Amplification Ratio and Period of the Earthquakes in Karaj,Iran

7/30/2019 Amplification Ratio and Period of the Earthquakes in Karaj,Iran

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Amplification Ratio and Period of the

Earthquakes in Karaj, Iran

Ali Ghanbari

Tarbiat Moallem University, Tehran, Iran

[email protected]

Amin Hassanzadeh

Research Student, Tarbiat Moallem University, Tehran, Iran

S. Sadrodin Zarangzadeh

Science and Research Campus of Islamic Azad University, Tehran, Iran

ABSTRACT

Karaj is one the largest and rapidly developing cities of Iran, located west of Tehran, the capital.

Considering its vicinity to the active faults with high seismicity and occurring strong earthquakes in

this area, the amplification ratio and period of earthquakes in different regions of Karaj have beenselected as the subject of current research. By studying more than one hundred bore holes, the required

data relating to the subsurface layers are collected and accordingly, physical and mechanical properties

of the soil in the area under study have been obtained. The study area is divided into six individual

layers. In each layer, the results of a large number of in situ and laboratory tests to determine

geotechnical properties of the soil are classified and analyzed. Using some correlation formulas, thevelocity of shear wave is calculated and assuming one-dimensional non-linear behavior being valid for

the alluvial soil, the response of site to probable quakes is determined. Finally, the response of

available structures has been classified into three groups based on their height and considering theestimated periods, the study area has also been divided into two sub domains. Ultimately, a maximum

height for the structures of each domain is suggested based on calculated amplification ratios.

KEYWORDS: Amplification ratio, Site effect, Karaj, Ground response

INTRODUCTION

Amplified response of alluvial sites can change the main characteristics of earthquake to a great

extent. Such variety is usually observed as an increase in maximum acceleration as well as duration of the

quakes. Moreover, most of cities and urban areas are constructed on alluvial soils and therefore studying

the amplification phenomenon which is usually defined as an increase in the ground motion due to the

presence of the soil deposits will be crucial.


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Many researchers have shown that the amplification ratio at soft sites is generally longer than hard

ones (Shoji et al., 2005; Kamalian et al., 2008 and Hasancebi and Ulusay, 2006). Shoji et al. (2005) also

reported lengthening the duration of the ground movements in soft sites. Shoji et al. (2005) demonstrated

that alluvial sites mainly affect seismic waves in upper 30 meters of earth, near the grounds surface.

In recent years, a number of papers on the existence of seismic hazard for the Iranian region has

appeared (Shafiee and Azadi, 2007; Amiri et al., 2006). City of Karaj is one of the important

municipalities in Iran because of its high population, large area as well as presence of many industrial

centers. This city is adjacent to some active faults like North Tehran and Mosha faults which are capable

of generating quakes with magnitudes greater than Ms=7 (Zafarani et al., 2009).

In this paper the S-waves velocity (Vs) for different layers of the soil in Karaj alluvium is acquired by

using a correlation formula between the velocity of shear wave andSPT

N . Using a computer code which

simulates the one-dimensional response of the ground considering non-linear behavior of the soil, the

effect of alluvium on seismic waves has been investigated. In order to study the amplification ratio, the

suggested method by technical committee of earthquake geotechnical engineering (TCEGE) (1999) for 2

and 3 degrees of freedom has been applied and the results obtained from two mentioned approaches have

been compared. Finally, the isovalue lines related to the variance of amplification ratio and period of

earthquake are presented for the area under study.

Introducing the study area

Karaj is a metropolitan area of Iran with a population of about 1,732,275 people based on 2006

census. Heavily congested with industrial firms and located in the neighborhood of Tehran, the capital,

Karaj city has witnessed the increase in the number of population and tall buildings constructed in it to

accommodate this large number of people. Karaj is located on an alluvial site known as Karaj alluvium.

Karaj alluvium is situated on the southern piedmont of central Alborz Mountains. General geological

conditions and tectonics of this area usually follow the pattern of central Alborz zone and mostly, all

northern peaks in the study zone can be associated to Karaj formation. Generally the age of Karaj

formation dates geologically from the Middle Eocene period to its end and in some places can lasts to the

end of Late Eocene. Green tuffs in this formation, observable everywhere, are a distinctive feature of

Karaj formation. Peaks of northern Karaj are usually made up of tuff. These tuffs play the main role in

formation of fragments and elements of Karaj alluvial plain and hence are of great importance as a source

rock in identification of Karaj alluvium.

The study area of current research is located on young alluvial sediments without any special folding.

Alluvial sediments in Karaj are resulted from Karaj river activities coupled with rivers and seasonal

floods originating from valleys of North Mountains. Symptoms and conditions of river sediments can be

clearly observed in excavated cuts and in some parts where the sediments have remained on bed of the old

river canals, evidence of imbrications can be viewed and the dominant direction of stream might be

considered as North-North East, South-South West. It must be noted that formation of sediments has been

greatly affected by the weather conditions as well.More than 8 faults capable of producing earthquakes with magnitudes bigger than MS=7 have been

recognized within max 100 km off Karaj city. Barbarian (1976) has shown that the focal depth of faults in

this area is smaller than 15 km. Fig. 1 illustrates the seismotectonic map of the study area. Many previous


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earthquakes in recent 50 years with magnitudes of greater than 6 (Ms>6) in distances up to 100 Km from

the point of study are noted in Table 1.

Figure 1: Active faults and important earthquake locations around Karaj

Table 1: Important earthquakes around Karaj in last 50 years

Event name year/mm/dd Mw Latitude(deg) Longitude(deg) Depth(km)

Rudbar 1990/06/20 7.3 36.96 49.33 12

Changureh 2002/06/22 6.4 35.63 49.20 10

Boueen Zahra 1962/09/01 7.2 35.71 49.81 ?

Classification of Karaj alluvium

Field investigations and experiments performed by authors reveals that six independent layers can bediscerned as overall representative layers in the studied alluvium. Fig. 2 shows a longitudinal section of

Karaj alluvium based on suggested classification. Points A and B have been depicted in order to facilitate

the superposition of section with plan. Characteristic features and distribution of six considered zones are

described in the following sections of this article.


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Figure 2: Sample section from Karaj alluvium extracted based on

the results of current study in 6 classified zones

It must be noted that despite dominant presence of proposed classification, sandy and sometimes

gravely lenses with thicknesses less than one meter have been observed in each of the mentioned layerswhich are usually arisen from change in conditions of sedimentation.

Clayey and silty layers (C1 & C2)

Karaj alluvium, in proposed layers, is dominantly constituted from clayey and silty soils with

considerable amount of sand. Theses layers are located in the east and central parts of the study area and

usually under fill materials of Karaj alluvium. They can be observed from surface layers to depths of

maximum 14m having interfinger connections in lateral boundaries with clayey and silty layers of C2 and

top connections with sandy layers of 1 and 2 and gravely layers of 1 and 2.

Gradation and mechanical properties for layers C1 and C2 are indexed in Table 2. According to thedata gathered in this research, gradation of soil in the mentioned layers includes fine-grained soils of CL,

ML and CL-ML. The main difference between these two layers (C1 and C2) is that C2 layer is of more

density than C1, the cause of which being the condition of sedimentation. Thus, the number of SPT and

the internal friction angle in C2 layer have been much bigger than C1.

Table 2: Geotechnical properties of Karaj alluvium for C1 and C2 layers

Soil Type S1 S2

MIN. MAX. AVE. MIN. MAX. AVE.

Clay and Silt Percentage 5 49 26.6 5 49 29

Sand Percentage 28 87 53 33 81 49

Gravel Percentage 4 41 20.4 8 44 23.4

Plasticity Index (PI) 1 16 5 1 15 7Number of SPT (N) 15 40 29 40 >60 55

Undrained Cohesion (kg/cm2) 0.2 0.7 0.29 0 1.05 0.34

Internal Friction Angle (Degrees) 23 35 30 30 41 35

Unconfined Compressive Strength (kg/cm2) 0.89 1.0 0.93 0.51 0.92 0.72

Dry Specific Weight (g/cm3) 1.58 2.0 1.75 1.8 1.9 1.85

Shear Wave Velocity (m/sec) 142 267 233 188 309 355


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Sandy layers (S1 & S2):

These layers are scattered in central parts of the study area and more concentrated in west areas of

the site. They are usually spread under fill materials and sometimes under clayey and silty layers of 1 and

2, having interfinger boundary with sandy layers and top obvious connections with clayey and silty layer

1 and gravely layers of 1 and 2. The thickness of this layer in some western parts exceeds 30 meters.Mechanical properties and gradation of S1 and S2 layers are indicated in Table 3. Soil gradation of this

layer has been determined as SC, SM, SC-SM, SP-SC and SP-SM groups and from mineralogical point of

view, its been mostly made up of fractured pieces of Quartz and Feldspar.

S2 layer is of greater density than S1 with more percentage of gravel and higher specific volume.Hence, the internal friction angle and number of SPT are bigger in S2 layer than S1. Generally speaking,

moving from the center of study area to the western regions, S2 layer gradually becomes less obvious

while S1 layer gets more observable. All in all, S1 and S2 layers can be found in central and western areas

of the study area. Inside S1 and S2 layers, there are clayey and gravely lenses which are mostly thin.

Table 3: Geotechnical properties of Karaj alluvium for S1 and S2 layers

Soil Type S1 S2MIN. MAX. AVE. MIN. MAX. AVE.

Clay and Silt Percentage 5 49 26.6 5 49 29

Sand Percentage 28 87 53 33 81 49

Gravel Percentage 4 41 20.4 8 44 23.4

Plastic Index (PI) 1 16 5 1 15 7

Number of SPT (N) 15 40 29 40 >60 55

Undrained Cohesion (kg/cm2) 0.2 0.7 0.29 0 1.05 0.34


Unconfined Compressive Strength (kg/cm2) 0.89 1.0 0.93 0.51 0.92 0.72

Dry Specific Weight (g/cm3) 1.58 2.0 1.75 1.8 1.9 1.85

Shear Wave Velocity (m/sec) 142 267 233 188 309 355

Gravely layers (G1 & G2)

The gravely layer (G1) has lower volume compared with other layers of the site and can be observed

in outcrop in most regions, especially west zones of the study area. Maximum depth of this layer is 20

meters and it has interfinger boundary with G2 layer as well as top obvious connections with other layers.

Gradation in this layer consists of GC, GP, GM, GP-GC and GP-GM groups and from mineralogical

point of view, its constituent pieces are usually from gravel stones separated from rocks of the Karaj site(Tuff, Lime Tuff, Shale, and Lime Shale and ).

The gravely layer (G2) is scattered in central and western areas and more concentrated in easternparts. This layer is the thickest layer of Karaj alluvium and its thickness exceeds 30m in some parts

having interfinger boundary with gravely layer 1 and top obvious connections with other layers.

Gradation of soil in this layer is consisted of GW-GM, GW-GC and GC-GM in addition to the mentioned

gradation for G1 layer.

From lithological point of view, this layer consists of pieces and fractures of Karaj formation and its

difference with G1 layer is in the percentage of fine-grained and coarse-grained components. The

percentage of gravel in G2 layer is much more than G1 and coarse-grained pieces have been observed


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with dimensions of 40cm in eastern parts of the study area. Generally, the shear strength, shear wave

velocity and the number of SPT have all been bigger in G2 layer compared with G1. In a small area

within the gravely layers of 1 and 2, sandy and clayey lenses with thicknesses less than 2m have been

observed. Mechanical properties and gradation of the mentioned layers are noted in Table 4. These layers

have the biggest internal friction angle and shear wave velocity in Karaj alluvium. Fine-grainedpercentage in them is less than the other layers of Karaj alluvium.

Table 4: Geotechnical properties of Karaj alluvium for G1 and G2 layers

Soil Type G1 G2

MIN. MAX. AVE. MIN. MAX. AVE.

Clay and Silt Percentage (%) 5 39 17 0 35 10.4

Sand Percentage (%) 23 41 34 0 43 19.3

Gravel Percentage (%) 28 62 49 39 100 70.5

Plastic Index (PI) 2 10 5 1 18 7

Number of SPT (N) 28 44 37.5 45 >60 56


Dry Specific Weight (g/cm3) 1.8 1.9 1.85 1.8 1.9 1.86Shear Wave Velocity (m/sec) 188 355 309 195 330 365

Based on findings of the current research and the presented discussions in previous sections of this

paper, Karaj alluvium has been evolved in a river environment and tends to a more fine-grained structure

from North-East to South-West areas. Deposition of coarse-grained sediments in North-East regions of

the river has sometimes formed pieces of rocks whereas in west and South-West areas the percentage of

fine-grained sediments increases. In central parts because of the change in river conditions clayey layers

have been deposited, as well.

Field investigations and results

In this research an area of Karaj including several important tall buildings is selected. Fig. 3 illustratesthe study area and locations of more than 100 boreholes mostly with 30 meters depth.

Field tests can play an influential role in studying the engineering geology conditions of a region.Specifically, the estimation of the shear wave velocity using the CPT-seismic cone or flat dilatometer can

be mentioned in this regard, which in addition to the geotechnical specifications determine the shear wave

velocity directly.

In the region under study about 100 boreholes and hand borings have been drilled, the overall length

of which being about 2700m. Also 1300 standard penetration tests have been carried out in all boreholes

with 1.5m distances from each other. Besides the usual tests of determining the physical properties of the

soil, 14 consolidation tests, 111 irect shear tests, 24 mono axial tests, and 32 triaxial tests have been

performed. Also among the field tests, a limitted number of the in-situ direct shear tests, field penetrationtests, and plate bearing tests have been carried out whose results have been used in the present research.

According to Shoji et al. (2005), Borcherdt et al. (1994) and Dobry et al. (2000), the alluvial layer

near the surface of the earth (about 30 meters closed to the surface) is responsible for most variations of

seismic waves. In each borehole, the standard penetration test (SPT) has been conducted in depth of 1.5

meters and samples are extracted for laboratorial tests. Fig. 4 shows an example of the variations in NSPT

with depths for two boreholes, H7 and H17.


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Figure 3: Study area and location of boreholes

Figure 4: Two typical engineering logs illustrating the subsurface ground conditions

and Nspt in study area


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Estimation of amplification ratio from the velocity of shear wave

There are four basic waveforms generated within a semi-infinite elastic halfspace: compression (or P-

waves), shear (or S-waves), surface or Rayleigh (R-waves), and Love waves (L-waves). The P- and S-waves are termed as body waves and they are the most commonly-utilized terms in geotechnical site

characterization. The other two types are special types of hybrid compression/shear waves that occur at

the free boundary of the ground surface (R) and soil layer interfaces (L).

S-wave velocity is one of the key parameters in construction engineering. For example, Imai and

Tonouchi (1982) studied P- and S-wave velocities in an embankment and also in alluvial, diluvial, and

Tertiary layers, showing that S-wave velocities in such deposits correspond to the N-value (Craig, 1992),

an index value of the formation hardness used in soil mechanics and foundation engineering (Xia et al.,

1999).

In this research, S-wave velocities are calculated by correlation formulas between the number of SPT,

NSPT, and the velocity of shear wave. Using empirical relations and with the aid of computationalmodeling, explained in next the sections of this paper, the amplification ratio of the site has been

estimated.

Calculating the velocity of shear wave fromSPT

N

Several researches have been conducted to find a relation between VS and NSPT. Considering 192

samples, Imai and Yoshimura (1975) presented an empirical correlation between the velocity of shear

wave and some properties of the soil. Iyisan (1996) reported the similarity in values of VS obtained from

the number of SPT by the available correlations for soils, except gravels. As an alternative solution,

instead of using average interpolated relations and after studying 327 data set related to different regions

of Turkey, Ulugergerli and Uyanik (2007) proposed two equations for upper and lower bound values ofVS with respect to NSPT.

Many other correlations have been proposed between VS and NSPT, some of which are indicated in

Table 5. (Ohba and Toriuma, 1970; Ohta and Goto, 1978; Seed and Idriss, 1981; Okamoto et al., 1989;

Lee, 1990; Kanai, 1996; Pitilakis et al., 1999; Kiku et al., 2001; Tamura and Yamazaki, 2002; Hasancebiand Ulusay, 2006 and Dikmen, 2009)

In this research two relationships suggested by Ohta and Goto (1978) and Tamura and Yamazaki

(2002) in which the effect of depth has been taken into account are chosen for calculation of VS in order

to study the Karaj alluvium. Although the investigation of results show a small overestimation by the

relationships proposed by Tamura and Yamazaki (2002), no significant difference can be inferred

between the two equations and the variance has not been more than 10m/s.

Fig. 5 depicts the small difference between the results of these two relationships in depth of 30

meters. Finally, both groups of the results have been employed to estimate the velocity of shear wave in

Karaj alluvium. If the Karaj formation is to be classified based on IS-2800 (2002), as the V S varies

between 175 m/s to 375 m/s, it must be categorized as a formation of degree 3 . However, according to

NEHRP (2003), since the VS in study area differs from 180 m/s to 360 m/s therefore the site will be of

Class D.


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Table 5: Some correlations had been demonstrated

Researchers Equation

Imai and Yoshimura (1975)33.076NV

s=

Ohba and Toriumi (1970)31.084NV

s=

Ohta and Goto (1978)* 212.017.0

69 FFDNVs =

Okamoto et al. (1989)3.0125NV

s=

Tamura and Yamazaki (2002)179.0187.08.105 DNV

s=

Hasancebi and Ulusay (2006)309.090NV

s=

Dikmen (2009)39.0

58NVs=

*:1

F and2

F depend to soil type and D is depth in meters

Figure 5: Shear wave velocity estimated at depth 30 meter

Estimation of amplification ratio by empirical equations

Based on the previous researches, the velocity of shear wave in surface layer is an appropriate

parameter for calculating the amplification ratio of the site. Shima (1987) showed that estimated

amplification ratio has a linear relationship with the ratio of VS for surface layer to the VS of bedrock.

After investigation of many earthquakes, some researchers have demonstrated an agreeable consistency

for a certain depth between the average VS in surface layer and amplification ratio (Brocherdt et al., 1991;Midorikawa 1987).

In this research, two empirical relationships between VS and the amplification ratio, presented by

Brocherdt et al. (1991) and Midorikawa (1987) and recommended by TCEGE (1999) are employed

(Equations (1-1) and (1-2) are proposed by Brocherdt et al., 1991 while equations (2-1) and (2-2) have

been presented by Midorikawa, 1987).

330

340

350

360

370

380

390

400

410

0 10 20 30 40 50SPT-N

Shearwavevelosity(m/s)

Ohta and Goto (1978)

Tamura and Yamazaki (2002)


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sVAHSA 701=

Low strain data 1-1

sVAHSA 598= Loma Prieta strong-motion 1-2

6.0

68

=s

VA

smVs

1100 2-2

In the above equations, VS is the average velocity of shear wave (m/s) 30 meters closed to the surface,

A is the amplification ratio for maximum velocity of ground and AHSA is the average horizontal

spectrum amplification in periods between 0.4 and 2.0 seconds. The average velocity of shear wave, V s,

has been calculated in depth of 30m by equation (3) proposed by NEHRP (2003).

=

== n

isii

n

ii

s

Vd

dV

1

1

(3)

where Vs is the velocity of shear wave, id is the thickness of ith layer of soil and Vsi is the velocity of

shear wave in related layer.

Taking notice of the fact that the calculated V s by equation (3) is smaller than 1100 m/s in all parts of

the study area, the equation (2-1) has been employed for determination of the amplification ratio. Also

since the probable earthquakes in this research are assumed to be strong shakes (M>7), equation (1-2) has

been designated. After fulfilment of the calculations, the amplification ratio obtained by the equations (1-

2) and (2-1) are found to be within the ranges of 2.19 to 2.72 and 1.95 to 2.82, respectively. In most cases,

the calculated results from the two equations have been close to each other.

Estimation of amplification ratio based on one-dimensionalanalysis of the ground response

Analytical method employed in this research is based on one-dimensional equivalent-linear modeling

of the soil layers. Numerical simulation has been implemented by a computer code developed for this

purpose.

Main assumptions in one-dimensional analysis of the ground response are as follows:

1. Movement of shear waves is considered vertical to the soil layers.

2. Boundaries of layers are all assumed to be horizontal.

3. Surface of the soil and bedrock are assumed to be laterally infinite.

Based on this method, the amplification frequency is mainly dependant upon the geometry (thickness)

and material properties (Vs). Description of applied method is presented in Fig. 6 for one-dimensional

analysis of site response. One advantage of this algorithm is namely its ability to determine the

transformation function in a desired frequency for amplification or damping of passing waves through the

soil (Kramer, 1996). Accepted assumptions of this function in current research are associated with the

stratus of the soil damping on elastic bedrock. The situation of the considered structure with one degree of


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freedom and layering of the soil are demonstrated in Figs. 7 and 8. In these figures G is the shear

modulus, D is damping ratio, is the shear strain and is the rate of shear strain.

Although G and D vary during the earthquake (Ishihara, 1996) and thus the response of the soil will

be non-linear, in this method the shearing modulus (G) and damping of soil (D) are considered to be

constant, yet to overcome this weakness, equivalent linear method has been applied in order to determinethe properties of the soil in one-dimensional analysis of the ground response. The whole procedure is

illustrated in an algorithm shown in Fig. 9. To perform calculations of the equivalent linear method

(Estimation of new G and D with respect to the shear strain), charts of 0G G versus proposed by Sun

et al. (1988) for clays and those presented by Seed and Idriss (1970) for sand and gravel as well as curves

ofD against suggested by Idriss (1990) for clays, gravel and the sand have been applied, one of which

is shown in Fig. 10 as an example.

Dynamic properties of the soil are determined by above-mentioned charts ( 0

GG D ).

Specific gravity of the soil is calculated based on the experimental data and velocity of shear wave is

obtained using mentioned equations in previous sections of this article. These data constitute the input of

the employed computer code. Applying seismic loads to the bedrock and performing calculations, output

of computer code has been recorded for further study.

Figure 6: Employed algorithm for one dimensional analysis of ground response

Specifying soils reduction function based on

response reduction function of systems with

ingle degree of freedom

Changing the displacement history of bedrock to

Fourier series by FFT

Multiplying each part of Fourier series of bedrockdisplacement by reduction function. Result is

displacement Fourier series of ground surface.

Changing the displacement Fourier series into

displacement history by IFFT


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Figure 7: One degree of freedom model used for simulating of soil behavior

Layer Properties Thickness

1111

,,DG 1

h

2222

,,DG

. . .

. . .

. . .

NNNN

DG ,, N

h

Figure 8: Schematic soil stratification employed for one dimensional analysis of gound response


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Figure 9: Employed algorithm for modeling of equivalent linear behaviour of soil

Figure 10: Dynamic properties of soil used for equivalent linear modeling of soil behaviour

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1 10

Shear Strain (%)

G/Gmax

0

5

10

15

20

25

30

DampingRatio(%)

Shear Modulus (sun et al., 1988)

Damping Ratio (Idriss, 1990)

Estimating first G andD for each soillayer ( for low strains)

Calculating ground response (shear strain history) based on estimated

G andD

Specifying effective shear strain for each layer ( details are available

in Kramer (1996) )

Estimating new values for

Gand

Dbased on effective shear

strain specified in last stage

Difference between new

G andD , and last G andD is less than a

desired value

Finish


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Seismic load used in the current research has been the real earthquake occurred in Manjil and Rudbar

at 21:00 on June 20, 1990 with the magnitude of 7.3 and maximum horizontal acceleration of 0.6g,

recorded in Qazvin accelerograph station. The reason for selecting this earthquake has been the similarity

between functionality of its originating fault with the chief faults near Karaj as well as Qazvin

accelerograph station situated at quiet neighbourhood of the study area. Fig. 11 shows the accelerogramof the mentioned earthquake. This technique is accepted by the TCEGE (1999) as a Grade-3 method for

investigation of the site effects. Grade-3 method considers the effect of the site through using

geotechnical data gathered from the site and available analytical and numerical techniques.

Figure 11: Accelerogram of earthquake used in this research

Amplification ratios obtained in this research vary between 1.83 to 3.4 values. Amplification ratios

against fluctuations and the response spectrum for three damping ratios of 0, 0.5 and 10 percent in BH122

borehole are depicted in Fig. 12. Contours shown in Fig. 13 illustrate the variation of amplification ratios

in study zone. The obtained results from empirical equations and computational modelling are

demonstrated in Fig. 14 for some boreholes which reveal the relative harmony between the two methods.

Figure 12: Amplification ratio and response spectra for BH122

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 10 20 30 40

Time (sec)

Acceleration(g)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 5.00 10.00 15.00 20.00 25.00

Frequensy (Hz)

Amplificationratio

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.01 0.10 1.00 10.00

Period(s)

Spectralacceleration(g)

0% damping

5% damping

10% damping


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Figure 13: Amplification ratio values Estimated with computer code in study area

Figure 14: Comparison of amplification ratios in study area

Period of the site

To determine the main period of the site, as previously applied by Hasancebi and Ulusay (2006) in

their own research, the frequency of amplification or the frequency in which maximum amplification

ratio occurs is gained and then the period of considered soil column has been calculated by the following

equation:

1=T (4)

where T is the period of the site in seconds, s, and is the frequency in Hz. Since the frequency of

amplification in most parts of the study zone lies in the range of 1.2 to 1.4 Hz, the period calculated by

equation (4) will naturally be limited to 0.71 and 0.83 s which does not differ a lot with suggested period

for the sites of degree 3 as recommended in second edition of IS-2800 (2002). Fig. 15 shows variations of

the period as contours for the study area.

0

0.5

1

1.5

2

2.5

3

3.5

4

3 14 21 34 48 57 65 72 81 93 100 108 117 126

Borehole number

Amplificationratio

Software

Empirical (Brocherdt et al.,1991)

Empirical (Midorikawa et al., 1987)


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Figure 15: Period values at study area

In order to determine which types of building would be better to avoid in each district, firstly an

attempt has been made to divide the study area into four zones based on their period. But because of

observing the small variations in the period (0.71-0.83) the study area has been divided into two zones,

both of which are shown in Fig. 16. The periods of the first zone vary somewhere between 0.71 to 0.77

seconds and the periods relating to the second zone vary between 0.77 to 0.83 s.

Figure 16: Classified zones based on site period


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Using the suggested methods by IS-2800 (2002) and NEHRP (2003), the type and height of the

buildings which to be avoided in these two districts are determined. The indicated formulas in the

mentioned codes and limitations for height of the buildings relating to each zone are noted in Table 6.

Table 6: Equations for determination of buildings period by IS-2800 (2002) and NEHRP (2003) andheight limitations in study area

Standard Building type Period EquationZone 1

(height (m))

Zone 2

(height (m))

NEHRP (2003)

Steel frame 8.00724.0 hT= 17-19.5 19-21

Concrete frame 9.00466.0 hT= 20.5-22.5 22-24.5

Braced 75.00731.0 hT= 20.5-23 23-25.5

Other 75.00488.0 hT= 35.5-39.5 39-44

IS-2800

(2002)

Steel frame 75.008.0 hT= 18-20.5 20-23

Concrete frame 75.007.0 hT= 22-24.5 24-27

Other75.0

05.0 hT= 34-38.5 38-42.5

Generally if the buildings are classified into three groups of 1-5, 5-10 and 10-15 story buildings, as

schematically shown in Fig. 17, it will be inevitable to accept a limited period in each zone for

constructing safe buildings. Table 7 shows the available regulations for the buildings based on two codes

of IS-2800 (2002) and NEHRP (2003). If the buildings period does not lie between 0.69 and 0.79 seconds

in zone 1 and between 0.75-0.85 seconds in zone 2, there would be no limitation for such buildings,

hence, they are presented as OK in Table 7.

Table 7: Classification of buildings based on their height in study area

Standard Building type Zone 1-5Stories

5-10Stories

10-15Stories

NEHRP

(2003)

Steel Frame1 OK - OK

2 OK - OK

ConcreteFrame

1 OK - OK

2 OK - OK

Braced1 OK - OK

2 OK - OK

Other1 OK OK -

2 OK OK -

IS-2800(2002)

Steel Frame1 OK - OK

2 OK - OK

ConcreteFrame 1 OK - OK2 OK - OK

Other1 OK OK -

2 OK OK -


18/22

Vol. 15 [2010], Bund. G 756

Karaj (Alvand)Karaj (Danesh Amouz)

Karaj (Leylestan)

A: 1 5 Story Buildings B: 5 -10 Story Buildings C: 10 15 Story Buildings

Figure 17: Schematic presentation of building height classification (a) 1-5 stories, (b) 5-10 stories and (c)

10-15 stories


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- 757 -

CONCLUSION

In the present study, the available formulas betweens

V andSPT

N proposed by previous researchers

were firstly reviewed and consequently the relationships suggested by Ohta and Goto (1978) and Tamura

and Yamazaki (2002) were chosen for further investigations. The study site was then classified based on

the values ofsV obtained by these equations, resulting in the site to be classified as degree 3, based on

IS-2800 (2002) and D class according to NEHRP (2003).

The amplification ratio of the study site has been investigated by the empirical equations as well as

numerical modelling with the aid of computer code for one-dimensional analysis of the ground response,

assuming equivalent linear behaviour for the considered soil. The results of calculations proved that the

range of amplification ratio for the site varies from 1.83 to 3.40. Period of the site has been determined

based on the frequency of amplification and was shown to be in the range of 0.71 to 0.83s. Finally

according to achieved periods for the study site and periods of different buildings mentioned in Is-2800

(2002) as well as NEHRP (2003), the study area has been classified with respect to the type and height of

the structures. Overall procedure followed throughout the current research is demonstrated as an

algorithm in Fig. 18.


20/22

Vol. 15 [2010], Bund. G 758

Figure 18: General algorithm used for this research

Perform in situ and laboratory tests,

specially SPT

Specify the relation between shear wave

velocity and SPT-N, and specifys

V inresearch area

Classifying the investigated site based on the values ofs

V andintervals of each site grade suggested by Iranian 2800 standard

andNEHRP(2003)

Selecting the relationships between amplification ratio and shear

wave velocity for 30(m) layer, and estimating the amplification

ratio in researched site

Estimating amplification ratio by use of 1-D analysis of site

response and based on equivalent linear behaviour of soil, with

software, and showing the results on a map

Estimating site period based on resonance frequency

Grading structures based on their

height, and specifying the

limitations ofeach grade in site

based on buildings and site period

Site grading based on site

period, and specifying the best

buildingsin each site grade based

on their period


21/22

- 759 -

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Documents

Amplification Ratio and Period of the Earthquakes in Karaj,Iran