = 0 m (case 1), the RC structure was assumed to be

fixed base (cantilever). The resonance effects on the RC structure were discussed in

accordance with the outcomes of displacement, velocity, acceleration, shear force and

bending moment.

The soil effect on the structure in the resonance cases can be obviously seen by the time

history results of acceleration and displacement (Fig. 9). It is shown from the figure that

the influence of resonance increases with the increased SLT. This clearly emphasizes the

role of SLT inherently associated with the shear wave velocities of soils. From the analysis

of SSI, a careful study of the time history results considering the height of story versus the

amplitude (i.e., displacement, velocity and acceleration) and the amplitude ratio (i.e., the

ratios of displacement, velocity and acceleration of SLT to the fixed base) is given in

Figs. 10, 11, 12. The results reveal the observations of remarkable more increasing in the

lateral displacement of SSI models in resonance case (Fig. 10). As mentioned above, the

resonance effect changes with respect to the soil layer thickness. The increase in SLT of

25, 50 and 75 m is relatively greater than the fixed base structure (SLT = 0 m). However,

increment rate appears nearly to be similar for the higher SLT (from 50 to 75 m) where the

shear wave velocities are varied from 600 to 900 m/s or may be to higher values. This can

be clearly seen by the results from Fig. 9, which is attributed to the stiffness of the soil. The

ratios of story lateral displacement of SSI models to the fixed base model on the ground

surface (or ground story) are 5.5, 4.7 and 2.7, respectively, for the soil layer thicknesses of

75, 50 and 25 m. These ratios are slightly increasing toward to higher story (Fig. 10).

Similar observations can be obtained in the amplitudes of velocity and acceleration such

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.01 0.1 1 10

Period (sec)

Spe

ctra

l Am

plifi

catio

n

Fig. 8 Spectral amplification forthe soil layers of 25, 50 and 75 m

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that the velocity and acceleration of story are increased with respect to SLT as the structure

height is raised (Figs. 11, 12). However, the increment ratio with respect to the fixed base

is more pronounced on the ground floor. This is an expected result that may be attributed to

the effect of shaking which often occurred on the ground surface intensively. It is clear that

one of the contributing factors to the resonance effect on the RC structure in this study is

the site amplification which was approximately computed as 2.8 from the site response

analysis of SHAKE (Fig. 8). Its size seems to be cable of creating a larger resonance effect.

Fig. 9 The time history versus amplitude at the top of structure with respect to SLT

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This amplification value has similar amplification and fundamental period with the

response spectra of strong ground motion of 2002 Cay-Eber Earthquake (Ulusay et al.

2004) where collapses and heavy damages occurred in some of the midrise buildings

(Yesilcay apartment blocks) due to the resonance phenomenon as previously mentioned. It

is evident that local site conditions especially the soil layer thickness and shear wave

velocity of soil deposit play a significant role on the seismic response of buildings under

the resonance conditions. As a consequence of Figs. 9, 10, 11, 12, it is demonstrated that

the RC structure produces similar responses under the resonance cases of higher SLTs (i.e.,

[50 m) or higher shear wave velocities of soil (i.e., [600 m/s).

Distribution of shear force and bending moment of the SSI models for the fixed base and

three different SLT cases was investigated by selecting outside column at left side. The

shear forces of selected column for all the SSI models and the ratios of story shear forces of

models to the fixed base model are given in Figs. 13, 14, respectively. It can be seen from

Fig. 13 that the shear force on the ground floor of the RC building proportionally increases

with the increased SLT under the resonance. As the height of building increases, the shear

force on the RC structure decreases as expected. It is interesting to note that the top story of

the building produces similar shear forces no matter how SLT is varied (or shear wave

velocity of soil is varied). It is observed from the ground floor that the larger SLTs (i.e.,

[50 m) or larger Vs values (i.e., [600 m/s) produce similar effects of the shear force

probably due to the similar rigidity characteristics of soil. The findings from Fig. 13 clearly

indicate that even though the SLT owns good rigidity characteristics (i.e., Vs [ 600 m/s), it

may be capable of producing considerable shear forces by the larger soil layer thicknesses

(i.e., [50 m) on the ground story under the resonance conditions, for the RC building

investigated in this study.

As for the examination of the results from Fig. 14, that it can obviously be seen that the

rate of shear force increments is more pronounced on the midstory as compared with the

Fig. 10 a The storydisplacements of SSI modelswith respect to SLT. b The ratiosof story lateral displacement ofSSI models to the fixed basemodel (cantilever) with respect toheight of story

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ones of remaining storys. This may be explained by means of the energy absorption

processing throughout the structural system of the RC building considered in this inves-

tigation (Lysmer and Kuhlemeyer 1969; Zhang et al. 1999). Some of the energy is

absorbed by the loop of shear forces, but this is probably less than the one from the loop of

bending moments on the structure. The shear failure developed in the structural system is

brittle and has no ductility. As a result of the shear failure, the strength of structural

elements in the buildings rapidly decreased. This may provide some contribution to the

explanation of the heavily damage on the midrise buildings under the resonance at some

past earthquakes (1998 Adana-Ceyhan Earthquake, 1999 Kocaeli, etc.). As mentioned

before, Celebi (2002) resulted that the collapses and heavy damage on the midrise

buildings in 1998 Adana-Ceyhan Earthquake were possibly occurred due to double reso-

nance. However, a possible change in the rate of shear forces in the midstorys might trigger

progression of the damage and increase the severity of damage or collapses as well as the

effects from double resonance. The findings from Fig. 14 reveal that since the moment

failure in the structure mostly becomes ductile, it is very important that the energy

absorption throughout the structural system is more convenient to be carried out by the

loop of moments.

The story bending moments of the RC structure are presented in Fig. 15. It is realized

from the figure that the moments in the cantilever case are significantly lower than the ones

from all the other cases of SLT. It is clear that the moments in the storys decrease with the

increased height of story. Moreover, the moments of higher SLTs ([50 m) or higher shear

wave velocities ([600 m/s) in the storys appear to be very close to each other. From the

results of Fig. 15, it can be said that the ground floor of the RC structure under the

resonance can be considerably suffered from the larger soil layer thicknesses (i.e.,[50 m),

Fig. 11 a The story velocities ofSSI models with respect to SLT.b The ratios of story velocities ofSSI models to fixed base modelwith respect to SLT

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similar to the finding from Fig. 13, even though the soil layer has good engineering

characteristics (i.e., Vs [ 600 m/s).

The ratios of story lateral bending moments of SSI models to the fixed base model are

shown in Fig. 16. When focusing on the midstorys, it can be observed that the normalized

moment ratios do not produce a significant increment rate for the remaining storys below.

Fig. 12 a The storyaccelerations of SSI models withrespect to SLT. b The ratios ofstory accelerations of SSI modelsto fixed base model with respectto SLT

Fig. 13 The story shear forcesof SSI models with respect toSLT

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This can be interpreted as robust evidence for the role of the shear forces of midstorys on the

heavily damage in the resonance cases, as mentioned before (Fig. 14). The moment ratios

(Fig. 16) are approximately yielded as 3, 4.5 and 5.5 for the SLTs of 25, 50 and 75 m,

respectively. Presumably, these ratios can be proposed for representing the factor of safeties

for the design of RC structure under the resonance. However, the factor of safety from the

moment ratios appears to be excessively high, which obviously indicates to higher bending

moments and large response amplification of the structure as well as the soil amplification. As

a result of Fig. 16, it can be concluded that the buildings designed for the resonance condi-

tions require high factor of safeties that could be proportionally involved with the normalized

moment ratios obtained in this study. But, in reality, it would not be economical approach to

design the buildings with the high factor of safety. Hence, increasing the rigidity of buildings,

using some instruments and techniques to absorb the energy and base isolation systems can be

used to decrease the resonance effect on the structures.

As well as the notifications in the past studies (Dutta and Roy 2002; Dutta et al. 2004), it

can be emphasized that the most conventional attempt in practice during the design process of

buildings is usually to ignore the SSI effect and to assume that the bedrock is to be fixed base.

However, using the SSI methodology in this study obviously shows that the responses on the

structure under the resonance are considerably influenced by the local site conditions (SLT,

Vs). Therefore, the buildings subjected to a possible resonance should be carefully designed

by taking the SSI effect into account. It should be noted that from a methodological point of

view, other investigations should be accomplished. The results presented here correspond to

only the excitation of 1940 El Centro Earthquake. Thus, a further work is needed particularly

to assess the earthquake dependence of resonance using different strong ground motion

records. The cases studied in the resonance situation can be surveyed in the aspect of multiple

layered soils rather than the single ones. This investigation is a numerical-based study,

however, can be extended to a laboratory work which may improve the applied methodology

as well as it may produce guidelines for the effect of SSI in a future course of study. Even

though all these tasks may enhance our insight on the resonance, the complicated nature of

resonance always has to be regarded in design. It is believed that the findings in this study are

valuable and will help for code provision purposes as well as attract attention to engineers in

practice to be careful when designing structures against resonance.

Fig. 14 The ratios of story shearforces of SSI models to fixedbase model with respect to SLT

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6 Conclusion

In this preliminary study, the effects of resonance on the response of structure under the

seismic loading in the elastic range of vibration have been investigated by performing 2D

dynamic SSI analysis. The 4 soil–structure models (single homogenous soil layers with a

RC structure resting on the ground surface) adjusted to be in resonance have been used in

the investigation (Fig. 3). Direct method has been applied for the SSI analysis by using

Fig. 15 The story bendingmoments of SSI models withrespect to SLT

Fig. 16 The ratios of storybending moments of SSI modelsto fixed base model with respectto SLT

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FEM for modeling the entire soil–structure system (Fig. 4). The applicability and accuracy

of the FEM for the fundamental periods of soil layers were confirmed by the most common

evaluation formula (Eq. 3) and the site response analysis by SHAKE (Figs. 6, 7, 8).

The investigation results that (Figs. 9, 10, 11 12, 13, 14, 15, 16) the resonance effect

(i.e., the amplitudes, shear force and moment) on the RC structure increases with the

increased SLT. For higher SLTs, this effect seems close to each other. The responses under

resonance are strongly influenced by soil amplification (Figs. 9, 10, 11, 12). Even though

the soil layer has good engineering characteristics (i.e., Vs [ 600 m/s), the ground floor of

the RC structure under the resonance can be considerably damaged from the larger soil

layer thicknesses (i.e.,[50 m) (Figs. 13, 14, 15, 16). The rate of shear force increments are

more pronounced on the midstorys as compared with the ones of remaining storys

(Fig. 14). This may contribute at the explanation of the heavy damage on the midrise

buildings under the resonance at some past earthquakes. The moment ratios (Fig. 16) are

likely supposed to be factor of safeties which are calculated relatively high due to the

resonance effect on the RC structure, as expected. The overall evaluation of this investi-

gation reveals that the resonance effects estimated from the SSI analysis fairly produce

greater responses on the RC structure. The practical relevance of the findings obtained in

this study can be considered to be high. They can be beneficial for gaining an insight into

code provisions as well.

Acknowledgments This study is supported by The Scientific Research Project Unit of University ofGaziantep. Dr K.Hazirbaba is gratefully acknowledged by the corresponding author of this paper forproviding post-doctorate fellowship at his research project (Grant No. G3238-33650) at University of AlaskaFairbanks. The authors are grateful to the anonymous reviewers for carefully reviewing the manuscript andproviding valuable comments.

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