STUDY ON LONG PERIOD DESIGN SPECTRUM
And ATTENUATION RELATIONSHIP

Institute of Mechnics Engeneering China
Earthquake Administration
Zhou zhenghua
Liu peixuan

Along with the number of long period structures increasing
rapidly, such as skyscraper, super-large bridge etc, the seismic designof long period buildings has become a problem that needs urgentsolution. The period of those structures is longer than 8s，and react
violently with long period ground motion. It’s seismic design needs
parameters of long period ground motion.
The period of design response spectrum in current chineseseismic design codes is only several seconds, which can’t satisfy theneed of long period stuctures’ seismic design. For example, thelongest period of design response spectrum is 6s in the Code for
Seismic Design of Building (GBJ50011-2010)and is 7s in the Codefor Seismic Design of Structure (GBJ0191-93).
On the whole, the study of long period ground motion juststill is in an abecedarian phase. For lacking abservation data, it isdifficult to creat the attenuation relationship of long period groundmotion.

322 horizontal component acceleration records are collectedfrom the digital accelerograph records, which have long beforehand
record and basic site material. Those data is recorded in the Taiwan
Chi-chi Earthquake 1999, the 1985 Mexico Ms8.1 Earthquake andMs7.5 aftershock, the 1995, the 1994 Northridge Earthquake,
Tangshan aftershock records and the Taiwan SMART-1 Array records(table 1).
Because the sites information isn’t collected enough, the sites
are divided into 3 types: bedrock, general soil and soft soil.

Table 1 Digital Accelerograph Record
EarthquakeBedrock

General soil

Soft soil

Chi-Chi Earthquake810546Earthquake

3826Earthquake

4162

Northridge Earthquake

14248aftershock

5SMART-1 Array44

For the long period spectrum attenuation part, use two methods.
1、single-stage method⎧⎪1 + (C − 1) Ti⎪
T1⎪
Si = ⎨C⎪
0 .9T⎛⎞⎪ g⎪⎜⎜ T ⎟⎟ C⎩⎝ i ⎠0 ≤ Ti < T1
T1 ≤ Ti < TgTg ≤ Ti

2、two stage methodTi⎧
1+(C−1)⎪T1⎪C⎪
Si = ⎨ T 0.9⎛ ⎞⎪⎜ g ⎟ C⎪⎜⎝ Ti ⎟⎠⎪ 0.2 0.9 − 0.02(Ti − 5Tg ) C⎩()0 ≤ Ti < T1
T1 ≤ Ti < Tg
Tg ≤ Ti < 5Tg
5Tg ≤ Ti

Fitting result:
1、 Average acceleration response spectrum and fitting responsespectrum of bedrock.
3

β2

1

statistic response spectrum
fitting spectrum 1
fitting spectrum 2

00.01

0.1

T(s)

1

10

2、Average acceleration response spectrum andfitting response spectrum of general soil.
3.0

2.5

β

2.0

1.5

1.0
统计反应谱拟合谱1
拟合谱2

0.5

0.0
0.01

0.1

1T (S)

10

3、 average acceleration response spectrum and fitting
response spectrum of soft soil.
3β21

sta tistic re sp o n se sp e ctru mfittin g sp e ctru m 1
fittin g sp e ctru m 2

00 .0 10 .1

1T (s )

10

Characteristic value of fitting curves
characteristic value of fitting curves
decrease part use two-stage

decrease part use single-stage

Tg

Βmax

Tg

Βmax

Bed rock

0.58

1.93

0.57

1.95

General soil

0.76

1.97

0.76

1.97

Soft soil

1.81

1.91

1.81

1.91

Type of site

The fitting results of the two methods are almost same, and thesingle-stage fitting result is better than the two-stage fitting result.
The characteristic period in fitting results is much bigger than it in
the current criterion. Response spectrum platform values are around
2.0 for different the sites and are lower than the current criterion’s.

• The problem how to evaluate the long period
ground motion longer than 8s is a hot subject
in current earthquake engineering field. This
study is to evaluate the long period groundmotion based on the attenuation relationship.

The Numerical Simulation• a larger number of earthquake records is needed
for studing attenuation relationship of long
period groud motion. But for the lacking
earthquake area, we attempt to use one typesite’s attenuation relationship to stand for othersites.
• Because of lacking the bedrock earthquake
records, the records of overburden layer is used
to stand for the bedrock earthquake records. The
thickness of overburden layer is the primaryeffact factor to the ground motion.

• Choose the seven site model: bedrock , hardsoil (5m, 15m), moderately hard soil (25m,40m), soft soil (60m, 80m).
• Use three artificial ground motion : large (601gal), medium (283 gal) and small (119 gal), to
calculate every sites’ response spectrum.

1、seismic response spectrum – large eq
B
1000

gal

100

100.1

1Time(s)102、seismic response spectrum – medium eq
B

gal

100

1010.1

1Time(s)10

3、seismic response spectrum – small eq
Bgal

100

1010.1

1

A

10

� From the point of view of the numericalsimulation we can see, the difference at long
period seismic spectrum part is very small.

Verify the result of numerical simulation• To prove the result of numerical simulation,
use three group earthquake records tocompare their long period seismic response
spectrum.

1、江油地震台和江油重华
gal

gal
1000

1000

100

100

N-S

E-W
10
100.1

110s

A0.1

1B

gal

100

红色为江油地震台
黑色为江油重华

U-D
100.1

1C

10s

10s

2、茂县地办和茂县南新
gal

gal

1000

1000

100

100

N-S

E-W
10

100.1

110s

A

gal

0.1

110B

1000

100

红色为茂县地办黑色为茂县南新

U-D
100.1

1C10ss3、石棉草科、挖角和先锋
gal

gal

100

100

1010E-W

N-S

1

10.1110s

Agal

0.1

1

B

B

100

红色为石棉草科
蓝色为挖角
黑色为先锋

10U-D
10.1

1C

10s

10s

Thank you !