deconvolution effect of near-fault earthquake ground ... · earthquake motion that will be applied...

Nat. Hazards Earth Syst. Sci., 12, 1151–1157, 2012www.nat-hazards-earth-syst-sci.net/12/1151/2012/doi:10.5194/nhess-12-1151-2012© Author(s) 2012. CC Attribution 3.0 License.

Natural Hazardsand Earth

System Sciences

Deconvolution effect of near-fault earthquake ground motions onstochastic dynamic response of tunnel-soil deposit interactionsystems

K. Hacıefendioglu

Ondokuz Mayıs University, Department of Civil Engineering, 55139 Samsun, Turkey

Correspondence to:K. Hacıefendioglu ([email protected])

Received: 29 February 2012 – Revised: 3 April 2012 – Accepted: 3 April 2012 – Published: 24 April 2012

Abstract. The deconvolution effect of the near-fault earth-quake ground motions on the stochastic dynamic responseof tunnel-soil deposit interaction systems are investigated byusing the finite element method. Two different earthquakeinput mechanisms are used to consider the deconvolutioneffects in the analyses: the standard rigid-base input andthe deconvolved-base-rock input model. The Bolu tunnelin Turkey is chosen as a numerical example. As near-faultground motions, 1999 Kocaeli earthquake ground motion isselected. The interface finite elements are used between tun-nel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the twoinput models are compared with each other.

1 Introduction

It is usually accepted that underground structures sufferless from earthquakes than superstructures. However, re-cent earthquakes as in the Kobe, Japan earthquake (EQESummary, 1995; Sinozuka, 1995), Chi-Chi, Taiwan earth-quake (Chen et al., 2002; Wang et al., 2001; Uenishi et al.,1999) and Kocaeli, Turkey earthquake (Hashash et al., 2001)caused extensive failure in tunnels. Underground structuredamages were also observed in different earthquakes, suchas 1976 Tangshan earthquake in China (Wang, 1985) andthe Loma Prieta earthquake in USA (Schmidt and Hashash,1998). It is obvious that the safety of mountain tunnels inseismically active areas is still an important issue to tunnelengineers. The studies relating to tunnels under the seismiceffects are performed by various researchers in recent years(Kirzhner and Rosenhouse, 2000; Karakostas and Manolis,

2002; Gazetas et al., 2005; Hashash et al., 2005; Liu andSong, 2005; Pakbaz and Yareevand, 2005; Kouretzis et al.,2006).

It is clear from the literature review that the effect of earth-quake ground motions on the underground structures was in-vestigated by many researches. All of these studies wereperformed by deterministic methods. Almost all the stud-ies except for the study performed by Kirzhner and Rosen-house (2000) considered the earthquake motions theoreti-cally acting at an infinite depth as a simplification. In thisstudy the earthquake motion will be applied at a plane whichis located under the bottom of the tunnel-soil deposit inter-action system. For this purpose, two different earthquakeinput mechanisms are used to consider the deconvolution ef-fect of the near-fault ground motions on the stochastic dy-namic response of tunnel-soil deposit interaction systems:namely, the standard rigid-base input model (Model-I) andthe deconvolved base-rock input model (Model-II) (Legerand Boughoufalah, 1989; Hacıefendioglu, 2010).

In the standard rigid-base input model (Model-I), theearthquake motion that will be applied to the base of thetunnel-soil deposit interaction system, is an accelerogramwhich is recorded previously by a strong motion seismographlocated at the soil surface. The obvious deficiency of Model-I is that the motions actually occurring at the base of thetunnel-soil deposit interaction system cannot be the same asthose recorded at its free surface. Accordingly, in the modela correction must be made to overcome this deficiency bycalculation of a modified base rock motion by deconvolutionof the free-field surface.

Near-fault ground motions causing much of the damagein recent major earthquakes (Northbridge in 1994, Kobe in

Published by Copernicus Publications on behalf of the European Geosciences Union.

1152 K. Hacıefendioglu: Deconvolution effect of near-fault earthquake ground motions

1995, Chi-Chi in 1999, Kocaeli in 1999) are characterizedby pulse-like motions that expose the structure to a high inputenergy at the beginning of the record. The study of near faultearthquake ground motion characteristics is a very importanttopic for both seismological and engineering communities.For this reason, three earthquake ground motions are selectedto determine the effect of the near-fault earthquake groundmotions on the stochastic dynamic response of the tunnel-soil deposit systems.

The interaction effects between tunnel and soil depositsare also taken into account in this study. For this purposetwo dimensional interface finite elements are used betweenthe soil deposit and structure. This is achieved by program-ming this feature into the general purpose computer programfor the stochastic dynamic analysis of structural systems sub-jected to random ground motion, SVEM (Dumanoglu andSoyluk, 2002).

2 Stochastic analysis formulation

Since the formulation of the random vibration theory for thespatially varying ground motion is given previously by manyresearchers (Harichandran et al., 1996; Hacıefendioglu andSoyluk, 2011; Haciefendioglu, 2006), in this study, the fi-nal equations will be used directly without any derivation.The random vibration theory provides an approximate esti-mate of the mean of the absolute maximum response of thestructure in terms of the power spectral density function anda coherency function. The free response can be decomposedinto pseudo-static and dynamic parts, i.e.,z = zs + zd whenthere is a differential excitation at the supports. Assumingthe stationary excitation, the total variance responses can beobtained from

σ 2z = σ 2

zd+ σ 2

zs+ 2Cov(zs,zd) (1)

in whichσ 2zd

andσ 2zs

are the dynamic and pseudo-static vari-ances, respectively, andCov(zs,zd) is the covariance be-tween the dynamic and pseudo-static responseszd and zs

(Harichandran et al., 1996).Depending on the peak response and standard deviation

(σz) of z(t), the mean of maximum value,µ, in the stochasticanalysis can be expressed as

µ = pσz (2)

in whichp is a peak factor, which is a function of the time ofthe motion and the mean zero crossing rate (Der Kiureghianand Neuenhofer, 1991).

3 Spatially varying ground motion model

The seismic analysis and design of lifelines, such as earth-fill dams, bridges, pipelines, require information about the

spatial variability of the seismic ground motions at the sup-ports of these extended structures. The spatial variabilityof ground motion may significantly affect the seismic re-sponses and induce additional stresses in the structure. Thisvariation causes internal forces due to quasi-static displace-ments. For uniform ground motion case, quasi-static dis-placements normally do not produce internal forces. There-fore, while analyzing large structures, the spatially varyingearthquake ground motions should be considered and totaldisplacements have to be used in expressing the governingequation of motion. Der Kiureghian and Neuenhofer (1991)identified three phenomena that are responsible for the spatialvariation of the ground motion. In this study, the stochasticresponse of the underground structures when applied to thespatially varying ground motion is investigated. The site re-sponse effect is ignored in the analyses.

The spatial variability of the ground motion is character-ized by the coherency functionγlm(ω). In the case of a ho-mogeneous soil site, the cross-power spectral density func-tion between the accelerationsugl

and ugm at the supportpointsl andm is written as

Suglugm(ω) = γlm(ω).Sug(ω) (3)

in which γlm(ω) is the coherency function andSug (ω)

is the power spectral density function of uniform surfaceand deconvolved ground accelerations. Recently, Der Ki-ureghian (1996) proposed a composite model of the co-herency function as

γlm(ω) = γlm(ω)i exp[i(θlm(ω)w] (4)

in which, γlm(ω)i characterizes the incoherence effect(Harichandran, 1991),γlm(ω)w represents the wave passageeffect, andγlm(ω)s defines the complex valued site responseeffect, respectively. For the incoherence effect, the modeldeveloped by Harichandran and Vanmarcke (1986) based onthe statistical analysis of strong ground motion data from theSMART-1 dense array is considered.

4 Application

The Bolu tunnel is part of the Transit European Motorwayin an area where squeezing rock masses occur. The cross-ing of the Bolu Mountain is included in the 120 km sectionbetween Gumusova and Gerede. The last 25 km stretch, themost challenging, runs parallel to the North Anatolian Fault.This stretch, under construction, includes several viaductsand the Bolu tunnel. The Bolu tunnel is a 3360 m long twinbored three lanes tunnel. The average excavated radius is8 m, corresponding to an x-section area between 190 and260 m2. The width of the ground pillar between tubes variesfrom about 28 m at portals to almost 48 m. Depths are up to250 m; on 86 % of the total length, overburdens are higherthan 100 m and on 48 % higher than 150 m.

Nat. Hazards Earth Syst. Sci., 12, 1151–1157, 2012 www.nat-hazards-earth-syst-sci.net/12/1151/2012/

K. Hacıefendioglu: Deconvolution effect of near-fault earthquake ground motions 1153

6

Gümüşova and Gerede. The last 25 km stretch, the most challenging, runs parallel to the North

Anatolian Fault. This stretch, under construction, includes several viaducts and the Bolu tunnel. The

Bolu tunnel is a 3360 m long twin bored three lanes tunnel. The average excavated radius is 8 m,

corresponding to an x-section area between 190 and 260 m2

Fig.1. Bolu Tunnel-longitudinal profile (Amberk and Russo, 2001)

Table 1. Material properties for A-A cross section of the Bolu Tunnel.

. The width of the ground pillar between

tubes varies from about 28 m at portals to almost 48 m. Depths are up to 250 m; on 86% of the total

length, overburdens are higher than 100 m and on 48% higher than 150 m.

Bolu tunnel longitudinal profile is sketched and the lithology encountered is indicated in Fig.1.

A wide range of soils is represented, mainly highly tectonised series of mudstones, siltstones and

limestones, fault gouge clays. The consistence of the soil varies from competent rock requiring

blasting to very weak clayey zones where heavy advancement problems were encountered. A-A cross

section at the Ankara portal is selected in order to investigate the stochastic response of the Bolu

tunnel. The selected cross section details and finite element model of the tunnel with soil deposit are

plotted in Fig.2. The properties of the Bolu tunnel, the soil deposit surrounding the tunnel and

interface elements between soil deposit and tunnel are given in Table 1.

Materials Modulus of Elasticity (N/m2

Poisson’s Ratio )

Unit weights (kN/m3)

Tunnel (Concrete) 2.00E10 0.15 24.00 Metacristalline 2.67E10 0.24 26.38 Clay 1.77E9 0.45 20.30 Interface Element 1.40E10 0.25 24.00

63+000 63+500 64+000 64+500 800 m

900 m

1000 m Elevation

To Ankara

A

A

Metacristalline

Clay

Metacristalline

Fig. 1. Bolu Tunnel-longitudinal profile (Amberk and Russo, 2001).

Table 1. Material properties for A-A cross section of the Bolu Tun-nel.

Materials Modulus of Poisson’s Unit weightsElasticity (N m−2) Ratio (kN m−3)

Tunnel (Concrete) 2.00E10 0.15 24.00Metacristalline 2.67E10 0.24 26.38Clay 1.77E9 0.45 20.30Interface Element 1.40E10 0.25 24.00

Bolu tunnel longitudinal profile is sketched and the lithol-ogy encountered is indicated in Fig. 1. A wide range of soilsis represented, mainly highly tectonised series of mudstones,siltstones, limestones and fault gouge clays. The consistenceof the soil varies from competent rock requiring blasting tovery weak clayey zones where heavy advancement problemswere encountered. A-A cross section at the Ankara portalis selected in order to investigate the stochastic response ofthe Bolu tunnel. The selected cross section details and finiteelement model of the tunnel with soil deposits are plotted inFig. 2. The properties of the Bolu tunnel, the soil depositssurrounding the tunnel and interface elements between soildeposit and tunnel are given in Table 1.

The tunnel-soil deposit interaction model subjected to ran-dom earthquake ground motions in the horizontal directionis presented Fig. 3. The horizontal input is assumed to travelacross the tunnel-soil deposit system from the left to rightwith finite velocity of 2000 m s−1. First 15 modes and 10 %damping ratio for the analyses are considered. Two transla-tional degrees of freedom are assigned to each node and aplane-strain assumption is used in the calculations.

5 Input ground motions

The stochastic analysis of the Bolu tunnel is performed forrandom earthquake ground motion by taking into accountthe incoherence and wave passage effects. For this purpose,two different near-fault earthquake ground motions are con-sidered in the analyses for the tunnel-soil deposit interactionsystem supports.

In this section, the 1999 Kocaeli near-fault earthquakeground motion record was selected as input motion, corre-sponding to station number IZT180. The time-history plot

7

Fig.2. Finite element model of the tunnel-soil deposit system and the detail of the Bolu tunnel for A-A

cross section

10.0

m

Section A-A

120.0 m

25.0

m

45.0

m

Four-noded interface element

17.16 m

14.5

3 m

INVERT

Shotcrete Lining d=40 cm

Bornold Lining d=50 cm

Inner Concrete Lining

d=60 cm

Section I-I

I

I

NP.1

NP.3

NP.9 NP.12

NP.1 NP.2

EL.2

EL.4

EL.11

EL.18

EL.20

Nodal Point Number Element Number

Fig. 2. Finite element model of the tunnel-soil deposit system andthe detail of the Bolu tunnel for A-A cross section.

8

The tunnel-soil deposit interaction model subjected to random earthquake ground motions in

the horizontal direction is presented Fig.3. The horizontal input is assumed to travel across the tunnel-

soil deposit system from the left site to right site with finite velocity of 2000 m/s. First 15 modes and

10% damping ratio for the analyses are considered. Two translational degrees of freedom are assigned

to each node and a plane-strain assumption is used in the calculations.

Fig.3. Materials surrounding A-A cross section of the Bolu Tunnel to random earthquake ground

motion

5. Input Ground Motions

The stochastic analysis of the Bolu tunnel is performed for random earthquake ground motion

by taking into account the incoherence and wave passage effects. For this purpose, two different near-

fault earthquake ground motions are considered in the analyses for the tunnel-soil deposit interaction

system supports.

In this section, the 1999 Kocaeli near-fault earthquake ground motion record was selected as

input motion, corresponding to station number IZT180. The time-history plot of acceleration and

Firm soil Vapp=2000 m/s

Firm soil Vapp=2000 m/s

Section A-A

Metacristalline

Metacristalline

Clay Tunnel

free-field acceleration

fgu

dgu

dgudeconvolved acceleration

Surface

Base

Fig. 3. Materials surrounding A-A cross section of the Bolu Tunnelto random earthquake ground motion.

of acceleration and velocities of Kocaeli earthquake recordis depicted in Figs. 4 and 5, respectively. The strong motionrecords are obtained from the PEER Strong Motion Database(PEER, 2012). This database gives information about the siteconditions and the soil types for the instrument locations.

www.nat-hazards-earth-syst-sci.net/12/1151/2012/ Nat. Hazards Earth Syst. Sci., 12, 1151–1157, 2012


9

velocities of Kocaeli earthquake record is depicted in Fig.4 and Fig.5, respectively. The strong motion

records are obtained from the PEER Strong Motion Database (PEER, 2006). This database gives

information about the site conditions and the soil types for the instrument locations. The properties of

the selected near-fault earthquake ground motion records are indicated in Table 2. These near-fault

earthquake ground motion records are recorded at firm soil site conditions.

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-2.0

-1.0

0.0

1.0

2.0

Acc

eler

atio

n (m

/s²)

0.152g

Fig.4. Time-history of the near-fault earthquake ground motion acceleration for the 1999 Kocaeli

earthquake

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-25.0-20.0-15.0-10.0-5.00.05.0

10.015.020.025.0

Vel

ocity

(cm

/s)

Fig.5. Time-history of the near-fault earthquake ground motion velocity for the 1999 Kocaeli

earthquake

Table 2. Properties of selected near-fault earthquake ground motion record

Near-Fault Strong Ground Motions

Earthquake Magnitude (M)

PGA (cm/s2

PGV (cm/s) )

Distance to the fault (km)

PGV/PGA(s)

Kocaeli 7.4 149.11 22.60 4.80 0.15

The deconvolved accelerogram of the selected near-fault earthquake ground motions are

calculated by using the computer program SHAKE91 (Idriss and Sun, 1992), which is based on one-

dimensional wave propagation theory. The theory considers the responses associated with vertical

propagation of shear waves through the linear viscoelastic system shown in Fig.3. The soil system

used for the deconvolution and simulation consists of one horizontal layer, which extends to infinity

in the horizontal direction and has a half space as the bottom layer. Each layer is homogeneous and

isotropic, and is characterized by the thickness, mass density, shear modulus and damping factor. The

Fig. 4. Time-history of the near-fault earthquake ground motionacceleration for the 1999 Kocaeli earthquake.

9

velocities of Kocaeli earthquake record is depicted in Fig.4 and Fig.5, respectively. The strong motion

records are obtained from the PEER Strong Motion Database (PEER, 2006). This database gives

information about the site conditions and the soil types for the instrument locations. The properties of

the selected near-fault earthquake ground motion records are indicated in Table 2. These near-fault

earthquake ground motion records are recorded at firm soil site conditions.

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-2.0

-1.0

0.0

1.0

2.0

Acc

eler

atio

n (m

/s²)

0.152g

Fig.4. Time-history of the near-fault earthquake ground motion acceleration for the 1999 Kocaeli

earthquake

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-25.0-20.0-15.0-10.0-5.00.05.0

10.015.020.025.0

Vel

ocity

(cm

/s)

Fig.5. Time-history of the near-fault earthquake ground motion velocity for the 1999 Kocaeli

earthquake

Table 2. Properties of selected near-fault earthquake ground motion record

Near-Fault Strong Ground Motions

Earthquake Magnitude (M)

PGA (cm/s2

PGV (cm/s) )

Distance to the fault (km)

PGV/PGA(s)

Kocaeli 7.4 149.11 22.60 4.80 0.15

The deconvolved accelerogram of the selected near-fault earthquake ground motions are

calculated by using the computer program SHAKE91 (Idriss and Sun, 1992), which is based on one-

dimensional wave propagation theory. The theory considers the responses associated with vertical

propagation of shear waves through the linear viscoelastic system shown in Fig.3. The soil system

used for the deconvolution and simulation consists of one horizontal layer, which extends to infinity

in the horizontal direction and has a half space as the bottom layer. Each layer is homogeneous and

isotropic, and is characterized by the thickness, mass density, shear modulus and damping factor. The

Fig. 5. Time-history of the near-fault earthquake ground motionvelocity for the 1999 Kocaeli earthquake.

The properties of the selected near-fault earthquake groundmotion records are indicated in Table 2. These near-faultearthquake ground motion records are recorded at firm soilsite conditions.

The deconvolved accelerogram of the selected near-faultearthquake ground motions are calculated by using the com-puter program SHAKE91 (Idriss and Sun, 1992), which isbased on one-dimensional wave propagation theory. The the-ory considers the responses associated with vertical propaga-tion of shear waves through the linear viscoelastic systemshown in Fig. 3. The soil system used for the deconvolu-tion and simulation consists of one horizontal layer, whichextends to infinity in the horizontal direction and has a halfspace as the bottom layer. Each layer is homogeneous andisotropic, and is characterized by the thickness, mass den-sity, shear modulus and damping factor. The selected val-ues of modulus reduction and damping factors versus shearstrain for rock material is based on the expressions given inreference (Schnabel et al., 1972). The principal parametersin the analysis of the deconvolved accelerogram are the shearwave velocity and the damping ratio of the foundation soil.It should be noted that the accelerogram is affected by theshear wave velocity and the damping ratio of the foundationsoil. The values of the shear wave velocity and the dampingratio of the foundation rock are selected as 2000 m s−1 and10 %, respectively. The deconvolved time history of the Ko-caeli near-fault earthquake ground motion is shown in Fig. 6.The acceleration and displacement spectral density functionof the free-surface and deconvolved ground acceleration aredepicted in Figs. 7 and 8, for the selected ground motion, re-

10

0.0 10.0 20.0 30.0 40.0 50.0Frequency (rad/s)

0.000

0.005

0.010

0.015

Acc

eler

atio

n Po

wer

Spe

ctra

l D

ensit

y Fu

nctio

n (m

²/s³)

Free-Surface Ground Motion

Deconvolved Ground Motion

selected values of modulus reduction and damping factors versus shear strain for rock material is

based on the expressions given in reference (Schnabel et al. 1972). The principal parameters in the

analysis of the deconvolved accelerogram are the shear wave velocity and the damping ratio of the

foundation soil. It should be noted that the accelerogram is affected by the shear wave velocity and

the damping ratio of the foundation soil. The values of the shear wave velocity and the damping ratio

of the foundation rock are selected as 2000 m/s and 10%, respectively. The deconvolved time history

of the Kocaeli near-fault earthquake ground motion is shown in Fig.6. The acceleration and

displacement spectral density function of the free-surface and deconvolved ground acceleration are

depicted in Fig.7 and Fig.8, for the selected ground motion, respectively. It is apparent in Fig.6 that

local soil conditions considerably affect the frequency contents and amplitudes of the ground

acceleration records and the deconvolved ground acceleration values become larger than the values

recorded at the free-surface. However, as the acceleration spectral density function values obtained

from Model-I are larger than those from Model-II at the low frequencies, they are smaller than those

from Model-II at the high frequencies (Fig.7).

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-3.0-2.0-1.00.01.02.03.0

Acc

eler

atio

n (m

/s²) 0.296g

Fig.6. Time-histories of the deconvolved ground motion accelerations for the 1999 Kocaeli

earthquake

Fig.7. Acceleration spectral density function of the free-surface and deconvolved ground acceleration

for the 1999 Kocaeli earthquake

Fig. 6. Time-histories of the deconvolved ground motion accelera-tions for the 1999 Kocaeli earthquake.

10

0.0 10.0 20.0 30.0 40.0 50.0Frequency (rad/s)

0.000

0.005

0.010

0.015

Acc

eler

atio

n Po

wer

Spe

ctra

l D

ensit

y Fu

nctio

n (m

²/s³)



selected values of modulus reduction and damping factors versus shear strain for rock material is

based on the expressions given in reference (Schnabel et al. 1972). The principal parameters in the

analysis of the deconvolved accelerogram are the shear wave velocity and the damping ratio of the

foundation soil. It should be noted that the accelerogram is affected by the shear wave velocity and

the damping ratio of the foundation soil. The values of the shear wave velocity and the damping ratio

of the foundation rock are selected as 2000 m/s and 10%, respectively. The deconvolved time history

of the Kocaeli near-fault earthquake ground motion is shown in Fig.6. The acceleration and

displacement spectral density function of the free-surface and deconvolved ground acceleration are

depicted in Fig.7 and Fig.8, for the selected ground motion, respectively. It is apparent in Fig.6 that

local soil conditions considerably affect the frequency contents and amplitudes of the ground

acceleration records and the deconvolved ground acceleration values become larger than the values

recorded at the free-surface. However, as the acceleration spectral density function values obtained

from Model-I are larger than those from Model-II at the low frequencies, they are smaller than those

from Model-II at the high frequencies (Fig.7).

0.0 5.0 10.0 15.0 20.0 25.0 30.0Time (s)

-3.0-2.0-1.00.01.02.03.0

Acc

eler

atio

n (m

/s²) 0.296g

Fig.6. Time-histories of the deconvolved ground motion accelerations for the 1999 Kocaeli

earthquake

Fig.7. Acceleration spectral density function of the free-surface and deconvolved ground acceleration

for the 1999 Kocaeli earthquake

Fig. 7. Acceleration spectral density function of the free-surfaceand deconvolved ground acceleration for the 1999 Kocaeli earth-quake.

spectively. It is apparent in Fig. 6 that local soil conditionsconsiderably affect the frequency contents and amplitudes ofthe ground acceleration records and the deconvolved groundacceleration values become larger than the values recorded atthe free-surface. However, as the acceleration spectral den-sity function values obtained from Model-I are larger thanthose from Model-II at the low frequencies, they are smallerthan those from Model-II at the high frequencies (Fig. 7).

6 Displacements

The horizontal displacements along the Section I-I (Fig. 2)of the tunnel are calculated for two earthquake input mech-anisms: the standard rigid-base input model (Model-I) andthe deconvolved-base-rock input model (Model-II). Two dif-ferent near-fault earthquake ground motions are used to de-termine the effect of the base-rock characteristics on thestochastic response of the tunnel-soil deposit interaction sys-tem. The acceleration spectral density functions determinedat the free-surface are used for input Model-I and those



Table 2. Properties of a selected near-fault earthquake ground motion record.

Near-Fault Strong Ground MotionsEarthquake Magnitude (M) PGA (cm s−2) PGV (cm s−1) Distance to the fault (km) PGV/PGA(s)

Kocaeli 7.4 149.11 22.60 4.80 0.15

11

0.0 2.0 4.0 6.0 8.0 10.0Frequency (rad/s)

0.00000.00010.00020.00030.00040.00050.0006

Disp

lace

men

t Spe

ctra

l D

ensit

y Fu

nctio

n (m

²s)



Fig.8. Displacement spectral density function of the free-surface and deconvolved ground for the 1999

Kocaeli earthquake

6. Displacements

The horizontal displacements along the Section I-I (Fig.2) of the tunnel are calculated for two

earthquake input mechanisms: the standard rigid-base input model (Model-I) and the deconvolved-

base-rock input model (Model-II). Two different near-fault earthquake ground motions are used to

determine the effect of the base-rock characteristics on the stochastic response of the tunnel-soil

deposit interaction system. The acceleration spectral density functions determined at the free-surface

are used for input Model-I and those from the deconvolved accelerogram are considered for input

Model-II (Fig.6).

In order to investigate the effect of two different earthquake input mechanisms on the quasi-

static, dynamic and total horizontal displacements, the mean of maximum values of horizontal

displacements obtained along the Section I-I of the tunnel is depicted in Fig. 9(a-c) for the Kocaeli

earthquake in 1999.

In these figures, it is observed that the quasi-static, dynamic and total displacement values

obtained from Model-I are larger than those of Model-II for the Kocaeli earthquakes.

Fig. 8. Displacement spectral density function of the free-surfaceand deconvolved ground for the 1999 Kocaeli earthquake.

from the deconvolved accelerogram are considered for inputModel-II (Fig. 6).

In order to investigate the effect of two different earth-quake input mechanisms on the quasi-static, dynamic and to-tal horizontal displacements, the mean of maximum valuesof horizontal displacements obtained along the Section I-I ofthe tunnel is depicted in Fig. 9a–c for the Kocaeli earthquakein 1999.

In these figures, it is observed that the quasi-static, dy-namic and total displacement values obtained from Model-Iare larger than those of Model-II for the Kocaeli earthquakes.

7 Stresses

The mean of maximum stress values of the tunnel are alsocalculated for two earthquake input mechanisms: the stan-dard rigid-base input model (Model-I) and the deconvolved-base-rock input model (Model-II). Two different near-faultearthquake ground motions are used to determine the effectof the base-rock characteristics on the stochastic response ofthe tunnel-soil deposit interaction system.

Section I-I shown in Fig. 2 is selected for the comparisonof the mean of maximum quasi-static, dynamic and total hor-izontal, vertical and shear stresses. The stress components onSection I-I are depicted in Figs. 10–12 for the two earthquakeinput mechanisms mentioned before. The stresses due to the

Kocaeli earthquake are obtained at the center points of thefinite elements.

Figures 10–12 illustrate the quasi-static, dynamic and totalhorizontal and vertical stresses induced by the Kocaeli earth-quake. It is obvious that, while the stresses obtained fromModel-I and Model-II for the quasi-static and total compo-nents are close to each other, the dynamic stresses obtainedfrom Model-I are larger than those of Model-II. The mean ofmaximum quasi-static, dynamic and total shear stresses in-duced by the Kocaeli earthquake are shown in Fig.12. As thequasi-static stresses due to Model-I and Model-II are closeto each other, the dynamic and total stresses obtained fromModel-I are significantly larger than those of Model-II.

As defined in Eq. (1), the quasi-static component is depen-dent on the displacement spectral density function (Fig. 8).Because the variances of ground displacements determinedby Model-I and Model-II for selected earthquakes groundmotion are close to each other, it is natural to have nearlythe same pseudo-static stresses.

8 Conclusions

In this paper, the deconvolution effect of the random near-fault earthquake ground motions on the stochastic dynamicresponse of tunnel-soil deposit interaction systems are in-vestigated by using the finite element method. For this pur-pose, two different earthquake input mechanisms: namely,the standard rigid base input model (Model-I) and thedeconvolved-base-rock input model (Model-II) are used.The response components, quasi-static, dynamic and covari-ance components, caused by the random near-fault earth-quake ground motion are presented for two different earth-quake input mechanisms. To investigate the effect of thenear-fault earthquake ground motion on the stochastic dy-namic behavior of the Bolu tunnel, 1999 Kocaeli earthquakeground motion is considered in the analyses.

The mean of maximum values of the quasi-static, dynamicand total displacements obtained for Model-I are larger thanthose of Model-II for the Kocaeli earthquake.

It is observed that as the quasi-static stresses induced byModel-I and Model-II are generally close to each other, thedynamic stresses induced by Model-I are generally largerthan those of Model-II. As for the total stresses, the stressesdue to Model-I have sometimes small or large values accord-ing to Model-II. It is thought that the reason for this situation



12

(a) (b) (c) Fig.9. Mean of maximum (a) quasi-static, (b) dynamic and (c) total displacements for the Kocaeli

earthquake in 1999, respectively

7. Stresses

The mean of maximum stress values of the tunnel are also calculated for two earthquake input

mechanisms: the standard rigid-base input model (Model-I) and the deconvolved-base-rock input

model (Model-II). Two different near-fault earthquake ground motions are used to determine the

effect of the base-rock characteristics on the stochastic response of the tunnel-soil deposit interaction

system.

Section I-I shown in Fig.2 is selected for the comparison of the mean of maximum quasi-static,

dynamic and total horizontal, vertical and shear stresses. The stress components on Section I-I are

depicted in Figs.10-12 for the two earthquake input mechanisms mentioned before. The stresses due

to the Kocaeli earthquake are obtained at the center points of the finite elements.

Figs.10-12 illustrate the quasi-static, dynamic and total horizontal and vertical stresses induced

by the Kocaeli earthquake. It is obvious that, while the stresses obtained from Model-I and Model-II

for the quasi-static and total components are close to each other, the dynamic stresses obtained from

Model-I are larger than those of Model-II. The mean of maximum quasi-static, dynamic and total

shear stresses induced by the Kocaeli earthquake are shown in Fig.12. As the quasi-static stresses due

to Model-I and Model-II are close to each other, the dynamic and total stresses obtained from Model-I

are significantly larger than those of Model-II.

0 3 6 9 12 15 18 21Nodal Point

4.20

4.30

4.40

4.50

4.60

Disp

lace

men

t (cm

)

0 3 6 9 12 15 18 21Nodal Point

4.20

4.25

4.30

4.35

4.40

Disp

lace

men

t (cm

)

0 3 6 9 12 15 18 21Nodal Point

0.00

0.10

0.20

0.30

0.40

0.50

Disp

lace

men

t (cm

)

Model-I Model-II

Fig. 9. Mean of maximum(a) quasi-static,(b) dynamic and(c) total displacements for the Kocaeli earthquake in 1999, respectively.

13

(a) (b) (c)

Fig.10. Mean of maximum (a) quasi-static, (b) dynamic and (c) total horizontal stresses for the

Kocaeli earthquake in 1999, respectively

(a) (b) (c)

Fig.11. Mean of maximum (a) quasi-static, (b) dynamic and (c) total vertical stresses for the Kocaeli


(a) (b) (c)

Fig.12. Mean of maximum (a) quasi-static, (b) dynamic and (c) total shear stresses for the Kocaeli


0 4 8 12 16 20Element Number

0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)


0.0E+01.0E+52.0E+53.0E+54.0E+55.0E+56.0E+5

Hor

izon

tal S

tress

(N/m

²)

Model-I

Model-II


2.5E+5

5.0E+5

7.5E+5

1.0E+6

1.3E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)

Model-I

Model-II


0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Ver

tical

Stre

ss (N

/m²)


0.0E+0

1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

Shea

r Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+5

Shea

r Stre

ss (N

/m²)

Model-I

Model-II


1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

9.0E+5

Shea

r Stre

ss (N

/m²)

Fig. 10. Mean of maximum(a) quasi-static,(b) dynamic and(c) total horizontal stresses for the Kocaeli earthquake in 1999, respectively.

13

(a) (b) (c)



(a) (b) (c)



(a) (b) (c)




0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)


0.0E+01.0E+52.0E+53.0E+54.0E+55.0E+56.0E+5

Hor

izon

tal S

tress

(N/m

²)Model-I

Model-II


2.5E+5

5.0E+5

7.5E+5

1.0E+6

1.3E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)

Model-I

Model-II


0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Ver

tical

Stre

ss (N

/m²)


0.0E+0

1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

Shea

r Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+5

Shea

r Stre

ss (N

/m²)

Model-I

Model-II


1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

9.0E+5

Shea

r Stre

ss (N

/m²)

Fig. 11. Mean of maximum(a) quasi-static,(b) dynamic and(c) total vertical stresses for the Kocaeli earthquake in 1999, respectively.

13

(a) (b) (c)



(a) (b) (c)



(a) (b) (c)




0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)0 4 8 12 16 20

Element Number

0.0E+01.0E+52.0E+53.0E+54.0E+55.0E+56.0E+5

Hor

izon

tal S

tress

(N/m

²)Model-I

Model-II


2.5E+5

5.0E+5

7.5E+5

1.0E+6

1.3E+6

1.5E+6

Hor

izon

tal S

tress

(N/m

²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+59.0E+5

Ver

tical

Stre

ss (N

/m²)

Model-I

Model-II


0.0E+0

3.0E+5

6.0E+5

9.0E+5

1.2E+6

1.5E+6

Ver

tical

Stre

ss (N

/m²)


0.0E+0

1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

Shea

r Stre

ss (N

/m²)


0.0E+01.5E+53.0E+54.5E+56.0E+57.5E+5

Shea

r Stre

ss (N

/m²)

Model-I

Model-II


1.5E+5

3.0E+5

4.5E+5

6.0E+5

7.5E+5

9.0E+5

Shea

r Stre

ss (N

/m²)

Fig. 12. Mean of maximum(a) quasi-static,(b) dynamic and(c) total shear stresses for the Kocaeli earthquake in 1999, respectively.



is the characteristic properties of the near-fault earthquakeground motion.

It can be also observed that, while the pseudo-static re-sponse components are sensitive to the displacement spec-tral density functions of the ground motions, the dynamic re-sponse components are sensitive to the acceleration spectraldensity functions.

It can be concluded from these analyses that the standardrigid-base input model (Model-I) is inadequate to evaluatethe stochastic dynamic response of tunnel-soil deposit inter-action systems subjected to the random near-fault earthquakeground motions. For this purpose, the deconvolved-base-rock input model (Model-II) should be used to obtain moreaccurate results in the analyses of underground structures.

Acknowledgements.This research was supported by OndokuzMayıs University.

Edited by: M. E. ContadakisReviewed by: H. B. Basaga and another anonymous referee

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