strong ground motions

1

1

Strong Ground Motion and Concept of Response Spectrum

March 2013

Sudhir K Jain, IIT Gandhinagar

Sudhir K. Jain March 2013

EQ Ground Motions

Low Amplitude Vibrations

Long distance events

Usually displacements

Earth Scientists

0 200 400 600 800 1000 1200

Am

pli

tud

e

Time (s)

Teleseismic Earthquake Recording

P PP S Surface Waves

Sudhir K. Jain Slide 2 March 2013

2

Strong Ground Motions

Near-field ground motions

Usually accelerations

Engineers

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 10 20 30 40 50 60 70 80

Ac

cn

. (g

)

PGA=0.32g

Time (seconds)

EQ Ground Motions…


Peak Ground Parameters

Acceleration (PGA)

Velocity (PGV)

Displacement (PGD)


3

(Martinez-Pereira, 1999)

Maximum Recorded Motion


Parameters…

Duration of Significant Shaking

Frequency Content

0 10 20 30 40 50 60

0.5g

Time (sec)

1985 Mexico Earthquake (SCT 1A; N90E)

1940 Imperial Valley Earthquake (El Centro; S00E)

1971 San Fernando Earthquake (Pacoima Dam; N76W)

1991 Uttarkashi Earthquake (Uttarkashi, N75E)

Characteristics…


4

Influence of

Magnitude of EQ

Source mechanism

Type of faulting

Distance from source

Soil/rock medium along travel path

Local soil site, geology, topology, etc.,. Attenuation with Distance

Fault

Fault

Characteristics


Sudhir K. Jain March 2013 Slide 8

Accelerogram

During ground shaking, one can measure ground acceleration versus time (accelerogram) using an accelerograph

Accelerograph is the instrument

Accelerogram is the record obtained from it

Accelerogram is the variation of ground acceleration with time (also called time history of ground motion)

5


Typical Accelerograph

This is a typical analog instrument. These days, digital instruments are becoming popular (photo from Earthquakes by Bolt)

Typical Accelerograms

From Dynamics of Structures by A K Chopra, Prentice Hall

Time, sec


6


Response Spectrum (contd…)

If the ground moves as per the given accelerogram, what is the maximum response of a single degree of freedom (SDOF) system (of given natural period and damping)?

Response may mean any quantity of interest,

e.g., deformation, acceleration

T=2 sec,

Damping =2%

Ground motion time history Time, sec

a(t)/g



Using a computer, one can calculate the response of SDOF system with time (time history of response)

Can pick maximum response of this SDOF system (of given T and damping) from this response time history

See next slide

7


Time, sec

a(t)/g


Ground motion time history

Time History of Deformation (relative displacement of mass with respect to base) response

Maximum response = 7.47 in.

T=2 sec,

Damping =2%

Time, sec

d(t)



Repeat this exercise for different values of natural period.

For design, we usually need only the maximum response.

Hence, for future use, plot maximum response versus natural period (for a given value of damping).

Such a plot of maximum response versus natural period for a given accelerogram is called response spectrum.

8


Time, sec

ag(t)/g


Displacement Response Spectrum for the above time history

Time, sec

d(t)/g

d(t)/g

d(t)/g

T=0.5 sec =2%

T=1.0 sec =2%

T=2.0 sec =2%

dm

ax

T, sec Figure After Chopra, 2001



Response Spectrum is useful to obtain maximum response of any SDOF system for that accelerogram and for that value of damping.

See example on next slide

9


Example

Ground Acceleration Time History

Acceleration Response Spectrum for the above accelerogram for 5% damping (Fig. from Seed and Idriss, 1982)

Mass = 10,000kg

Natural Period T=1 sec

Damping =5% of critical

From Response Spectrum:

Spectral Acceleration (for T=1sec) = 0.48 g

Max. Base Shear = Mass x Spectral Accln. =(10,000kg) x (0.48x9.81m/sec2) = 47,000 N = 47 kN

Max. Base Moment

=(47kN) x (3m) = 141 kN-m

3m

Undamped Natural Period T (sec)

Time (sec)

Maxim

um

Acc

ele

ration, g

Acc

ele

ration, g



May repeat the entire process for different values of damping

Velocity response spectra for N-S component of 1940 El Centro record (damping values of 0, 2, 5 and 10%)

Fig From Housner, 1970 Natural Period T (sec)

Maxim

um

Velo

city

, in

/sec

10



Unless otherwise mentioned, response spectrum is based on a linear elastic system



By response we may mean any response quantity of interest to us, for example: Absolute acceleration of the mass

Termed as Acceleration Response Spectrum

Relative velocity of the mass with respect to base

Termed as Velocity Response Spectrum

Relative displacement of the mass with respect to base

Termed as Displacement Response Spectrum

Word Spectra is used to denote plural of Spectrum.

11



Since SDOF system responds maximum to the waves of frequency near its own natural frequency,

Response spectrum is also a very good way to

characterize the strong ground motion from

engineering view point.

For instance, relative strength of low frequency versus high frequency waves

See example on next slide


Example: Velocity spectra from two accelerograms

Note that the two response spectra above show very different frequency content. Ground motion B has more energy at low periods. An expert may be able to make out from these spectra that B is recorded at a short distance (say 15km) from a small earthquake, while A is recorded from a large earthquake at a large distance (say 100km) (Fig. edited from Housner, 1970)

Natural Period T (sec)

Velo

city

, ft

/sec

12



Response spectrum is a very powerful tool.

Uses of response spectrum:

To obtain maximum response of a SDOF system

(to the original accelerogram using which

response spectrum was obtained)

To obtain maximum response in a particular

mode of vibration of a multi degree of freedom

(MDOF) system

It tells about the characteristics of the ground

motion (accelerogram)



Different terms used in IS:1893 Design Acceleration Spectrum (clause 3.5)

Response Spectrum (clause 3.27)

Acceleration Response Spectrum (used in cl. 3.30)

Design Spectrum (title of cl. 6.4)

Structural Response Factor

Average response acceleration coefficient (see terminology of Sa/g on p. 11)

Title of Fig. 2: Response Spectra for ….

It is better if the code uses the term consistently.

13


Smooth Response Spectrum

Real spectrum has somewhat irregular shape with local peaks and valleys

For design purpose, local peaks and valleys should be ignored Since natural period cannot be calculated with

that much accuracy.

Hence, smooth response spectrum used for design purposes

For developing design spectra, one also needs to consider other issues We will discuss this later.


Smooth Response Spectrum (contd…)

Acceleration Spectra Velocity Spectra Displacement Spectra

Shown here are typical smooth spectra used in design for different values of damping

(Fig. from Housner, 1970)

Period (sec) Period (sec) Period (sec)

14


Ground Acceleration (contd...)

Note the term Peak Ground Acceleration

(PGA) is max acceleration of ground.

Because of deformation in the structure, the

motion of its base and the superstructure will be

different

Max acceleration experienced by mass of the

structure will be different from the PGA (except if

the structure is rigid)


Ground Acceleration

ZPA stands for Zero Period Acceleration.

Implies max acceleration experienced by a

structure having zero natural period (T=0).

15


Zero Period Acceleration

An infinitely rigid structure

Has zero natural period (T=0)

Does not deform:

No relative motion between its mass and its base

Mass has same acceleration as of the ground

Hence, ZPA is same as Peak Ground Acceleration

For very low values of period, acceleration

spectrum tends to be equal to PGA.

We should be able to read the value of PGA

from an acceleration spectrum.


Peak Ground Acceleration (contd…)

Average shape of acceleration response spectrum for 5% damping (Fig. on next slide) Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA

There can be a stray peak in the ground motion; i.e., unusually large peak. Such a peak does not affect most of the

response spectrum and needs to be ignored.

Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11) There are also other definitions of EPGA, but we

will not concern ourselves with those.

16


Typical shape of acceleration spectrum

•Typical shape of acceleration response spectrum

•Spectral acceleration at zero period (T=0) gives PGA

•Value at 0.1-0.3 sec is ~ 2.5 times PGA value (for 5% damping)

PGA = 0.6g 0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Period (sec)

Spectr

al A

ccele

ration (

g)


What is Design Spectrum

Seismic Design Force can be specified in terms of Response Spectrum:

Termed as Design Spectrum

17


Response Spectrum versus Design Spectrum

Consider the Acceleration Response Spectrum

Notice the region of red circle marked: a slight change in natural period can lead to large variation in maximum acceleration

Undamped Natural Period T (sec)

Spect

ral Acc

ele

ration, g


Response Spectrum versus Design Spectrum (contd…)

Natural period of a civil engineering structure cannot be calculated precisely

Design specification should not very sensitive to a small change in natural period.

Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum

18


Design Spectrum

Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure.

The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well.

See Fig. next slide.


Design Spectrum (contd…)

Natural vibration period Tn, sec

Sp

ectr

al A

ccel

erat

ion

, g

Fig. from Dynamics of Structures by Chopra, 2001

19



Design Spectrum is a design specification

It must take into account any issues that have bearing on seismic safety.



Design Spectrum must be accompanied by:

Load factors or permissible stresses that must be

used

Different choice of load factors will give different seismic safety to the structure

Damping to be used in design

Variation in the value of damping used will affect the design force.

Method of calculation of natural period

Depending on modeling assumptions, one can get different values of natural period.

Type of detailing for ductility

Design force can be lowered if structure has higher ductility.

20


Soil Effect

Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site

Period (sec)

Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996


Soil Effect (contd…)

This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites.

Sp

ectr

al A

ccel

erat

ion

Coef

fici

ent

(Sa /

g)

Period(s)

Fig. from IS:1893-2002

21


Shape of Design Spectrum

The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes.

In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected.


Design Spectrum for Stiff Structures

For very stiff structures (T < 0.1sec), ductility is not helpful in

reducing the design force.

Actual shape of response spectrum (may be used for higher modes only)

T(seconds)

Sp

ectr

al a

ccel

erat

ion

Design spectrum assumes peak extends to T=0

Concept sometimes used by the codes for response spectrum in low period range.

As a stiff structure gets damaged during the shaking, its period elongates

i.e., during the same ground shaking, a very stiff structure may ride up the ascending part of the graph.

Codes tend to

disallow the reduction

in force in the period

range of T < 0.1sec

strong ground motions

Documents