STATE OF THE ART

IN CRITERIA FOR EARTHQUAKE-RESISTANT

DESIGN IN BUILDINGS:

AN APPLICATION TO THE PRINCIPAL CITIES IN

UPPER EGYPT

Submitted By

Dr. Raafat El-Shafei Fat-Helbary

In partial fulfillment of the requirements for the

Degree of Professor of Applied Seismology

National Research Institute of Astronomy and Geophysics

Earthquake Department

Egyptian National Seismic Network Lab.

Helwan, Cairo, Egypt

March 2006

i

TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1.1. MOTIVATION AND STEPS .........1 CHAPTER 2: SEISMIC HAZARD ASSESSMENT 2.1. INTRODUCTION . ....... .3 2.2. DETERMINISTIC METHODOLOGY.........5 2.3. PSHA METHODOLOGY...........5 2.3.1. Seismic Source Model......7 2.3.2. Earthquake Occurrence Model.....8 2.3.3. Ground Motion Attenuation Model......9 2.3.4. Probabilistic Seismic Hazard Model..10 2.4. CASE STUDY OF SEISMIC HAZARD IN UPPER EGYPT........................................................13 2.4.1. Method........13 2.4.2. Earthquake Source Geometry.....14 2.4.3. Maximum Earthquake Magnitudes....14 2.4.4. Earthquake Recurrence Rates. ...14 2.4.5. Ground Motion Attenuation Model .......15 2.4.6. Expected Maximum Acceleration at Surface Layers.....16 CHAPTER 3: ASSESSMENT AND MITIGATION OF SEISMIC RISK 3.1. INTRODUCTION..........18 3.2. VULNERABILITY ASSESSMENT.........19 3.2.1. Vulnerability Index Assessment.....20 3.2.2. Proposed Vulnerability Functions......23 3.2.3. Damage Evaluation....23 3.2.4. Damage Probability Matrices.........24 3.2.5. Damage Models and Vulnerability Function.25 3.2.6. Loss Function Estimation...........26 3.2.7. Monetary Losses.....27 3.2.8. Human Losses....28 3.3. CASE STUDY OF ASSESSMENT OF SEISMIC RISK IN ASWAN CITY (UPPER EGYPT)....30

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CHAPTER 4: LOCAL SITE EFFECTS AND DESIGN GROUND MOTIONS 4.1. INTRODUCTION......40 4.2. EFFECT OF LOCAL SITE CONDITIONS ON GROUND MOTION.....41 4.2.1. Ground Response Analysis....41 4.2.2. Transfer Function for Layered, Damped Soil on Elastic Rock..43 4.3. CASE STUDY OF GROUND-RESPONSE ANALYSIS IN UPPER EGYPT......46 4.3.1. Input Data.......48 4.3.2. Calculated Ground Response.........51 CHAPTER 5: SEISMIC CODE OF BUILDINGS 5.1. INTRODUCTION......56 5.2. EGYPTIAN CODE OF BUILDINGS......58 5.2.1. Seismic Loads....58 5.2.2. Scope and General Fundamentals......58 5.2.3.1. Lateral design forces.........61 5.2.3.2. Distribution of lateral force..63 5.2.4. Response Spectra Method......64 5.2.5. Dynamic Response Method...64 5.2.6. Torisonal Moment......65 5.2.7. Lateral Displacement and Joints........65 REFERENCES......66

CHAPTER 1

INTRODUCTION

1

CHAPTER 1

INTRODUCTION

1.1. MOTIVATION AND STEPS:

Most hazards generated by earthquakes are directly related to the

shaking of ground caused by the passage of seismic waves. The rapid

movement of building foundations during an earthquake generates inertial

loads, that can lead to damage and collapse, which are the cause of the vast

majority of fatalities due to earthquakes. The basis for earthquake-resistant

design of buildings requires quantitative assessment of the ground motion,

that may be expected at the location of the project during its design life.

Hazard maps in terms of peak ground acceleration (PGA) are the basis of

zonation maps included in seismic design codes. For this reason, the main

focus of chapter 2, in the state of the art is seismic hazard assessment and

its application to the Aswan area in Upper Egypt.

Seismic risk at a particular location is widely understood as the

convolution of seismic hazard (the possibility of ground shaking or

collateral geotechnical hazard) with exposure (number of buildings and

people in the area) and vulnerability (the lack of seismic resistance in

buildings). Seismic hazard can generally be quantified but not altered,

hence the focus of earthquake risk mitigation is generally on engineering

measures to increase the seismic resistance of buildings, and hence to

reduce its vulnerability. However, it is also possible to reduce the level of

seismic risk by reducing the product of hazard and exposure, for example

by relocating settlements to areas of lower seismicity. In chapter 3, a brief

overview of seismic risk analysis and its application to four different types

of buildings constructed in Aswan city, as the case study is presented.

Local site effects play an important role in earthquake-resistant

design, and must be accounted for a case-by-case basis. This is usually

2

accomplished by the development of one or more design ground motions

(i.e., motions, that reflect the levels of strong motion amplitude, frequency

content and duration that, a structure or facility at a particular site should be

designed for). Number of research works related to the study of local site

effects and ground response analysis in different areas in Upper Egypt such

as: the proposed site of El-Kiefl Dam at the fourth Tushka depression,

proposed site of Tushka barrage on Tushka spillway canal and proposed

location of Aswan new city on the west bank of the River Nile are done. In

this state of the art, the study of local site effects and ground response

analysis of the proposed location of Aswan new city is presented as case

study in Chapter 4.

Finally the seismic code of buildings and regulation for earthquake-

resistant design of building in Egypt are summarized in chapter 5.

CHAPTER 2

SEISMIC HAZARD ASSESSMENT

3

CHAPTER 2

SEISMIC HAZARD ASSESSMENT

2.1. INTRODUCTION:

The seismic hazard analysis refers to the estimation of some measure

of the strong earthquake ground motion expected to occur at a selected site.

This is necessary for the purpose of evolving earthquake resistant design of

a new structure or for estimating the safety of an existing structure of

importance, like dams, nuclear power plants, long-span bridges, high-rise

buildings, etc. at the site. In earthquake engineering and related areas, it is

customary to distinguish between earthquake hazard and earthquake risk,

although the semantic of these two words are the same. Earthquake hazard

is used to describe the severity of ground motion at a site (Anderson and

Trifunac, 1977a, 1977b and 1978a), regardless of the consequences, while

the risk refers to the consequences (Jordanovski et al., 1991 and 1993).

By taking into account all the available database on seismicity

tectonics, geology and attenuation characteristics of the seismic waves in

an area of interest, the seismic hazard analysis is used to provide an

estimate of the site-specific design ground motion at the site of a structure

(Dravinski et al., 1980 and Westermo et al., 1980). One important

application of hazard analysis is the preparation of seismic zoning maps for

generalized applications (Lee and Trifunac, 1987, Trifunac, 1989a and

1990a and Anderson and Trifunac, 1977a, 1977b, 1978a and 1978b). By

estimating the amplitudes of a parameter describing ground motion or the

earthquake effect at a closely spaced grid of sites covering the complete

area of a big city or an entire state, zoning maps can be developed by

contouring the sub-areas with equal hazard. Such maps are useful for

applications in the earthquake-resistant design of common types of

structures, for which it is not possible to carry out the detailed site-specific

4

studies. The zoning maps are also useful for land-use planning, assessing

the needs for remedial measures, and estimation of possible economical

losses during future earthquakes (Trifunac, 1989b and Trifunac and

Todorovska, 1998).

The seismic hazard at a site can be described by a variety of

parameters of ground shaking. Before the actual instrumental

measurements of strong ground motions became available, various

intensity scales (MMI, MKS, etc.) based on the description of observed

damages were used to describe the severity of ground motion. Intensity

data are (and should be) still used as a supplement to the instrumental

recordings. Mores recently, peak ground acceleration, and to a much lesser

extent the peak velocity and displacement, had been popular instrumental

measurements of ground motion. Most of the existing code provisions, and

design procedures have been developed in terms of peak acceleration and a

normalized standard spectral shape (IAEE, 1984). However, to account for

the effects of earthquake magnitude and distance on the spectral shape, one

should define directly the spectral amplitudes at different frequencies by

using the frequency-dependent scaling equations for the spectral

amplitudes (Lee, 1987). For the seismic zoning one should thus prepare a

separate zoning map in terms of the response spectrum amplitude at each

frequency (Trifunac, 1989a and 1990a). In addition, there may be other

derived parameters like peak strain or liquefaction potential, for example,

to quantify the seismic hazard and preparation of zoning maps (Todorovska

and Trifunac, 1996a, 1996b and 1999).

There are two basic philosophies for the seismic hazard analysis,

viz., deterministic and probabilistic. The former proposes design for the

maximum earthquake, that is the one that will produce most severe ground

motion at a site. The latter advocates that, likelihood of occurrence should

also be considered in view of the fact that, the life of a structure is very

5

short compared to the recurrence intervals of large events. The first basic

step in seismic hazard analysis is to collect the input data on tectonic,

seismicity and ground motion scaling models. One should then decide the

methodology of hazard analysis, which may be deterministic (scenario

earthquake) or probabilistic (an ensemble of earthquakes). The hazard may

be characterized in terms of a variety of ground motion parameters (e.g.,

peak amplitudes, duration of shaking, Fourier and response spectra,

differential motions, artificial time histories, etc.) or the effects of ground

shaking on structure (displacement, shear and bending moment envelopes)

and site response (liquefaction occurrence, slope stability, permanent

displacements, etc.). However, the present study addresses mainly the issue

of estimating the strong-motion parameters of interest for earthquake-

resistant design and seismic safety assessment purposes.

2.2. DETERMINISTIC METHODOLOGY:

The deterministic approach for seismic hazard analysis is not well

documented in literature, and it is practiced differently in different parts of

the world and even in different application areas. In its most commonly

used form, the deterministic method first assesses the maximum possible

earthquake magnitude for each of the seismic sources (important faults or

seismic provinces) within an areas in circle shapes of about 300 km radius

around the site of a structure of interest. Then, by assuming each of these

earthquakes to occur at a location, that places the focus at the minimum

possible distance to the site, the ground motion is predicted by using an

empirical attenuation relation or some other appropriate technique.

2.3. PSHA METHODOLOGY:

The probabilistic seismic hazard methodology involves integrating

the probabilities of experiencing a particular level of a selected strong

motion parameter due to the total seismicity expected to occur in the area

(in circle shapes about 300 km radius) of a site of interest during a

6

specified life period (Cornell, 1968 and Anderson and Trifunic, 1977a,

1977b and 1978a). This approach is able to consider the inherent random

uncertainties and scattering present in the input database as well as in the

attenuation characteristics of ground motion parameters (Lee and Trifunac,

1985 and Gupta, 1991). It is thus able to provide the estimate of ground

motion with a specified confidence level (probability of not exceeding).

The probabilistic approach is convenient to compare risks in various parts

of a country, and to compare the earthquake risk with other natural and

man-made hazards. For example, the design loads should be such that the

risk of damage is equal through out the country, and that it is comparable to

other risks that, we are prepared to take (e.g., risk of a traffic accident, or a

plane crash, or damage from floods and cyclones). The probabilistic

approach opens the possibility for risk-benefit analysis and respective

design motions. The motivation for such a design principle is that, at the

time of construction or strengthening, if it is invested in strength beyond

that required just to prevent collapse (e.g., by codes), the monetary losses

during future likely earthquakes may be reduced significantly.

The main idea of the probabilistic seismic hazard analysis (PSHA) is

to estimate the probability that, a certain peak ground acceleration (PGA)

will be exceeded during a known period of time at a certain site.

Achievement of this idea involves the development of four constituent

models (Algermission et al., 1975). These are: (1) a seismic source model,

that defines the spatial distribution of earthquakes within the region of

concern (Fig. 2.1A), (2) an earthquake occurrence model, that describes the

recurrence of events in time within the seismic source zones (Fig. 2.1B),

(3) a ground-motion attenuation model, that describes mathematically the

manner in which earthquake ground motions decrease with distance from

an earthquake source for various magnitude levels (Fig. 2.1C), and (4) a

probability model for calculating the expected maximum amplitude of

7

ground motion within a given period of time corresponding to a chosen

probability level for a number of individual sites in the region and the result

is shown in figure (2.1D).

Fig. (2.1): Elements in the seismic hazard method (after Algermission et al., 1975). 2.3.1. Seismic Source Model:

Based on geological evidence, geotectonical province, historical

seismicity, geomorphic investigation and any other subjective input,

seismic sources can be identified and modeled as line source, area source

and point source. In fact, the numerical computation of the seismic hazard

at the site is carried out by dividing the line and area sources into a number

8

of discrete point sources. The line source is used to model faults or fault

provinces. In a geographical region, where recorded earthquakes can not be

related to any well-defined fault system, the concept of seismotectonic

provinces is invoked, and the region is represented by a set of area sources,

or seismogenic zones. A source, whether a line source or an area source, is

distinguished by a uniform seismic activity; that is, the mean rate of

earthquake occurrence per unit length or unit area is constant over the

entire source. The seismic sources around a site are identified by studying

the epicentral locations of past earthquakes together with the geologic and

geomorphologic features of the site region. The inclusion of a source in the

hazard model depends on its contribution to the seismic hazard, which, in

turn, depends on the activity rate, the upper-bound magnitude or epicentral

intensity and the distance to the site

2.3.2. Earthquake Occurrence Model:

For each seismic source, the magnitude distribution was taken to be

exponential and of the form given in the Gutenberg-Richter relation of

occurrence frequencies (Gutenberg and Richter, 1965) (Fig. 2.1B):

log Nm = a - bm (2.1)

where, Nm is the number of earthquakes in a given time period having

magnitude greater than m; (a) and (b) are constants to be determined. The

parameter a depends on the level of seismicity, the length of time taken into

account and the extent of an area (Miyamura, 1962). The parameter (b)

depends on the ratio between the number of large events, and the number

of small events, and is very important as it has some association with

several important problems in seismology such as earthquake predictions

and stress generating in focal region.

If equation (2.1) is expanded to include an upper-bound as well as

lower-bound magnitude, the relationship becomes nonlinear at large

magnitudes. From equation (2.1), we can derive a probability density

9

function, that gives the probability that, if an earthquake occurs, it will be

of magnitude m. Incorporating minimum and maximum magnitudes mo

and m1 (EERI, 1989), this is the truncated exponential distribution of

earthquake magnitudes :

fM(m) = K e- b(m-m )o mo < m < m1 (2.2)

where: K = [1- e (m m )o1 ]-1

where, = b ln(10), K is a normalizing constant, and m1 is the earthquake thought to be the largest, that can occur in that source. Earthquakes larger

than m1 are excluded from the analysis, so the choice of m1 will have a

direct impact on low-probability assessments of hazard and risk. For fault

sources, m1 is often estimated from empirical correlation between

magnitude and rupture length (e.g. Bonilla et al., 1984). For area sources,

its determination is more problematic.

2.3.3. Ground Motion Attenuation Model:

An important aspect of the probabilistic ground-motion mapping

procedure is knowing how the ground motion produced by an earthquake is

modified by transmission from source to site (Fig. 2.1C). A research has

shown that, much of the variability in estimates of peak ground motion is in

attenuation models (Bender, 1984 and McGuire and Shedlock, 1981).

Attenuation is the decay in the amplitude of earthquake ground motion

parameters (e.g. peak ground acceleration, spectral velocity, peak

displacements and peak spectral content). The main factors affecting

attenuation are the source conditions, the transmission path characteristics,

and the local site conditions (Chung and Bernreuter, 1981). In general, the

attenuation model is an expression of the change of the ground motion

parameters with distance (R) at a certain magnitude (M). Attenuation

model is typically developed by applying statistical regression analyses to

10

data recorded by a strong-motion instrument, or derived from such

recordings, such as acceleration, velocity and displacement time series.

The most common formula is represented by the attenuation

relationship of the forms:

Y= b1 eb m2 (+r) b 3 (2.3) where

Y: Ground motion parameter of interest (such as

acceleration (a), velocity(v), or displacement (d) ).

b1, b2 and b3: Constants derived from regression analysis.

: Hypocentral distance. r : Constant for a given data source region.

Whenever strong motion data are not available, intensity attenuation

relationship is considered, such as a common assumption (Ipek et al., 1965,

Wiggins, 1964 and Kanai, 1961) that in the range of interest the intensity

(I) has the following dependence on magnitude (M) and focal distance ( R):

I = c1 + c2M - c3 Ln (R+r) (2.4)

where, c1,c2 and c3 are empirical constants.

2.3.4. Probabilistic Seismic Hazard Model:

The two models, most widely used in probabilistic forecasting of

earthquake occurrences, are the Poisson and Markov models. The Poisson

model characterizes events, that are independent and form a memoryless

process. In the Markov process, the occurrences of events in the future

depend on the occurrences of events in the past.

I. Poisson model of seismic occurrences:

For earthquake events to follow the Poisson probability law, the

following assumptions must be valid:

1. Earthquakes are space independent phenomena.

2. Earthquakes are time independent processes.

11

3. Probability of two earthquakes occurring simultaneously in the same

place is nil.

In principle, these assumptions are quite realistic and physically

match the phenomenon of earthquakes very well. The general term of

Poissons law is:

Pn (t) = e t)

n!

- n t ( (2.5) where, P n (t) = the probability of having n events in time period (t).

n = the number of events.

= mean rate of occurrence per unit time. II. Concept of return period:

Once the seismic activity rate per unit area or per unit length of fault

is determined for the seismic source zones of the region, and a ground

motion attenuation function is decided upon, a distribution of ground

motion is calculated for a number of individual sites located on an

appropriate grid pattern throughout the region (Paul, et al., 1989).

The relationship between return period (R y (a)), exposure time (T)

and probability of exceedance during that exposure time (1-Fmax,t(a)) is

explained by the following development.

First, the distribution of the expected number of occurrences of

ground motion at each location is calculated. The peak ground motion, for

example, the peak acceleration corresponding to some extreme probability,

is then calculated from the distribution of the expected number of

occurrences in the following manner. Let the peak acceleration to be (a),

then

F(a) = P[A a m mo ] (2.6) The probability (F(a)) that, an observed acceleration (A) is less than or

equal to the value (a), given that an earthquake with magnitude (M), greater

12

than some minimum magnitude of interest, has occurred. The calculation is

performed for every acceleration (a) of interest as follows:

F(a) =)ms(moccurrence expected ofnumber Totalmm and aA soccurrence expected ofNumber

o

o

(2.7)

F(a) is the probability that, the acceleration value (a) will not be exceeded,

given that an earthquake larger than minimum magnitude occurs in the

source zone. Therefore (1-F(a)) is the probability that, (a) will be exceeded.

The return period (R(a)), which is interesting from engineering

viewpoint, represents the average number of events, that must occur to get

an acceleration exceeding (a), and can be calculated by formula :

R y (a) = 1

1 F(a) (2.8)

The return period in years is given by:

R y (a) = R(a)

Expected number of events per year (M M ).min (2.9)

The cumulative distribution of the maximum acceleration of the N

accelerations is given (Algermissen, et al., 1975), if N has a Poisson

distribution with mean rate () as: Fmax (a) = e- (1-F(a)) (2.10)

If = t, where is the mean rate per year and t is the number of years in a period of interest, then:

Fmax,t (a) = e- t(1-F(a)) (2.11)

From (2.10) and (2.11):

t(1-F(a)) = taR ( )y

(2.12)

thus, from equations (2.11) and (2.12), the relationship between any

extreme probability and the corresponding return period can be represented

as:

Fmax,t (a) = e t/ ( )R ay (2.13)

13

and

ln (Fmax,t(a)) = tR (a)y

(2.14)

2.4. CASE STUDY OF SEISMIC HAZARD IN UPPER EGYPT:

A probabilistic seismic hazard analysis was conducted for assessing

the ground motion at 19 selected sites in the proposed Aswan new city area

(Fat-Helbary et al., 2004b). The objective of the analysis was to evaluate

the probability of exceedance of different levels of ground motion due to

earthquakes, that may occur in and around the proposed Aswan new city

area.

All data relating to known earthquakes with magnitude 3.0 around

Aswan new city site are collected and analyzed. This analysis includes:

1. All significant seismic sources in the area are identified.

2. For each seismic source, the rate of earthquakes at different

magnitudes is determined by a statistical analysis on all data related

to that source.

2.4. 1. Method:

For this work the Cornell approach (Cornell, 1968) was applied. In

this approach the fundamental elements, that enter into a seismic hazard

analysis, are arranged as in following steps:

1. Identification of the regional earthquake source zone model, that defines

the spatial distribution of earthquakes within the region of concern,

2. Assessment of maximum earthquake magnitudes and earthquake

occurrence model, that describes the recurrence of events in time within the

seismic source zones,

3. Selection of relationships of ground motion attenuation model, that

describes mathematically the manner in which earthquake ground motions

decreases with distance from an earthquake source for various magnitude

levels,

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4. Calculation of the probability of the expected maximum amplitude of

ground motion within a given period of time corresponding to a chosen

probability level for a number of individual sites in the region using inputs

from (1), (2) and (3) above.

2.4.2. Earthquake Source Geometry:

The Cornell method requires the seismicity of the region under

consideration to be divided into spatially distinct earthquake source zones.

Based on the spatial distribution of the catalogue of earthquake data for the

period from 1900 to 2003, the seismicity around Aswan new city area has

been modeled as 6 source zones significant to the studied area as shown in

figure (2.2).

2.4.3. Maximum Earthquake Magnitudes:

One of the most controversial and important variables in representing

a source of seismicity is the size of the maximum credible earthquake. In

this study for each seismic source area, the cutoff magnitude is taken to be

the observed maximum magnitude known for the source plus 0.5 (Al-

Hadad et al., 1992).

2.4.4. Earthquake Recurrence Rates

An earthquake occurrence model describes the recurrence of events

in time within each seismic source zones. A linear regression analysis was

carried out to estimate the coefficients of Gutenberg-Richters relationship

between magnitudes and their cumulative frequency of occurrence, i.e.,

Log Nm = a bm (2.15)

where, Nm is the number of earthquakes in a given period having

magnitude greater than or equal to m. The program used for this purpose is

the ESA program (Ahmed, 1991). The rate of occurrence at the minimum

magnitude as well as the value [ = b Ln (10)] are given in Table (2.1).

15

2.4.5. Ground Motion Attenuation Model:

Ground motion attenuation model describes mathematically the

manner in which earthquake ground motions decrease with distance from

an earthquake source for various magnitudes. Attenuation model developed

from peak ground acceleration for Aswan area (Fat-Helbary, 1995) was

used.

Ln A = 1.895 mb 0.938 Ln () 3.715 ( = 0.558) (2.16)

where, A represents the peak ground acceleration in cm/s2 , mb is the body

wave magnitude and is the hypocenteral distance in km. The residuals of

this equation are log normally distribution with standard deviation ()

0.558.

26 27 28 29 30 31 32 33 34 35 36 37

Longitude

22

23

24

25

26

27

28

Latit

ude

Aswan New City

(1)

(2)

(3)

(4) (5)

(6)

0 75 150 km

Fig. 2.2. Epicentral distribution of the catalogued events in the period from 1900 to 2003 and the significant earthquakes source zones to Aswan new city site (after Fat-Helbary et al., 2004b).

16

Table (2.1): Parameters of seismic recurrence curve for each source.

Source No.

Mag. (mb)

No. of events

Occurrencerate ()

Average depth

A1 5.3 36 1.441 0.375 9.28 A2 4.7 27 2.121 0.281 10.70 A3 6.1 488 2.256 4.743 10.80 A4 5.8 294 2.120 0.677 16.31 A5 4.9 51 2.231 0.531 7.75 A6 4.2 29 2.141 0.302 6.55

2.4.6. Expected Maximum Acceleration at Surface Layers:

The maximum amplitude of ground motion expected within a given

period of time and corresponding to a chosen probability level using inputs

from steps (2.4.2) - (2.4.5) is calculated (Table 2.1). The computer program

used for this purpose is EQRISK (McGuire, 1976). The program yields the

expected accelerations with 90 percent probability of not being exceeded in

exposure times of 100 years. The procedure of analysis is repeated

systematically in the 19 selected sites on the proposed Aswan new city

area. The results show that, the expected acceleration at the 19 sites is

almost the same and in range from 42 to 47 cm/sec2. For use, as input

motions at the bottom of the actual soil columns, one must remove from the

computed motions the effects of free-surface boundary conditions, which

invoke certain components of the stress tensor to be zero. To achieve this,

the free-surface motions are divided by a factor of 2 (Jacob et al., 1995).

Local site conditions play an important role in changing the

characteristics of seismic waves. It is often associated with the extent of

damage and destructiveness of a site incurs due to a strong earthquake.

Therefore, it is important to incorporate some type of site factor into the

analysis of risk such as amplification factor. The amplification factors at

the 19 selected sites are calculated by Fat-Helbary et al. (2004a), and were

used in the present study.

17

The computed amplification has its minimum value of about 1.61 at

the central western part of the area, while the maximum value is about 4.46

at the southern and northwestern

parts of the area, where the

sediments are loose and thick.

Finally the maximum surface

acceleration was estimated by the

multiplication of peak acceleration

at the base rock with the relative

amplification factor for the surface

layers. The maximum ground

accelerations and their

distributions at the ground surface

in exposure time 100 years are

represented by a contour map as

shown in figure (2.3). The

calculated acceleration has its

minimum value of about 36 gals at

the central eastern part, while the

maximum value is about 64 gals at

the southern part of the studied

area.

32.84 32.85 32.86 32.87Longitude

24.16

24.17

24.18

24.19

24.2

24.21

24.22

Latit

ude

0.0 0.5 1.0km Fig. 2.3: Surface acceleration for expected values in 100 years (in gals) (after Fat-Helbary et al., 2004a)

CHAPTER 3

ASSESSMENT AND MITIGATION

OF SEISMIC RISK

18

CHAPTER 3

ASSESSMENT AND MITIGATION OF SEISMIC RISK

3.1. INTRODUCTION:

Seismic risk assessment is an important activity in any community

living in an earthquake region. It enables choices to be made in the level of

protection employed. The three principal components of a seismic risk

analysis are seismic hazard assessment, inventory and categorization of the

elements at risk and vulnerability assessment for each element of risk. The

idea that, earthquake risk can be minimized by a degree of planning and

preparedness, has long been advocated, and the detailed study of the ways

in which damage and injury are caused and contributing factors to the risk

faced is seen as being necessary to inform the process of risk reduction

planning. The actual evaluation of risk is necessary in order to appreciate

the magnitude of the seismic problem, its comparative importance with

other problems faced by a community, and the value of measures taken to

reduce it (Karink, 1981 and 1982). By attempting to evaluate risk, an

overall framework of assessment, which can structure the study and

understanding of settlements in earthquake areas can be proposed. To do

so, the detailed definitions of hazard, population and seismic performance

are required in a form, which can be applied as a planning tool for any

particular community.

Risk is most easily assessed in terms of direct economic loss, and is

defined by UNDRO (1979) as:

[RI] = [H] [V] NE (3.1)

where: [H] is the natural hazard, the probability of experiencing in a

certain degree of ground shaking within a given time period.

19

[V]: is the vulnerability, the average expected proportion of damage, that

would be caused by that degree of ground shaking, measured in specific

loss.

N: is the quantity of elements at risk, e.g. the number of buildings in the

community.

E: is the element value, e.g. each of the buildings as a replacement cost.

NE: represents the total value of elements, e.g. buildings stock in a

community)

[RI]: is the risk, the probable loss as a probability of replacement cost.

[RI* ] is the specific risk, can be used, where [RI* ] = [H] [V], the probable

loss as a percentage of the total value of the elements at risk.

The specification of hazard has been discussed in chapter (2). The

vulnerability method will be discussed in this chapter. Also the seismic risk

analysis was performed on four different samples of buildings constructed

in Aswan city as the case study. The numerical results of inventory and

analysis are given and discussed in the following sections.

3.2. VULNERABILITY ASSESSMENT:

General Approach:

As defined earlier, vulnerability is the degree of loss to a given

element at risk resulting from the occurrence of specified earthquake. For

loss assessment over a population of buildings (or other elements at risk)

we need:

1. a mean of specifying the earthquake hazard.

2. a classification of the buildings or other facilities into distinct types,

whose performance in earthquakes is likely to be similar both in nature and

degree.

3. a method of defining loss to that the extent of loss to a particular

building or population of buildings can be quantified.

20

4. a mean of estimating the distribution of losses to each building type of

each discrete level of ground shaking (if intensity scales are used), or as a

function of ground shaking (if a continuous parameter of ground shaking is

used).

There are two principal methods of vulnerability assessment, which

have been referred to as predicted vulnerability and observed vulnerability.

Predicted vulnerability refers to the assessment of expected performance of

buildings based on calculation and design specification, or if no other

method is available, on judgment based on the assessors experience.

Observed vulnerability refers to assessment based on statistics of past

earthquake damage. The former is suitable for use primarily with

engineering structures and facilities, where a reasonable estimate of

earthquake resistance may be made, but for which only a limited amount of

damage data, if any, is available. The latter method is more suitable for use

with non-engineered structures made with low-strength materials such as

timber or unreinforced masonry, whose earthquake resistance is more

difficult to be calculated, but for which substantial statistical damage data

may be available. The use of observed vulnerability is increasingly relevant

in the case of very common forms of engineered construction, such as

reinforced concrete frame structures, as the amount of damage data

increases over time. Observed and predicted vulnerability methods are

likely to converge in the future as theoretical models of earthquake

performance of buildings improve, and as statistical data become available

for less common building types (Coburn and Spence, 1992).

3.2.1. Vulnerability Index Assessment:

In order to account for the vulnerability indices of different

structures, eight items were selected from the factors affecting

vulnerability. The main criteria in selecting these items were to obtain a

21

rapid survey form, to collect information about different components for

each building included in the studied area, based on visual inspection of the

building, without benefit of entry to the building, or review of structural

drawings. For each element a grade (as in Table 3.1) is assigned out of

three classes 1 (score 0, low vulnerability) refers to situations, which may

be considered as conforming to the prescriptions of aseismic design,

whereas class 2 (score 10) refers to medium vulnerability, and class 3

(maximum score 20, high vulnerability) refers to unsafe configuration.

Weights are also assigned to each element. The vulnerability index is the

sum of the partial parameters times the relevant weight factor (El-Remaily,

1992).

Table 3.1: Vulnerability index evaluation scheme

Element Class 1 2 3

Weight factor

1- Proportionality of building dimensions. 2- Horizontal size. 3- Number of stories. 4- Construction quality. 5- Vertical irregularity. 6- Plan irregularity. 7- Soft story. 8- Pounding.

0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20 0 10 20

1.0

1.0 1.5 2.0 2.0 1.5 2.0 1.5

It should be noted that, the seismic quality of single items (and of the

building as a whole) increases with the decrease of vulnerability index

values. These values are indirect expressive estimates to the seismic quality

of the building and of its structural and non-structural parts. The distinctive

feature of the method consists in the possibility of a practically continuous

description of the seismic quality of the buildings, capable of taking into

account any possible morphological configuration. As will be described

later, this description can be easily handled numerically in risk evaluation

procedures, and may be accounted for prior strengthening. If, for instance,

22

the original poor quality is improved by adding new well designed or by

strengthening the old ones, item 4 will move from class 3 (score 20) to

class 1 (score 0), and the total VI will change accordingly.

Table 3.2: The rules and instructions followed by the surveyors during the field investigation.

Element Class 1 Class 2 Class 3 1-Proportionality of building dimension.

Buildings with length to depth ratio (R1) < 2 and height to depth ratio (R1) < 4

Buildings with R1 > 2, or R2 > 4.

Buildings with R1 > 2 and R2 > 2

2-Horizontal size. Buildings with length (L) < 15 m

Buildings with L >=15 m and 30 m

3- Number of stories.

Buildings with number of stories (N) 5 and

23

The rules and instructions to be followed by the surveyors during the

field investigation are summarized in Table 3.2.

3.2.2. Proposed Vulnerability Functions:

The derivation of vulnerability functions is essentially based on data

obtained from damaged caused by previous earthquakes. In the absence of

such kind of data for Egypt, vulnerability functions have to be reasonably

assumed based on studies carried in other countries, and are modified by

expert judgment. The suggested vulnerability functions are based on those

given by Benedetti and Benzoni (1985) for stone masonry structures in

Italy. Some modifications were made by El-Remaily (1992) to apply this

method in Egypt. The suggested vulnerability functions for stone masonry

structures are given in figure (3.1) and represented by the relationship

between the damage degree and vulnerability index.

Based on the relative vulnerability functions given by Coburn (1986)

and values given by UNDRO (1991) correlating damage of different

building types the following average relative vulnerabilities are assumed in

order of increasing susceptibility to damage:

RC structures 1

BM structures 1.45

SM structures 1.6

By this way the vulnerability functions for RC and BM are obtained.

3.2.3. Damage Evaluation:

Quantification of structural damage presents a number of difficulties.

The mechanisms of damage are different for each building type; in some

cases it is possible to avoid these differences by quantifying and comparing

damage in financial terms. The most commonly used economic measure of

damage is repair cost ratio. This is the ratio of the cost of repair and

reinstatement of the structure (or building) to the cost of replacing the

24

structure (or building). The evaluation of damage in terms of economic cost

is unsatisfactory for many purposes, though, because of its dependence on

the economy at that time and place. Repair cost ratio varies, because there

are different ways of repairing and strengthening, and construction costs

also vary from place to place and through time; it is also significantly

affected by the type of building.

Figure (3.1): Proposed vulnerability functions for Stone masonry structures (after El-Remaily, 1992).

For these reasons, the evaluation of damage in terms of structural

damage is becoming more common. This has the advantage that, if it is

defined with sufficient accuracy, it can be converted into a repair cost in

any economic situation. The definition of structural damage generally used

involves a sequence of damage states, with broad descriptors such as

light,moderate,severe,collapse, elaborated with more detailed

descriptions, which may use quantitative measures such as crack widths. In

this study damage is rated in 4 categories as shown in Table 3.3.

25

3.2.4. Damage Probability Matrices:

The expected damage data are converted into damage probability

matrix format through the following equation (Ergunay and Gulkan, 1990).

Pk (D i ) = AA

D

i (3.2)

where:

Pk (D i ): ratio of type k buildings subjected to intensity falling in

damage state D,

Ai : total gross area of building of type K within region subjected to

intensity earthquake,

AD : gross area of buildings in damage state D.

Table 3.3: Definition of damage states.

Damage

Level Damage Range

Damage State

Description

1 2 3 4

0 - 20

20 - 40

40 - 60

60 100

Slight Moderate Heavy Collapse

Thin cracks in walls (width of cracks less than 1 mm); moderate damage to infill walls. Structural cracks less than 5 mm wide and/or heavy damage to infill walls. Large structural cracks more than 5 mm wide and/or partial collapse of infill walls. Partial or total collapse of the main structural system.

3.2.5. Damage Models and Vulnerability Function:

Effective correlation of ground motion with damage requires

consideration of the way ground motion affecting structures response and

of the type and degree of damage caused. To correlate the ground motion

26

intensity with structural damage, a damage model is needed. The damage

model can be effectively described with the following two variables.

(a) Damage Ratio (DR):

DR = Number of buildings damaged Total number of buildings

(3.3)

(b) Damage Cost Factor (DCF): DCF = Damage repair cost

Value of building (3.4)

These two nondimensional parameters are quite general, and can be

used for a geographical area or subarea as well as for various building

classification or types of construction.

3.2.6. Loss Function Estimation:

Loss function is defined as the probability of the loss of value in a

certain element due to seismic hazard or, in more general terms, as the

expected loss due to a particular natural phenomenon as a function of both

hazard and vulnerability. Since vulnerability is linked with a particular

element (building type), the term specific risk has been introduced for

such cases. Vulnerability functions such as that shown in figure (3.2)

(Coburn and Spence, 1992) may be combined with the hazard data defined

as shown above in order to estimate the probable distribution of losses for

all possible earthquake events in a given time period and thus to determine

the risk to that element or set of elements at risk. This definition may also

be expressed mathematically, in a way, which facilitates the computation of

risk. The general equation for the calculation of risk can be given as:

[RI ij ] = [H i ] [V ij ] (3.5)

where, for an element at risk (e.g. an individual building) j :

[RI ij ] is the risk; the probability or average rate of loss to element j due to

earthquake ground motion of severity i .

27

[H i ] is the hazard; the probability or average expected rate of experiencing

earthquake ground motion (or other earthquake-related damaging event) of

severity i .

[V ij ] is the vulnerability; the level of loss, that would be caused to element

j as a result of experiencing earthquake ground motion of severity i

(where loss is the specific loss; loss as a proportion of the total value of

element j ).

By summing the risk from all levels of hazard, (min i max), the total risk to any individual element can be derived.

Fig. (3.2): Risk is a product of hazard and vulnerability: typical

curve shapes (after Coburn and Spence, 1992).

3.2.7. Monetary Losses:

The cost of the expected value of damage within the considered

sectors referred to 100 m.sq. is evaluated as follows (Benedatti et al.,

1988):

L = C Aj jj i

N

=

K R (3.6)

where: L i : loss due to an event of intensity i ,

28

N : the total number of buildings,

C j : the cost factor corresponding to damage level of building number j

at intensity i , (see Table 3.4)

A j : gross area of building number j ,

R : the cost of rebuilding per square meter,

K : a factor taking into account indirect monetary damage.

Table 3.4: Cost factors for the various damage levels.

Damage Level

Damage Range

Cost Factor C j

0 1 2 3 4

0 0 - 20 20 - 40 40 - 60

60 - 100

0 0.2 0.4 0.8 1.0

A value of K = 2 has been assumed here. The values of C j factor

account for fraction of damage cost, pertaining to a certain damage level,

with respect to the cost of reconstruction are calculated. It must be noted

that, for heavy damage (level 3), the cost of rehabilitation is rather high,

owing to the need of highly sophisticated technical interventions. However,

it must be noted that, the numerical values of K and C j assumed herein are

mainly based on judgment.

The expected annual loss is given by UNDP/UNIDO (1985) as follows:

Expected annual loss = PLi ii 5

io

= (3.7)

where, Pi is the annual expected occurrence of intensity (i) at the site under

consideration and Li losses due to intensity (i).

3.2.8. Human Losses:

The casualty rate depends on many factors. The majorities of them

are the seismic input motion to man-made structures, the occupants

29

behavior and the situation under which they are attacked by the earthquake.

The first one, is considered most influential, and is evaluated by the degree

of structural damage as a function of seismic intensity (Ohta and Satoh,

1980; Ohta and Ohashi, 1983 and Ohta, et al., 1986). The behavioral

performance depends on the variety of personal attributes. The situation,

when an earthquake attacks, is a time factor depending mostly upon

whether it occurs during daytime or at night. However, it is very difficult to

account for the last two factors.

Empirical relations have been developed between fatality and heavy

damage and collapse totals. The expression below was given by Ergunay

and Gulkan (1990).

D = 0.003 to 0.010H1.32 (3.8)

where:

D = total number of deaths,

H = total number of collapsed and heavily damaged buildings

The range 0.003 to 0.010 depends on the building type as follows:

For reinforced concrete buildings : 0.003

For wood frame buildings : 0.005

For brick masonry buildings : 0.008

For stone or adobe masonry : 0.010

A fatality / injury ratio of 1/3 is assumed (Erguny and Gulkan, 1990).

The number of people made homeless is calculated based on the

assumption that, heavily damaged and collapsed buildings are out of use

after the earthquake. A population of 1 inhabitant per 20 m.sq. of gross

building area was assumed for calculating the expected human losses in

this study.

For emergency plans the number of houses collapsed and the number

of people killed is an indication of the relief and rescue needs in the first 3

30

days after the earthquake. Injuries are an indication of the medical facilities

needed, and the number of people made homeless is an indication of the

level of need for temporary shelter. The number of houses heavily or

structurally damaged represents levels of long term construction needed.

3.3. CASE STUDY OF ASSESSMENT OF SEISMIC RISK IN

ASWAN CITY (UPPER EGYPT):

The methodology was applied in a risk assessment on Aswan city,

Upper Egypt. The goals of this study are to improve the assessment of

seismic hazard, to investigate the vulnerability of the built environment and

finally to combine the results to elaborate risk scenarios as the first

fundamental step in the mitigation process.

Aswan city locally is divided into three districts: East, west and

south district. The representative classes or type of residential building

concentration varies from district to district, and in general they are

classified according to the material of structural vertical load bearing

elements in four types. Reinforced concrete structures (RC), brick masonry

buildings (BM), stone masonry buildings (SM) and mixed building as a

combination of any two, or more of the above stated types. The samples

from four local sectors were selected for vulnerability survey representing

all types of buildings in Aswan region.

I. Computer implementation:

A computer code named Seismic Risk Analysis (SRA), that was

developed (El-Remaily, 1992) for the purpose of interpreting the data in the

survey form, was used for calculating VI, combining them with

vulnerability functions and hazard curve to obtain an estimation of the

overall losses. Only one file is required as an input for this program

consisting of three major parts: 1) hazard curve for the region under

31

consideration, 2) the weights of different vulnerability items, and 3)

building data as obtained from the survey form.

The output of the program consists of building stock data and its

distribution in the given sample, some summary statistical results related to

VI and expected damage, and expected monetary and human losses, as well

as the effect of different strengthening strategies are calculated. The

application of the various strategies originates new distribution of

vulnerability index.

II. Seismic hazard at a selected site in Aswan city:

The probabilistic seismic hazard analyses were conducted in detail in

Aswan area (Fat-Helbary, 1995). According to the seismic hazard analysis

from area source model, the seismic hazard for a selected site with

coordinates (32.9oE, 24.09oN) in Aswan town is carried out. The resulting

hazard curves are shown in figure (3.3), and the numerical results are given

in Table 3.5. The intensities chosen in this table are based on the relation of

PGA vs intensity (in MSK scale) given by Medvedev and Sponheuer

(1969). The probabilities of occurrence per year for the range of

acceleration values defining the intensities from V to X in MSK scale are

calculated taking the difference of the probabilities of exceedance of each

pair of successive values.

III. Damage probability matrices:

The output analysis of the damage probability matrices for the four

predominant type of building in Aswan city is presented in bar chart form

in Figs. 3.4 to 3.7. By comparing the damage probability matrix from the

four types of buildings, it is clear in general that, the percentage of

buildings in low damage states decreases with increasing the intensity,

while the percentage of building in high damage states increases with

increasing the intensity. The damage probability matrix represents the

32

highest values for mixed buildings, while it represents the less value for the

RC buildings.

Table 3.5: Seismic hazard at selected site in Aswan city.

PGA Annual exceedance probability

Acceleration range

Intensity (MSK)

Annual occurrence probability

12.5 25 50

100 200 400

0.634E-01 0.214E-01 0.681E-02 0.162E-02 0.186E-03 0.715E-05

< 25 25 - 50

50 - 100 100 - 200 200 - 400

> 400

V VI VII VIII IX X

0.042 .01459 .00519

.001434 .00017885 .00000715

Fig. (3.3): Hazard curve at selected site in Aswan city

(after Fat-Helbary, 1995).

33

Fig. (3.4): Damage probability matrix for reinforced concrete buildings in

Aswan city (after Fat-Helbary, 1995).

Fig.(3.5): Damage probability matrix for brick masonry buildings in

Aswan city (after Fat-Helbary, 1995).

34

Fig. (3.6): Damage probability matrix for stone masonry buildings in

Aswan city (after Fat-Helbary, 1995).

Fig. (3.7): Damage probability matrix for mixed buildings in Aswan city

(after Fat-Helbary, 1995).

35

IV. Loss function estimation:

Vulnerability function is represented by the relationship between the

damage ratio (DR) and acceleration as in figure (3.8). DR was calculated as

a summation of damage from level 2 (moderate state) to level 4 (collapse

state) as in Table (3.6). By combining the vulnerability function (Fig. 3.8)

with the hazard function given by the curve in figure (3.3), the probable

losses for all possible earthquake events for buildings of the type RC, BM,

SM and mixed has been assessed as shown in figure (3.9). The numerical

results are tabulated in Table (3.6).

R(Aa) expresses the expected degree of loss within a given area caused by all earthquakes with acceleration equals or greater than a. The

total expected degree of loss (specific risk) is obtained from summation of

seismic risk of a=25 gals to a=400 gals.

V. Monetary losses:

The cost of rebuilding was assumed here as 800 Egyptian pound

(LE) per m.sq. for buildings in El-Syeal, where the buildings were

constructed mainly from RC. and 500 LE For other buildings. The

summary of monetary losses due to earthquakes of different intensities as

well as the annual losses are given in Table (3.7) in terms of LE per 100

m.sq. Column 3 gives the average loss due to intensity from V to X in

LE/100 m.sq. and column 4 gives the annualized expenses in LE/100 m.sq.

for each intensity. The mean values of annualized losses would be used to

decide on insurance needs and determine insurance premiums.

VI. Human losses:

The general levels of homelessness, deaths and injuries, which would

result from expressing ground motion of different intensities, are given in

Table (3.8).

36

Fig. (3.8): Vulnerability function of residential buildings in Aswan area

(after Fat- Helbary, 1995).

Fig. (3.9): Specific risk for building types in Aswan city

(after Fat-Helbary, 1995).

37

Table 3.6: Average percent of annual loss in the expected damaged area.

Peak acceleration 25 50 100 200 400 Hazard Prob. (P) .0214 .0068 .00162 .000186 .715E-05

Vulnerability(V):RC :BM :SM :Mix

0.0 0.0645 0.0169 0.0722

0.0256 0.5161 0.5730 0.8351

0.0897 0.8065 0.9719 0.9691

0.269 1.0

0.9943 1.0

0.423 1.0 1.0 1.0

RI(Aa)=V*P :RC :BM :SM :Mix

0.0 0.00138 0.000362 0.00155

0.000174 0.003503 0.003896 0.005679

0.000145 0.001307 0.001574 0.001570

0.000042 0.000186 0.000185 0.000186

.302E-05

.715E-05

.715e-05

.715e-05 Specific risk for : RC = 0.002 = 0.20 % : BM = 0.0064 = 0.64 % : SM = 0.0060 = 0.60 % : Mix.=0.009 = 0.90 %

Table 3.7: Estimated economic losses.

Intensity

Annual occurrence probability

Loss due to one event

LE/100 m.sq.

Annual loss

LE/100 m.sq. V VI VII VIII IX X

0.042 0.01459 0.00519

0.001434 0.00017885 0.00000715

1232.02 6983.51

18172.30 26988.81 35409.05 46369.70

51.74 101.96 94.31 38.59 6.34 0.33

Total 293.28

Table 3.8: General levels of estimated human losses .

I

% of houses with heavy damage or

collapse

% of people made

homeless

No. of injuries per

million

No. of fatalities per

million V VI VII VIII IX X

0.00 0.00 0.26

11.98 25.26 58.59

0.00 0.00 0.35 7.42

16.64 31.91

0.00 0.00 4.21

520.91 1248.06 3896.62

0 0 2

174 416

1299

38

VII. Effects of selected strategies:

The application of the various strategies originates new distributions

of the vulnerability index. The three effective elements were selected, and

modifying the present vulnerability index distributions as follows:

1. Stiffening of soft story; thus moving element (7) to class (1).

2. Enhancing construction quality: thus moving element (4) to class (1).

3. Separating adjacent buildings: thus moving element (8) to class (1).

Considering this technical investigation, the new annual damage

probabilities have been evaluated. Results are shown in figures (3.10) and

(3.11) for economic and human losses respectively, together with the

probability curve for the present situation. Table (3.9) shows the annual

expected cost of damage for the various strategies and the decrements with

respect to the present situation.

Table 3.9: Effect of different strategies on expected annual damage referred to 100 m. sq.

Strategy Expected

annual loss

Variation of expected damage with respect to present situation

Present situation Soft story elimination Enhancing quality Pounding elimination

293.28 220.51 133.49 124.12

-------- - 26.61 % - 60.64 % - 64.07 %

Although this is a rough estimation of the monetary benefits of the

strategies considered, the above results show that, a prior strengthening

campaign is economically advantageous as it reduces the monetary losses

considerably. Also, it is worth noting that, even the implementation of the

lowest strengthening gives rise to a considerable decrement of the risk to

human life.

39

Fig. (3. 10): Annual probability of damage for Aswan city in the present situation and after implementation of different strength- ening strategies (after Fat-Helbary, 1995).

Fig. (3.11): Effect of different strengtheni- ng strategies on fatal- lities for Aswan city (after Fat-Helbary, 1995).

CHAPTER 4

LOCAL SITE EFFECTS AND

DESIGN GROUND MOTIONS

40

CHAPTER 4

LOCAL SITE EFFECTS AND DESIGN

GROUND MOTIONS

4.1. INTRODUCTION:

The influence of local geological and soil conditions on the intensity

of ground shaking and earthquake damage has been known many years

before. Wood (1908) and Reid (1910) showed that, the intensity of ground

shaking in the 1906 San Francisco earthquake was related to local soil and

geological conditions. Gutenberg (1927) developed site-dependent

amplification factors from recordings of microseisms at sites with different

subsurface conditions. Since these early observations, the effects of local

site conditions on ground motions have been illustrated in earthquakes

around the world. More recently, the availability of strong-motion

instruments has allowed local site effects to be measured quantitatively in

recent years.

Local site effects play an important role in earthquake-resistant

design and must be accounted for a case-by-case basis. This is usually

accomplished by the development of one or more design ground motions

(i.e., motions, that reflect the levels of strong motion amplitude, frequency

content, and duration that a structure or facility at a particular site should be

designed for).

Despite considerable evidence, the existence of local site effects was

a matter of some debate in past years. Indeed, provisions specifically

accounting for local site effects did not appear in building codes, until the

1970s. This part discusses procedures, that are commonly used for the

development of site-specific design ground motions, and reviews the

41

manner in which local site effects are treated in the specification of design

ground motions by contemporary building codes and standards.

4.2. EFFECT OF LOCAL SITE CONDITIONS ON GROUND

MOTION:

Local site conditions can profoundly influence all of the important

characteristics- amplitude, frequency content, and duration of strong

ground motion. The extent of their influence depends on the geometry and

material properties of the subsurface materials, on site topography and on

the characteristics of the input motion. The nature of local site effects can

be illustrated in several ways: by simple, theoretical ground response

analyses and by measuring of ground surface motions from sites with

different subsurface conditions.

4.2.1. Ground Response Analysis:

There are important theoretical reasons why ground surface motions

should be influenced by local site conditions. At most sites the density and

S-wave velocity of materials near the surface are smaller than at greater

depths. If the effects of scattering and material damping are neglected, the

conservation of elastic wave energy requires that, the flow of energy from

depth to the ground surface must be constant.

Under ideal conditions, a complete ground response analysis would

model the rupture mechanism at the source of an earthquake, the

propagation of stress waves through the earth to the top of bedrock beneath

a particular site, and would then determine how the ground surface motion

is influenced by the soils, that lie above the bedrock. In reality, the

mechanism of fault rupture is so complicated and the nature of energy

transmission between the source, and the site is so uncertain that, this

approach is not practical for common engineering applications. In practice,

empirical methods based on the characteristics of recorded earthquakes are

used to develop predictive relations of the different types of ground

42

motions. These predictive relationships are often used in conjunction with a

seismic hazard analysis to predict bedrock motion characteristics at the site.

The problem of ground response analysis then becomes one of determining

the response of the soil deposit to the motion of the bedrock immediately

beneath it. Seismic waves may travel through tens of kilometers of rock

and often less than 100 m of soil, the soil plays an important role in

determining the characteristics of the ground surface motion.

The influence of local soil conditions on the nature of earthquake

damage has been recognized for many years. Since the 1920s, seismologist

and more recently, geotechnical earthquake engineers have worked toward

the development of quantitative methods for predicting the influence of

local soil conditions on strong ground motion. Over the years, a number of

techniques have been developed for ground response analysis. The

techniques are often grouped according to the dimensionality of the

problems that, they can address, although many of the two-and three-

dimensional techniques are relatively straightforward extensions of

corresponding one-dimensional techniques (Kramer, 1996).

One-dimensional ground response analyses are based on the

assumption that, all boundaries are horizontal and that, the response of a

soil deposit is predominantly caused by SH-waves propagating vertically

from the underlying bedrock. For one-dimensional ground response

analysis, the soil and bedrock surfaces are assumed to extend infinitely in

the horizontal direction. Procedures based on this assumption are able to

predict ground response, that is in reasonable agreement with measured

response in many cases. An important class of techniques of the ground

response analysis is also based on the use of transfer functions. For the

ground response problem, transfer functions can be used to express various

response parameters, such as displacement, velocity, acceleration, shear

stress, and shear strain, to an input motion parameter given as bedrock

43

acceleration. Because this approach relies on the principle of superposition,

it is limited to the analysis of linear systems. Non-linear behavior can be

approximated, however, using an iterative procedure with equivalent linear

soil properties. Kramer (1996) derived transfer functions for a series of

successively more complicated geotechnical conditions. Although the

simplest of these conditions may only rarely be applicable to actual

problems, they illustrate some of the important effects of soil deposits on

ground motion characteristics without undue mathematical complexity. The

more complex cases are capable of describing the most important aspects

of ground response and are very commonly used in geotechnical

earthquake engineering practice.

4.2.2. Transfer Function for Layered, Damped Soil on Elastic Rock:

According to Kramer (1996), the key to the linear approach is the

evaluation of transfer functions. In the following, the transfer functions are

derived for multiple soil layers.

Real ground response problems usually involve soil deposits with

layers of different stiffness and damping characteristics with boundaries at

which elastic wave energy will be reflected and /or transmitted. Such

conditions require the development of transfer functions for layered soil

deposits.

Consider a soil deposits consisting of N horizontal layers, where the

Nth layer is the bedrock (Fig. 4.1). Assuming that, each layer of soil

behaves as a viscoelastic Kelvin-Voigt solid, the wave equation for time

displacement can be written as function of density (), shear modulus (G)

and viscosity () as follows:

tz

udz

uGdt

u

+= 23

2

2

2

2

(4.1)

The solution to the wave equation can be expressed in the form:

44

)()( **),( zktizkti BeAetzu + += (4.2) where, the circular frequency of ground shaking, k* is a complex wave

number and A and B represent the amplitudes of waves traveling in the z

(upward) and +z (downward) directions, respectively. The shear stress ()

is then given by the product of the complex shear modulus (G*) and the

shear strain (zu ) ,so:

zuiG

zuiG

zuGtz

+=+=

= )21()(),( * (4.3)

where, is known as damping coefficient.

Introducing a local coordinate system (Z) for each layer, the

displacement at the top and bottom of layer (m) will be:

timmmm eBAtZu)(),0( +==

tihikmhikmmmm eeBeAthZu mmmm )(),(** +== (4.4)

Displacements at layer boundaries must be compatible (i.e., the

displacement at the top of a particular layer must be equal to the

displacement at the bottom of overlying layer). Applying the compatibility

requirement to the boundary between layer (m) and layer (m+1), that is,

um (Zm =hm , t) = um+1 (Zm+1 =0,t) (4.5)

yields

mmmm hikmhikmmm eBeABA**

11

++ +=+ (4.6) The shear stresses at the top and bottom of layer (m) are:

timmmmmm eBAGiktoZ )(),( ** == (4.7) tihikmhikmmmmmm eeBeAGikthZ mmmm )(),( **** == (4.8) Since stresses must be continuous at layer boundaries,

),0(),( 11 tZthZ mmmmm === ++ (4.9) So

)( ***1

*1

**

11mmmm hik

mhik

mmm

mmmm eBeAGk

GkBA ++

++ = (4.10)

45

Adding equations (4.6) and (4.10) and subtracting equation (4.10) from

equation (4.6) gives the recursion formulae:

mm

mmhik

mmhik

mmm eBeAA*

*

)1()1( *21*

21

`1

+ ++= (4.11)

mmmm hikmmhikmmm eBeAB**

)1()1( *21*

21

1

+ ++= (4.12) where, *m is the complex impedance ratio at the boundary between layers (m) and (m+1)

1

*1

*

*1

*1

***

)()(

++++==

msm

msm

mm

mmm v

vGkGk

(4.13)

The complex velocity (Vs ) can be expressed as:

)1()1()21(*

*

iviGiGGv ss +=++== (4.14)

At the ground surface, the shear stress must be equal to zero, which

requires [from equation (4.7)] that, A1 = B1. If the recursion formulae of

equations (4.11 and 4.12) are applied repeatedly for all layers from (1) to

(m), functions relating the amplitudes in layer (m) to those in layer (1) can

be expressed by:

Am = am () A1 (4.15)

Bm = bm () B1 (4.16)

The transfer function relating the displacement amplitude at layer (i)

to that at layer (j) is given by:

)()()()()(

jj

ii

j

iij ba

bauuF +

+== (4.17)

Because uuu 2 == for harmonic motion, equation (4.17) also describes the amplification of acceleration and velocities from layer (i) to layer (j).

Equation (4.17) indicates that, the motion at any layer can be determined

from the motion at any other layer. Hence if the motion at any one point in

the soil profile is known, the motion at any other point can be contributed.

46

Layer Coordinate Properties Thickness

1 Z1 U2 G111 h1

2 Z2

Um

m Zm Gm m m hm

Um+1

m+1 Zm+1 Gm+1 m+1 m+1 hm+1

Zm+2 Um+2

N ZN UN GN N N hN= infinite

Fig. (4.1): Nomenclature for layered soil deposit on elastic bedrock

(after Kramer, 1996).

4.3. CASE STUDY OF GROUND-RESPONSE ANALYSIS IN UPPER

EGYPT:

Each layer in the analytical model is completely defined by its values

of shear modulus and damping ratio, density and thickness. These values

are independent of frequency. The responses in the analytical model are

caused by the upward propagation of shear waves or pressure waves from

the underlying bedrock. The strain dependence of modulus and damping of

the bedrock (half-space) on the calculated motions are included in the

procedure. The input motion can be given in any one layer in the model,

and new motions can be computed in any other layer.

The stress-strain characteristics of soils are strongly non-linear and

may significantly influence the dynamic response of a site subjected to

strong earthquake motions. The shear modulus reduces rapidly and

hysteretic damping increases as the strain, that develops in soil material

increases. A good site response analysis must therefore consider these non-

linear effects. It is known that, the non-linear behavior of soil material

47

cannot be fully described by constant elastic moduli and damping

coefficients. However, a good approximation of the effects of non-linear

behavior of soils on the response can be obtained by use of constant strain

compatible moduli and damping ratios in a sequence of linear analyses.

The equivalent linear method (Seed and Idriss, 1969) can be briefly

described in the following manner.

In a site response analysis, the equivalent linear method starts with a

linear analysis using low-strain properties of the soil system. The analysis

yields complete time histories of shear strain, from which the effective

shear strain amplitudes are calculated in each layer. The effective shear

strain (eff) is determined from maximum shear strain (max):

eff = R max (4.18)

where, R is the ratio of the effective shear strain to maximum shear strain,

which depends on the earthquake magnitude. R is the same for all layers.

Using the computed strain amplitudes, an improved set of soil moduli and

damping ratios are obtained from the appropriate soil data curves and new

linear analysis is performed with these properties. The process is repeated

until the differences between the computed values of shear modulus and

damping ratio in two successive iterations fall below some predetermined

value in all layers. Generally 8 iterations are sufficient to achieve

convergence.

The transfer functions are computed using obtained strain compatible

modulus and damping values. This technique has been widely used in

practice, because it is an efficient method, and is easy to

implement in a computer program.

Number of research works related to the study of ground response

analysis is done in different areas in Upper Egypt such as: the proposed site

of El-Kiefl dam at the forth Tushka depression, proposed site of Tushka

barrage on Tushka spillway canal and proposed location of Aswan new city

48

on the west bank of the River Nile. In this state of the art, the ground

response analyses at the proposed location of Aswan new city are presented

(Fat-Helbary et al., 2004a).

The software program selected for this study is called EERA (Bardet

et al., 2000). This program was developed from the same calculated

response of soil sites (Schnabel et al., 1972). EERA stands for equivalent-

linear earthquake site response analysis. EERAs input and output are fully

integrated within the spreadsheet program Excel.

4.3.1. Input Data:

To calculate the response of soil sites using the selected software

EERA, two types of data are used as input data known as geotechnical

input data and input rock motion data.

I. Geotechnical data:

Required soil parameters and properties for each layer include soil

layer thickness, shear wave velocity (Vs) the maximum shear modulus,

(Gmax), density () and unit weight (). The variation of shear modulus and

damping ratios of the bedrock with shear strains are also required. The

shallow seismic refraction survey was carried out using Strata Visor- NZ

48 channels instrument. Seismic refraction P-and S-waves profiles were

conducted in 19 sites on the proposed location of Aswan new city, as

shown in figure (4.2).

The survey was applied to obtain P-and S-waves velocities and the

thickness of each layer. The bulk density (), unit weight () and maximum

shear modulus (Gmax)are calculated as follows:

The bulk density( ): The bulk density( ) of soil layers are calculated

from an empirical relationship of Gardner et al. (1974), which shows the

increase in P-wave velocity (Vp) with density () as follows:

= a Vp0.25 (4.19)

49

where, a is a constant equal to 1670, when is given in kg/m3 and Vp is in

km/sec. This relationship makes it possible to make a rough estimation of

the P-wave velocity, when only the bulk density is known and vice versa.

Unit weight (): The unit weight is related to bulk density as follows:

= g. (4.20)

where, g is the acceleration of gravity equal to 9.81 m/sec2. The unit

weights for the soil layers of the profiles were calculated for all the

profiles.

Maximum shear modulus (Gmax):

Since most seismic geophysical tests

induce shear strains lower than about

3x10-4%, the measured elastic shear

wave velocities can be used to compute

the maximum shear modulus, (Gmax)

from the relation:

Gmax = Vs2 (2.21) The use of measured shear wave

velocities is generally a very reliable

means of evaluating in situ the value of

Gmax for a particular soil deposit.

Shear modulus reduction and

damping curves: A number of

investigators have studied the modulus

reduction and the damping behavior of

different soils and proposed standard

modulus reduction and damping curves

for those soils. In this study; the shear

modulus reduction curve proposed by Seed and Idriss (1970) was used for

dense and loose sand, along with the damping curve for sand proposed by

32.84 32.85 32.86 32.87Longitude

24.16

24.17

24.18

24.19

24.20

24.21

24.22

Latit

ude

19

18

3

17

141516

1311

12

108

9

46

5

7

21

Fig. (4.2) Location map of the

conducted refrection profiles

(after Fat-Helbary et al.,

2004a).

50

Idriss (1990). The Seed et al. (1984) shear modulus reduction and damping

curves for gravel were used, the shear modulus reduction and damping

curves for rock proposed by Schnabel et al. (1972) were used, whereas for

clay the shear modulus reduction proposed by Seed and Sun (1989) and

damping curves proposed by Idriss (1990) were used.

II. Input rock motion:

In the absence of a representative strong motion record in the vicinity

of the profiles site, one of rock outcrop motions was used as input motion

for the selected profiles to model the seismic response at the selected

profiles: A horizontal acceleration time history recorded on tonalite

bedrock from the 1985 Michoacan earthquake in Mexico, Ms = 8.1, that

was recorded at distance of 80 km at site Teacalco Villita. The Michoacan

earthquake in Mexico was used in this study, because it has a high

magnitude (8.1), and distance (80 km) from Teacalco Villita, as nearly the

same distance from the main active seismic area (Kalabsha area) to the

proposed location of Aswan new city.

The input rock motion was formatted to mach with the EERA input

data format. For use as input motions at the bottom of the actual soil

columns, one must remove from the computed motions the effects of free-

surface boundary conditions, which invoke certain components of the stress

tensor to be zero. To achieve this, the free-surface motions are divided by a

factor of 2. A low-pass corner frequency of 25 Hz was used to filter the

high frequencies from the input acceleration as shown in figure (4.3).

4.3.2. Calculated Ground Response: The results of calculation and site response analyses are summarized

in this section.

Response spectrum: The motions may be computed at any layer in the soil

deposits, but only the surface ground motions are calculated in the present

51

study. The computed motions are presented by acceleration time histories

and corresponding response spectra with 5% damping.

Fig. (4.3): Acceleration rock motion records used in analysis (after Fat- Helbary et al., 2004a).

From the corresponding maximum accelerations calculated at the

surface layer, figure (4.4) shows an example of the calculated maximum

acceleration at the surface layer for one profile (No. 19), and this was

repeated for each profile in the studied area.

The maximum acceleration at all profiles is plott