Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

1SEISMIC VULNERABILITY INDICESFOR GROUND AND STRUCTURES
USING MICROTREMOR
Yutaka NAKAMURAPresident
System and Data Research Co., Ltd., Tokyo, JAPAN
Telephone: +81-042-574-4536,
Facsimile: +81-042-574-4576
e-mail: yutaka@sdr.co.jp
Summary

Earthquake disaster never occurs whenever seismic force does notsurpass durability of ground and structures. Thus continuous watch ofearthquake motion is first of all necessary, in order to predict and monitor
the occurrence of earthquake disaster. For the ground and structures
exposed to earthquake motion, it is necessary to grasp their durability
precisely by executing investigations in advance. From the view point ofearthquake disaster prevention, to grasp the durability of ground andstructures is even more important than to monitor the earthquake motion.
In this paper, a new technique to investigate rapidly with precisiondurability against earthquake of various structures and surface ground byusing microtremor. Validity of the proposed method has been examinedby comparing the results of investigations by the new technique in theearthquake damaged areas (before or after the event) with actual
earthquake damage experienced.
If weak points of structures can be detected in advance byinvestigating the durability of various structures and ground, damage ofstructures can be decreased by taking appropriate countermeasures.
Besides, secondary disaster can be also decreased very much by adopting
precise immediate measures based upon accurate damage estimation whenearthquake occurs.
Key Words: Vulnerability indices, K-values, microtremor, earthquake,QTS, damage, spectral ratio H/V, surface ground, viaduct,embankment, derailment/overturnY. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

2Introduction
To increase the durability of ground and structures beyond the presumed seismic force isfundamental of earthquake disaster prevention.
However, although enough durability existed
initially, it may decrease under presumed seismic force due to deterioration in time. In very
cold weather area or very much rain fall area, durability of ground changes by seasons. Thento grasp precisely durability “at present” becomes fundamental to disaster prevention. For thestructures without enough durability due to deterioration in time or by past earthquake, it isnecessary to reinforce the weak points. New structures, of course, must be constructed withsufficient durability.
It is important to investigate in advance whether ground and reinforced old structures or
newly constructed structures are furnished with prescribed resistant power or not. If suchinitial dynamic characteristics are grasped, maintenance can be performed rationally anddamage extent will be quantitatively estimated.
Damaged points due to earthquake motions are weak points revealed by earthquake itself.
If weak points are investigated in advance, it is possible to reinforce the structures before
receiving damage by earthquake. In case of railway structures, if the weak point does nothinder train operation, it can be utilized as a monitoring point of earthquake damage occurrence.
In addition, if seismic characteristics of ground and structures are already known, seismic
intensity distribution of the area can be precisely estimated.
Occurrence of earthquake damage depends upon strength, period and duration of seismic
motions. These parameters, of course, depend upon earthquake itself but they are alsostrongly influenced by the seismic response characteristics of surface ground and structures.
Thus, the weak points can be found by investigating seismic characteristics of surface groundand structures.

Estimation of Seismic Characteristics of Ground and Structures
It is expected to increase the precision of damage estimation remarkably, if seismic
characteristics of surface ground affecting earthquake damage can be grasped not by boring but
by precise measurement. Characteristics of surface ground can be approximated by spectral
ratio of horizontal to vertical component (QTS: Quasi-Transfer Spectrum) of microtremor(Nakamura, 1989).
Seismic response characteristics of structures can be estimated by spectral ratios of
microtremors measured simultaneously on structures and their foundation ground surface.
QTS of microtremors on the structures are approximated by combined characteristics of groundand structures.
The results of microtremor measurements at every 100 m along railway lines arearranged as procedure sheets for disaster prevention. It suggests good correspondence of QTSof microtremors with geological and topographic structures. Until now microtremors ofgrounds and structures at more than 20,000 points along railway lines and elsewhere have beenmeasured. In 1995 and 1996, microtremors of ground and structures were observed in total atnearly 3,000 points in and near Kobe city after the 1995 Hyogo-Ken-Nanbu Earthquake.

Vulnerability Indices of Ground and Structures (K-values)
Vulnerability indices (K-values) derived from strains of ground and structures in time ofearthquakes are proposed as follow.

a) GroundFor ground, shear strain γ of surface ground is noticed. Table 1 shows relationship of γ
to ground disasters compiled by Ishihara (1978). It indicates that from γ ≅ 1000×10-6 ground
begins to show non-linear character and in γ > 10,000×10-6 large deformation and collapse
occur.

Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

Table-1

Strain Dependence of Dynamic Properties of Soil

10−6

Size of Strain γ
Phenomena

10−5

10−4

Wave, Vibration

Dynamic Properties

3Elasticity

10−310−2

Crack, Settlement

10−1

Landslide, Soil Compaction, Liquefaction

Elasto-Plasticity

Collapse
Repeat- Effect, Speed- Effect of Loading

Simplifying the shear strain deformation of surface ground as shown in Figure 1, average
shear strain γ of surface ground can be estimated by following formula, namely
γ = Ag×d/HAg ×d(1)where, Ag is amplification factor, H is thickness of surface layer,and d is seismic displacement of the basement ground.
Putting S-wave velocities of basement ground and surface
ground as vb and vs respectively, proper predominant frequency
Fg of surface ground is approximately expressed as
Fg = vb/(4Ag×H)

HVS

Basement Ground

(2)

Fig.1
Acceleration of basement ground αb is expressed asand γ is expressed by Fg, Ag and vb as follows:γ = (Ag×αb/(2πFg)2)×(4Ag×Fg/vb)= (Ag2/Fg)×(αb/(π2vb))(3)

If efficiency of applied dynamic force is assumed
to be e % of static force, effective γe is
γe = Kg(e)×αb
Kg(e) = e×(Ag2/Fg)/(π2vb)/100.

(4)
(5)

Surface Ground Strain

Marina District in San Francisco, U.S.A.
Kg-value for Surface Ground

αb = (2πFg) ×d2VB

500
Reclaimed Land: Severe Damage
10050
Hill side Area:
10510. 5

No Damage
Damaged Area
0500
1500 m100
Distance from0Coast LineFig. 2 Kg-values derived from QTSof Microtremor in S.F.
The value of vb is expected to be nearly constant in a broad area and Kg is a proper value
for measured point. Thus Kg can be considered as an index to indicate easiness ofdeformation of measured points which is expected useful to detect weak points of the ground.
As we can consider vb = 600 m/s, we obtain 1/(π2vb) = 1.69×10-6 (s/cm). If we put e =60 %, then Kg(e) ≅ Ag2/ F g and the effective strain can be estimated by multiplying Kg(e) value
with maximum acceleration of basement ground in Gal (= cm/s2).
Figure 2 indicates Kg-values obtained in San Francisco Bay Area after the 1989 LomaPrieta Earthquake. For Marina district the result along a line from sea coast to hillside isshown. It shows Kg at the sites where grounds deform much are bigger than 20 and Kg at thesites with no damage are very small. Considering the maximum basement accelerationsaround the area are estimated as 50 Gal based on observations, Kg = 1000×10-6 separates theareas liquefied or not.

b) Embankment
In the past, embankment was most common railway structures which roughly occupied
80 % of all railway lines in Japan. Thus to grasp seismic characteristics of embankment is

Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

4very important for the earthquake disaster prevention of railways. We found it is rather easy
to obtain characteristics of embankment body and its foundation grounds separately bymeasuring microtremors on the embankment and on the ground surface under the embankment
simultaneously. Vulnerability indices of embankment body and its foundation ground can beestimated separately and originated strains can also be calculated. Thus, it is expected
possible to discriminate the damage due to surface ground deformation and collapse ofembankment body itself. In addition, from the microtremor measurements on the embankmentalone vulnerability indices of the structures consisting of embankment and surface ground
together can be simply calculated. Embankment can be considered as a local additionalsurface layer and vulnerability index Kj for the embankment and surface ground together can bedefined as Kg defined for the surface ground when e = 60 %, namely,
Kj =A2/F,(6)

where F and A are predominant frequency and its amplification factor obtained from QTS ofmicrotremors observed on the embankment.
Embankments between Kayanuma and Gojikkoku along Sen-mou Line (KushiroAbashiri line in Hokkaido, Japan) were damaged by the 1994 Hokkaido-Toho-Oki Earthquake
again after the damaged parts by the 1993 Kushiro-Oki Earthquake were repaired.
Microtremors were measured on the shoulders of both sides of the embankments damaged by
the 1993 Kushiro-Oki Earthquake and Kj values were calculated. After the measurements the1994 Hokkaido-Toho-Oki Earthquake occurred and the measurement was considered as that
before earthquake.
Figure 3 shows comparison of Kj-values obtained before the earthquake in 1994 and thedamage degrees. It shows places with large Kj-values correspond to the sites with big damage.
Besides, Kj-values of left and right sides of the embankment show big difference and thedamage of the 1994 Hokkaido-Toho-Oki Earthquake ( subsidence of embankment ) was severe,
where Kj-values were larger, which suggests that Kj-values represent the vulnerability precisely.
T h e D a m a g e o n marsh side
E m b a n k m e n t n e a r K 7 p o int

hill side T h e D a m a g e o n h i ll sidemarsh side

E m b a n k m e n t n e a r K 7 p o int

100
10K4

Ｋｊ
K2

1

B e fore
K7

K10K11K1

32.1

K1232.2
32.332.4
32.5
D istance in km from K u shiro

Fig. 3 Relation between Embankment Damage and Kj-values measured before the earthquakec) Rigid Frame Viaducts
Rigid frame viaducts have become common now as railway structures. Earthquake
damage of rigid frame viaduct has occurred since many years ago. Concrete cover of upperand lower column ends of the viaducts were peeled off and inner-reinforcing iron rods wereexposed. In addition, middle layer beams of the viaducts of Shinkansen received big cracks.
Near the damaged viaducts of Keihin-kyuko Line and Tsugaru-Kaikyo Line, alarm
seismometers were installed and maximum seismic accelerations around 200-300 Gal wererecorded. The 1995 Hyogo-Ken-Nanbu Earthquake recorded acceleration bigger than 500 Gal(nearly twice of ever experienced seismic acceleration until then) and fatal collapse occurred.
Some viaducts suddenly collapsed by shear failures which essentially cannot be expected tooccur before bending failures. Other viaducts collapsed fatally by gradual large bending
failures.

Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

5In general, concrete structures are designed as bending failures precede at first andvulnerability index Ksg is here defined by noting marginal strains which appear at the upper andlower column ends. Basic idea is to calculate the marginal strains ε of upper and lower
column ends by multiplying Ksg and maximum seismic acceleration α of basement ground or of
surface ground together.
b m : m ass δAt first, bending deformation of the viaduct is
calculated by applying acceleration α multiplied by
combined amplification factor of surface ground andα sg = A sg α bh
= A s αsviaduct or by amplification factor of viaduct itself.
EIAccording to Figure 4, bending deformation δof a viaduct against seismic inertia force is as follow.
δ = m×α/k= Asg×αb/(2πFs)2 = 1/(4π2)×(Asg/Fs2)×αb= As×αs/(2πFs)2 = 1/(4π2)×(As/Fs2)×αsThen marginal strains ε of upper and lower
column ends are estimated from bending deformation
with characteristics and size of the viaduct.
ε = σ/E= (M/(EI))×(b/2)= (6EI/h2)×δ/(EI)×(b/2)= (3b/h2)×δ= (3b/h2)/(4π2)(Asg/Fs2)×αb= (3b/h2)/(4π2)(As/Fs2)×αsαs = A g αb

Surface G roundαb

B a sem ent G round(a) V iaductbδmα sg = A sg α b= A s αsh2h1EIαs = A g αb
Surface G roundαb

B a sem ent G round(b) 2-storied V iad u c twhere, Fs is predominant frequency in Hz,
Asg is combined amplification of ground andFig. 4 Deformation of Viaduct
viaduct at predominant frequency Fsg in Hz.
Fsg, Asg, Fs and As are derived from spectral ratio and QTS of microtremor.
Assuming the efficiency of dynamic load is e of static load for the effective strain εe,εe = e×(3b/h2)/(4π2)×(Asg/Fs2)×αb = Ksg(e)×αb= e×(3b/h2)/(4π2)×(As/Fs2)×αs = Ks (e)×αsKsg(e) = e×(3b/h2)/(4π2)×(Asg/Fs2)
Ks (e) = e×(3b/h2)/(4π2)×(As/Fs2)

(7)
(8)

where, Ksg for combined ground and viaduct and Ks for viaduct itself, are defined as above andit will be extended Ksg and Ks for 2-stories viaduct becomes as follow.
Ksg(e) = (75e/π2)(Asg/Fs2)(b×hi/(h13+h23)),Ks(e) = (75e/π2)(As/Fs2)(b×hi/(h13+h23)),(9)( 10 )

where b is width in vibrational direction of column, hi is height of i-th column and 75/π2 is acoefficients selected so as calculated result to be in 10-6 unit, taking structural size in m, seismic
acceleration in Gal and efficiency in %.
The formula shows Ksg or Ks of higher column layer is bigger for 2-storied viaduct whichsuggests more vulnerable to earthquake disaster. It corresponds well to the fact observed incase of Hyogo-Ken-Nanbu Earthquake that 2-storied viaducts with higher columns received
much bigger damage.
Figure 5 shows Ksg-values of viaducts measured at every 100m along Shinkansen before
the 1995 Hyogo-Ken-Nanbu Earthquake compared to the damage of viaducts. Here e = 100%is assumed. The figure indicates that collapsed viaducts correspond to Ksg peak values

Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

6fluctuating in the range of Ksg > 50. Ksg values measured in advance well correspond to actual
damage received. Thus Ksg values obtained before the earthquake are expected to predict thefuture earthquake damage precisely.

Ksg-value

150

100

T o k itom oShimokema

HansuiD a iichi-N o m a

50

100 %
Apparent Damage Rateof Viaduct Column

0522524526528530532

D istance from T okyo in km
Fig. 5 Comparison between Viaduct Damage and Ksg-values measured before the Earthquaked) Derailment/Overturn of Trains
To study derailment/overturn of trains work done per unit time (work rate) applied byearthquake motions is considered. Work rate w is proportional to the product of response
acceleration A×αb and response velocity A×v. As v = αb/(2πF),w = m×A×αb×A×v= (m/(2π))×(A2/F)×αb2= (m/(2π))×Kd×αb2,Kd = A2/F

( 11 )( 12 )

where m is mass of objects receiving seismic force for instance trains or stone. It may
possible to adopt Kd-value not only for train derailment/overturn but also structure damage orjumping stone by strong motion.
F and A are directly related to the seismic motion applied to the train body. The
dynamic characteristics of trains are known in general, F and A can be estimated from Fg andAg when a train stays on the ground surface, or from Fsg and Asg of both structures and groundwhen a train stays on the structure.
Site characteristics is reflected in Kd-value. In case of large Kd-value, work rate w andpossibility of derailment/overturn are also large. Thus Kd-value is considered as an index toindicate the vulnerability on derailment/overturn of trains.
Figure 6 shows derailment/overturn of stopping electric vehicles staying in the JRTakatori yard due to the 1995 Hyogo-Ken-Nanbu Earthquake. Severe derailments occur
approximately on the points with bigger Kd-values.
Figure 7 indicates derailments of running trains in time of the 1995 Hyogo-Ken-Nanbu
Earthquake and Kd-values near the derailment sites every 20m approximately. It shows thatwhether trains derailed or not closely depends on Kd-values of the sites where trains wererunning.

Concluding Remarks
Vulnerability indices (K-values) of ground and structures due to earthquake motions havebeen proposed. K-values can be calculated from microtremors measured easily everywhere

Y. NAKAMURA /World Congress on Railway Research, Florence, Nov. 1997

7and it is not impossible to estimate the vulnerabilities of all structures and ground concerned.
In the near future, the data of K-values will be accumulated and the plan to do vibration
rupture experiment to estimate damage degrees precisely from K-values and to examine validityof K-values as vulnerability indices will be done.

T: Train Condition

A-lineKdＤＣＢＡ３１７５９Fg10Ag

1Kd10F

3Ag

５ D&T３T

57 9

1B-lineF357 9T10Kd-value

Kd-value

A5A
1FA

Measuring Points
D 1 2 3 4 5

Measuring Points

Fg

７Fig.6

5TA

T

Kd-value

10Kd-value& 5C
BAC-line

5T
357 9

Measuring Points

1F

35T

7 9

Measuring Points

Relationship between Microtremor and Derailment/Overturn in JR-Takatori Yard

Vulnerability indices forderailment/overturn Kd

100DownUp

101.0

Start 80km/h
End
Train 9506:
DerailmentStartTrain 110C:
NormalEnd

80km/hStart

100km/hEnd
Train 5101M:
Derailment

0.1585km
Fig.7586km

Relationship between Kd Distribution and Actual Situation of Trains along Railway

Acknowledgments
This research was supported and cooperated by staffs of UrEDAS R&D Promotion
Division of Railway Technical Research Institute and System & Data Research Co., Ltd.. Iwish to extend my sincere gratitude to the people for their support and cooperation.

Bibliography
1)Ishihara, Kenji: Introduction to Dynamic Soil Mechanism, January 1978 (in Japanese).
2)Nakamura, Yutaka: A Method for Dynamic Characteristics Estimation of Subsurface using
Microtremor on the Ground Surface, Quarterly Report of RTRI, Vol. 30, No.1, Railway
Technical Research Institute, January 1989.