Experimental Methods and Analyses - 国立研究開発 … (3) Tests on Embedment Effects on Reactor...

VI: Experimental Methods and Analyses • Experimental study on nonlinear soil structure interaction of nuclear power plants using large

scale blast excitations, by Osamu Kontani, Atsushi Suzuki, Yoshio Kitada, and Michio Iguchi.

• Load bearing mechanism of piled raft foundation during earthquake, by Shoichi Nakai, Hiroyuki Kato, Riei Ishida, Hideyuki Mano and Makoto Nagata.

• Study on the dynamic characteristics of an actual large size wall foundation by experiments and analyses, by Masanobu Tohdo.

• Field method for estimating soil parameters for nonlinear dynamic analysis of single piles, by A. Anandarajah, J. Zhang and C. Ealy.

• Soil profile confirmation through microtremor observation, by Yuzuru Yasui and Tatsuya Noguchi.

• Evidence of soil-structure interaction from ambient vibrations—consequences on design spectra, by F. Dunand, P.-Y. Bard, J.-L. Chatelan, and Ph. Guéguen.

• Effects of soil-structure interaction at an earthquake observation station identified by micro-tremor measurement, by Toshiro Maeda.

• A study on dynamic soil-structure interaction effect based on microtremor measurement of building and surrounding ground surface, by Masanori Iiba, Morimasa, Watakabe Atsushi Fujii, Shin Koyama, Shigeki Sakai, and Koichi Morita.

1

Experimental Study on Nonlinear Soil Structure Interaction of Nuclear Power Plants using Large Scale Blast Excitations

Osamu Kontani,1) Atsushi Suzuki,1) Yoshio Kitada,2) and Michio Iguchi 3)

Extensive seismic vibration tests are proposed to promote better

understanding of the nonlinear soil-structure interaction of nuclear power plants

during large earthquake motions. The influence on structural responses caused by

geometrical nonlinearity (uplift) of the base mat as well as the material

nonlinearity of the soil under the base mat are the main issues to be investigated.

The proposed vibration tests will be performed at a coal mine. Ground

motions from large-scale blasting operations will be used as excitation forces for

the vibration tests. Significant aspects of this test method are that vibration tests

can be performed several times with different levels of input motions by choosing

blast areas at appropriate distances that will generate the desired accelerations at

the test sites, and that large scale model structures on the ground can be tested

with consideration of three dimensional effects and soil-structure interaction.

INTRODUCTION

“Regulatory Guide for Aseismic Design of Nuclear Power Reactor Facilities” (JNSC

1981) is presently undergoing extensive revision by the Japan Nuclear Safety Commission.

The following items are related to nonlinear soil-structure interaction (SSI) of nuclear power

plant buildings and might be introduced through the revision.

1. Introduction of New Methodology for Evaluating Basic Design Earthquake

2. Consideration of Dynamic Effects in Evaluating Vertical Seismic Design Load

3. Relaxation of Requirement of Building Construction on Firm Bedrock

1) Kajima Corporation, Nuclear Power Dept., 6-5-30 Akasaka, Minato-ku, Tokyo 107-8502, JAPAN 2) Japan Nuclear Energy Safety Org., 3-17-1 Toranomon, Minato-ku, Tokyo 105-0001, JAPAN 3) Tokyo University of Science, Faculty of Science and Engineering, 2641 Yamazaki, Noda-shi, Chiba

278-8510, JAPAN

Proceedings Third UJNR Workshop on Soil-Structure Interaction, March 29-30, 2004, Menlo Park, California, USA.

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4. Introduction of PSA for Evaluating Seismic Margin of Nuclear Building

The Nuclear Power Engineering Corporation (NUPEC 1998) had conducted extensive

experimental studies on the SSI of the nuclear power plants. The following is a series of

major studies related to the SSI of structures.

1. Verification Test for Seismic Analysis Codes.

(1) Model Tests on Dynamic Soil-Structure Interaction (1980-1986).

(2) Base Mat Uplift Tests of Reactor Building (1986-1995).

(3) Tests on Embedment Effects on Reactor Building (1981-1987).

(4) Model Tests on Dynamic Cross-Interaction of Structures (1994-2002).

2. Verification Test of New Siting Technology(1983-2000).

The above studies contributed greatly to understanding of SSI behaviors and development of

earthquake response analysis codes. However, they provide very little information on the

SSI of nuclear facilities subjected to large input motions, because the experimental conditions

were within the design levels. Therefore, more studies are needed on nonlinear SSI in order

to precisely evaluate responses of the nuclear power plants subject to larger earthquake

motions.

Common ways for performing seismic tests on structures are forced vibration tests,

earthquake observations, shaking table tests and centrifuge tests. These methods are very

useful in many ways. However, none are capable of shaking a large-scale SSI system at

larger amplitudes.

This paper describes the significance of experimental studies on nonlinear SSI of

nuclear power plants. It also provides a method for conducting seismic tests on large scale

model structures using ground motions caused by large scale blast excitations.

GREAT NEED TO INVESTIGATE NONLINEAR SSI

Introduction of New Methodology for Evaluating Basic Design Earthquake

Basic design earthquakes S1 and S2 are employed for the seismic design of nuclear

power plants in Japan. S1 is based on earthquake history and very active faults, whichever

has the greater influence. S2 is evaluated from active faults, the seismic tectonic structure

and shallow-focus earthquake of M6.5. Since the Great Hanshin-Awaji Earthquake in 1995,

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shallow-focus earthquakes of magnitude greater than M6.5 have been observed quite often.

It was therefore decided to increase the magnitude of the design shallow-focus earthquake.

This is currently under discussion. If the S2 level earthquake is increased, the SSI in the

nonlinear region would be very important in precisely evaluating earthquake responses of

nuclear structures against basic design earthquakes.

Consideration of Dynamic Effects in Evaluating Vertical Seismic Design Load

In current design practice, horizontal seismic design loads are evaluated from a

dynamic response analysis of the building. Vertical seismic design loads are static and are

evaluated from a vertical seismic coefficient that is uniform throughout the structural height.

After the revision of the regulatory guide, the vertical seismic design load will be evaluated

from a dynamic response analysis in the same way as the horizontal seismic design loads.

Therefore, it is very important to understand nonlinear SSI behavior and to develop methods

for precisely evaluating vertical responses of nuclear structures.

Relaxation of Requirement of Building Construction on Firm Bedrock

In current design practice, nuclear buildings are required to be constructed on the firm

bedrock layer. The revision may relax the construction requirement. Then, building

construction on quaternary deposits needs to be investigated in order to alleviate long-term

siting problems for nuclear power plants. Since the quaternary deposit is softer than the

bedrock, nonlinear SSI should be properly incorporated into the earthquake response analysis

method as well as seismic design.

Introduction of PSA for Evaluating Seismic Margin of Nuclear Building

The probabilistic technique is very important for investigating seismic redundancy of

nuclear structures, because deterministic methods are just too uncertain to deal with

earthquake hazard and building fragility. In order to evaluate fragility of nuclear buildings, it

is necessary to develop an earthquake response analysis method that can be employed during

large input motions.

Thus, understanding of nonlinear SSI of nuclear power plant buildings is very

important, and needs to be incorporated into an earthquake response analysis method that can

be used during large input motions, and also needs to be incorporated into seismic design of

nuclear structures. Major issues in nonlinear SSI are geometrical nonlinearity (uplift) of the

base mat and material nonlinearity of soil under the base mat.

4

SURVEY OF INFORMATION ON SOIL-STRACTURE INTERACTION

1. Verification Test for Seismic Analysis Codes

NUPEC had conducted extensive experimental studies on the SSI of nuclear power

plants. The following titles are major studies performed on the SSI as a part of a series of

“Verification Test for Seismic Analysis Codes.”

(1) Model Tests on Dynamic Soil-Structure Interaction (1980-1986)

A series of forced vibration tests and earthquake observations were performed in the

field to evaluate the SSI for rigid structures (Odajima 1987, Iguchi 1987). Three structural

models representing reactor buildings and two concrete block specimens were employed.

Figure 1 shows a structural model representing a BWR building. In the tests, the effects of

base mat size on dynamic soil stiffness, radiation damping and soil pressure distributions

were investigated. This study provided very basic and important information on the SSI that

is used practically nowadays.

(2) Base Mat Uplift Tests of Reactor Building (1986-1995)

Shaking table tests in the laboratory and forced vibration tests in the field were

conducted to investigate uplift phenomena of the rigid structures (Hangai 1991). Figure 2

shows one of two test specimens employed for the shaking table tests. The soil was modeled

with silicon rubber. This study provided the following findings. 1) As the contact ratio

decreased with increasing input motions, response amplification of the structure became low

and resonance frequencies of the SSI system shifted toward longer periods. 2) Horizontal

motions with higher frequency were induced by uplift phenomena.

RC Base Mat

Superstructure:Steel FrameFloor:RC

RC Base Mat

Superstructure:Steel FrameFloor:RC

Figure 1 BWR Building Model Figure 2 Uplift Test Specimen

5

(3) Tests on Embedment Effects on Reactor Building (1981-1987)

Forced vibration tests with exciter and earthquake observation were performed in the

field in order to investigate the embedment effects on SSI (Kobayashi 1991). Shaking table

tests using silicone rubber as soil model were also conducted to supplement field test. Two

types of structural models are shown in Figure 3. Model B is the 1/10 scale model of BWR

building. Major finding was that the embedment of the building reduced response of

structure and increased natural frequencies and damping factors of the SSI system.

Full Embedment

Backfill

8000

1050

0

1600

3400

2750

2750

2500

Half Embedment 2500

Model A Model B

（Unit:mm）Full Embedment

Backfill

8000

1050

0

1600

3400

2750

2750

2500

Half Embedment 2500

Model A Model B

（Unit:mm）

Figure 3 Models for Forced Vibration Tests

(4) Model Tests on Dynamic Cross-Interaction of Structures (1994-2002)

Experimental studies were performed to investigate dynamic cross-interactions of

structures (Yano 2000, Kusama 2003). Forced vibration tests and earthquake observations

were conducted in three different conditions as shown in Figure 4. Two identical building

models in the field test are shown in Figure 5. Vibration tests using a shaking table were

performed on 1/230 scale aluminum-building models as shown in Figure 6. It was found that

the two identical building models showed lower amplification in the series direction and

almost the same amplification in the parallel direction compared with the single building

model.

Single Building Model(Reactor Building)

Two Identical Building Model(Two Reactor Buildings)

Two Different Building Model(Reactor & Turbine Buildings)

ReactorTurbine

Single Building Model(Reactor Building)

Two Identical Building Model(Two Reactor Buildings)

Two Different Building Model(Reactor & Turbine Buildings)

ReactorTurbine

Figure 4 Building Model Arrangement

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Two Identical Building Model Figure 5 Building models in field Test Figure 6 Vibration test using shaker

Verification Tests of New Siting Technology (1983-2000)

For higher seismic resistance, nuclear structures are required to be constructed on

firm rock layers, which gave problems in finding new construction site. In order to alleviate

long-term siting problems for nuclear power plants, NUPEC performed an extensive

investigation program on soil stability during large earthquake, seismic safety of buildings,

and so on (Uchiyama 1992). Forced vibration tests were carried out on concrete blocks on

quaternary deposits, as shown in Figure 7. Block A was designed to provide the same

contact pressure as an actual reactor building. As a result, SSI behaviors were well-

understood and dynamic soil properties were obtained.

Block ABlock B

GL -12.5mWater Table

▽

12ｍ 9ｍ

8ｍ 16.5ｍ

10ｍ

8ｍ

30MN50MN

Exciter

GL -11.0ｍ

GL 0.0ｍ

Figure 7 Forced Vibration Tests on Concrete Block Specimens

The above studies contributed greatly to our understanding of SSI behaviors and

development of earthquake response analysis codes. However, the responses obtained from

forced vibration tests are relatively small, and the maximum observed acceleration at ground

level was 171cm/s2. They provide very little information on nonlinear SSI of nuclear

facilities with large input motions, because the experimental conditions were within the

design levels. Therefore, more studies are needed on nonlinear SSI to precisely evaluate

responses of the nuclear power plants subject to large earthquake motions.

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PROPOSAL FOR VIBRATION TEST AT MINING SITE

Basic Idea of Vibration Test at Mining Site

The vibration test method using ground motions caused by mining blasts is shown

schematically in Figure 8. This method has the following advantages over conventional test

methods, such as forced vibration tests, earthquake observations, shaking table tests and

centrifuge tests.

1. Large-scale structures can be tested.

2. Ground motions of various amplitudes can be applied to the test structure.

3. Three-dimensional effects can be considered.

4. The SSI in the actual ground can be considered.

Large-scale vibration tests can be conducted at Black Thunder Mine (BTM). BTM is

one of the largest coal mines in North America and is located in northeast Wyoming, USA.

Since its operation is very active, it provides many opportunities to observe large ground

motions.

At the mine, there is an overburden over the coal layers. The overburden is dislodged

by large blasts called "Cast Blasts" and the rubble is removed by huge earthmoving

equipment. After the coal surface is exposed, smaller blasts called "Coal Shots" are applied

to loosen the coal layers. The coal is then mined out by truck and shovel operation. The

ground motions caused by Cast Blasts were used for the vibration tests. The smaller Cast

Blasts or Coal Shots were used to check and calibrate the instrumentation.

Explosive

Blast Area

Mudstone Layer(Overburden)

Test Structure with Embedment

Coal Layer

Earthquake-likeGround Motion

20m

Mudstone Layer

40m

Surface Layer

Figure 8 Vibration Test Method at Mining Site

8

Soil Profile and Ground Motions at BTM

Figure 9 shows the typical soil profiles. The shear wave velocities at the surface layer

were around 200m/s. Below GL-5m, the shear wave velocities gradually increased from

400m/s to 600m/s with increasing depth.

Acceleration time histories

recorded at 100m points from the blast

areas and their response spectra are

shown in Figure 10 (NUPEC 1998).

They vary widely in terms of wave

forms and dominant frequency

components. The differences resulted

from the blast operations, particularly

the time lag between blasts. At 100m

points from the blast area, the maximum

acceleration usually exceeded 1G at the

ground surface. The duration of

motions was 2 to 3 seconds depending upon the length of the blast areas.

0 2 4 6 8

2000

-20002000

-2000Acce

lera

tion

(cm

/s2 )

Time (s.)

Max. Acc.=1,197cm/s2

Max. Acc.=2,196cm/s2

April 1997

Nov. 1997

0.01 0.05 0.1 0.5 21Period (s.)

Acce

lera

tion

(cm

/s2 ) 8000

4000

0

Nov. 1997April 1997Nov. 1997April 1997

h=5%

Figure 10 Acceleration Time Histories and Response Spectra

Surface Layer

Mudstone LayerSandstone Layer

Coal Layer

Mudstone Layer

Surface Layer

Mudstone LayerSandstone Layer

Coal Layer

Mudstone Layer

GL -5m

GL -40m

GL -60m--700m/s～

--600m/s

1.9

2.15

400m/s

600m/s

1.8200m/s

Density(ton/m3)

S-wave Velocity

--700m/s～

--600m/s

1.9

2.15

400m/s

600m/s

1.8200m/s

Density(ton/m3)

S-wave Velocity

Figure 9 Typical Soil Profile at BTM

9

Details of Scaled Model Structure

Scale model structures for vibration tests at BTM were investigated in the studies

conducted by NUPEC (Kitada 2000, 2001). The Advanced Boiling Water Reactor (ABWR)

building was selected to investigate its nonlinear SSI behavior. Scale model rules were

established to precisely simulate the motions of the real scale ABWR in the gravity field,

including SSI behaviors. The following are important aspects of these scale model rules.

1. Accelerations for the scale models should be the same as those for the real scale

ABWR building because gravity cannot be scaled.

2. The scale models should be dynamically weakened by reducing the dimensions of

the structural members and by adding extra weights, since the strength of the scale

model increases with increasing scale factor if the same materials are used.

In previous studies (Kitada 2000, 2001), a 1/5 scale model was proposed for large-

scale vibration tests at BTM. Figure 11 shows sectional views of the real scale ABWR

building and the 1/5 scale model. The shear wave velocity for the 1/5 scale model was

determined at 400m/s based on the soil profile shown in Figure 9. For construction, the test

site had to be excavated to 5m depth. The 1/5 scale model on the ground for Vs=400m/s

corresponds to the real scale ABWR building on the ground of Vs=894m/s through the scale

model rules.

The real scale ABWR building was scaled down by 1/5 in length. The shear wall

thickness was scaled by 1/25 to reduce the strength of the 1/5 scale model. Extra masses were

added to each floor of the 1/5 scale model to keep the axial stresses of structural members the

same as in the real scale ABWR. Time was scaled by 5/1 . Thus, the accelerations, stresses,

and strains of the 1/5 scale model were the same as those of the real scale ABWR. The floor

thicknesses were constant at 30 cm to support added mass. Therefore, uplift phenomena were

the same as for the real scale ABWR, but the vertical motions on the floors were out of scale.

Figure 12 shows details of the 1/5 scale model. Table 1 shows the dimensions and

weights of the models. According to the response analysis using a lumped mass model, the

1st natural frequency of the 1/5 scale model was 9.13Hz. The response analysis using the 1/5

scale model with the input motion recorded on April 1997 provided maximum strains in the

shear wall of 4,630 micro strain and a contact ratio of 46%. It is considered that the 1/5 scale

model can be used to investigate nonlinear SSI as well as nonlinear behavior of the walls.

10

EL 0.0m

EL 45.0m

EL -18.5m

60.0 m

Vs=894m/s

EL -3.7m

EL 0.0m

EL 9.0m

12.0 mVs=400m/s

Real Scale ABWR Building

1/5 Scale Model

Figure 11 Real Scale ABWR Building and Scaled Models

Model with Extra Weight Dimensions of Walls and Slabs Figure 12 Details of 1/5 scale model

Table 1 Model Dimensions and Weights

Real Scale ABWR 1/5 Scale ModelModel Height (m) 63.5 12.7Basemat Size (m) 60 X 60 12 X 12

RCCV Thickness (cm) 200 8Shear Wall Thickness (cm) 30 to 170 4* to 7Basemat Thickness (cm) 550 110

Slab Thickness (cm) 50 to 100 30*Model Weight (ton) --- 947Added Mass (ton) --- 653Total Weight (ton) 200,000 1,600

*: out of scale

Weight

Length

11

Outline of Proposed Vibration Test on Model Structure

The objective of these seismic vibration tests was to obtain a better understanding of

nonlinear SSI of nuclear power plants during large earthquake motions. The influences on

structural responses caused by uplift phenomena as well as material nonlinearity of the soil

were main issues to be investigated.

Figure 13 shows a schematic view of the vibration test plan at BTM. The width of the

blast areas was 60m and its length varied from 200m to 800m depending on the mining plans.

There were hundreds of downholes with explosions in the blast area. The explosions were

detonated from one side to the other. The detonation front remained at some angle to the blast

direction to efficiently remove mudstone at the adjacent pit bottom. There was a time lag

between detonations to reduce the maximum accelerations, in other words, to reduce

environmental influences that make ground motions look like earthquake.

An example of the vibration test sequence is shown in Figure 14. In this way, it is

possible to measure and record different vibration levels of the test models with different

levels of input motions by choosing blast areas at appropriate distances to generate the desired

accelerations at the test area.

CONCLUSIONS

First of all, this paper described the needs and significance of experimental studies,

that might be aroused from the major revision of the regulatory guide, on nonlinear SSI of

nuclear structures subject to large earthquake motions.

Then, by reviewing the extensive experimental studies on the SSI by NUPEC, it was

clarified that those studies contributed greatly to understanding SSI behaviors and developing

earthquake response analysis codes. It was also revealed that those studies provided very

little information on nonlinear SSI of nuclear buildings with large input motions because the

experimental conditions were within design levels.

Finally, the vibration tests at a mining site were proposed in order to promote better

understanding of nonlinear SSI of nuclear power plant buildings. The advantages of the

proposed test methods are that large-scale test structures could be tested using earthquake-

like ground motions caused by large-scale blast excitations and that the three dimensional

effects and the SSI in actual ground could be considered.

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Explosive

Blast Area

Mudstone Layer

Test Structure

Coal Layer

Array

Mudstone Layer

40m

20m Earthquake-likeGround Motion

Surface Layer

Direction of BlastDetonation Front

PitBottom

Explosive

Blast Area

Mudstone Layer

Test Structure

Coal Layer

Array

Mudstone Layer

40m

20m Earthquake-likeGround Motion

Surface Layer

Direction of BlastDetonation Front

PitBottom

Figure 13 Schematic View of Vibration Test at BTM

Very Large Level TestLarge Level TestMedium Level TestSmall Level TestInstrument Calibration(Very Small)

Very Small *0

Very Large7

Large6

Large5

Medium4

Small3

Medium2

Small1

LevelBlast #

Very Small *0

Very Large7

Large6

Large5

Medium4

Small3

Medium2

Small1

LevelBlast #

Blast Sequence

Blast Sequence

* : Instrument Calibration

AreaMined Out

Directionof Blast

Location ofTest Site

Figure 14 Sequence of Vibration Tests

13

REFERNCES

Odajima, M., Suzuki, S., and Akino, K. 1987. Analytical study on Model Tests of Soil-Structure Interaction, 9th International Conference on Structural Mechanics in Reactor Technology (SMiRT 9), Lausanne, Swiss, pp311-316

Iguchi, M., Akino, K., and Noguchi, K. 1987. Model Tests on Interaction of Reactor Building and Soil, 9th International Conference on Structural Mechanics in Reactor Technology (SMiRT 9), Lausanne, Swiss, pp317-322

Hangai, Y., Akino, K., and Kurimoto, O., 1991. Model Test of Base Mat Uplift of Nuclear Reactor Buildings Part 1:Laboratory Test, 10th International Conference on Structural Mechanics in Reactor Technology (SMiRT 10), Anaheim, USA, Vol. K, pp169-174

Kobayashi, Y., Fukuoka, A., Izumi, M., Miyamoto, Y., Ohtsuka, Y., and Nasuda. T., 1991. Forced Vibration Test on Large Scale Model on Soft Rock Site (Embedment Effect Test on Soil-Structure Interaction), 11th International Conference on Structural Mechanics in Reactor Technology (SMiRT 11), Tokyo, Japan, Vol. K, pp129-134 (K06/4)

Yano, Y., Kitada, Y., Iguchi, M., Hirotani, T., and Yoshida, K., 2000. Model Test on Dynamic Cross Interaction of Adjacent Buildings in Nuclear Power Plants, 12th World Conference on Earthquake Engineering (12WCEE), Auckland, New Zealand, (0477)

Kusama, K., Kitada, Y., Iguti, M., Fukuwa, N., and Nishikawa, T., 2003. Model Test on Dynamic Cross Interaction of Adjacent Buildings in Nuclear Power Plants-Overview and Outcomes of the Project, 17th International Conference on Structural Mechanics in Reactor Technology (SMiRT 17), Prague, Czech Republic, Paper# K06-1

Uchiyama, S., Suzuki, Y., Konno, T., Iizuka, S., and Enami, A., 1992. Dynamic Tests of Concrete Block on Gravel Deposits, 10th World Conference on Earthquake Engineering (10WCEE), Madrid, Spain, pp1859-1864

Nuclear Power Engineering Corporation (NUPEC), 1998. Report on Method for Evaluating Limit State Properties and Behaviors of Nuclear Power Plant Buildings, (written in Japanese)

Kitada, Y., Kinoshita, M., Kubo, T., Seo, K., and Konno, T., 2000. The Test Methodology to Evaluate Earthquake Response of a NPP Building using Earthquake Ground Motion by Blasting, 12th World Conference on Earthquake Engineering (12WCEE), Auckland, New Zealand, (0900)

Kitada, Y., Kubo, T., Seo, K., and Fukuwa, N., 2001. Proposal of A Test Methodology to Evaluate Non-Linear Soil Structure Interaction, The 2nd UJNR Workshop on Soil-Structure Interaction, March 6 to 8, Tsukuba, Japan

Japan Nuclear Safety Commission, 1981, Regulatory Guide for Aseismic Design of Nuclear Power Reactor Facilities, (written in Japanese)

1

Load Bearing Mechanism of Piled Raft Foundation during Earthquake

Shoichi Nakaia), Hiroyuki Katoa), Riei Ishidaa), Hideyuki Manob) and Makoto Nagatac)

This paper deals with the dynamic characteristics of a structure supported by a

piled raft foundation. A centrifuge model test and its simulation analysis are

discussed first, followed by a parameter survey based on the finite element

analysis. In the centrifuge models test, structures supported by a piled raft

foundation and by a piled foundation were considered. A parameter survey was

performed from the viewpoint of foundation types and types of connection

conditions between the raft and the piles. It was found from this study that,

although the effect of the pile head connection condition on the response

characteristics of a superstructure is fairy small when compared to the type of the

foundation, it does affect the load bearing characteristics of piles even when piles

are not connected to the raft foundation.

INTRODUCTION

The piled foundation is normally used when constructing buildings on soft soils. The

spread foundation, however, becomes an alternative when appropriate load bearing soil

layers do not exist. In the latter case, from the viewpoint that the excessive settlement and

differential settlement have to be avoided, the use of a composite foundation is becoming

very popular in recent years. This composite foundation consists of a spread foundation,

usually a raft foundation, and a comparatively few number of friction piles and is called a

piled raft foundation. In the case of a piled raft foundation, the load bearing mechanism is

fairly complex because a load is transmitted to the ground through a raft and piles.

The vertical load bearing mechanism has been extensively investigated by a number of

researchers by applying the elasticity theory (Poulos 1994, Randolf 1994) and the finite

a) Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan b) Shimizu Corporation, 3-4-17 Etchujima, Koto-ku, Tokyo 135-8530 c) Nippon Steel Corporation, 2-6-3 Otemachi, Chiyoda-ku, Tokyo 100-8071


2

element method (Yamashita 1998). Based on these results, piled raft foundations are

becoming popular in practical use (Yamada et al. 1998).

The study on the load bearing mechanism under horizontal loading or during earthquakes,

however, is very limited (Mano and Nakai 2000, Horikoshi et al. 2003). This is partially

because piled raft foundations are considered as raft foundations in the current design

practice. Since the behavior of a piled raft foundation during earthquakes is considered fairly

complex due to dynamic interaction among a raft, piles and a soil, the design procedure

should include the effect of this mechanism in an appropriate manner.

In the areas where the seismic activity is considered high, such as in Japan, load that piles

have to carry during an earthquake is quite large. Especially, when the inertial force of a

superstructure is large, which is often the case, stresses of a pile at its head become

prohibitive since the connection condition between the foundation and the piles is usually a

fixed condition. In order to avoid this situation, quite a few attempts have been made in this

decade in Japan. In most cases the fixed condition is relaxed to some extent or completely by

installing special devices at the pile head (Sugimura 2001, Wada et al. 2001). Another

attempts include supplementary friction piles of very short length in addition to existing end

bearing piles.

The objective of this paper is to investigate the effect of the connection condition between

piles and a raft on the dynamic characteristics of a structure supported by a piled raft

foundation. In this regard, a series of dynamic centrifuge model tests have been conducted,

followed by a parameter survey based on the finite element analysis.

CENTRIFUGE MODEL TESTS

In order to examine the effect of the connection condition between a raft and piles on the

dynamic behavior of a structure supported by a piled raft foundation, a series of centrifuge

model tests have been conducted. As shown in Figure 1, four cases were considered in the

model test: (1) a piled foundation consisting of a raft and free standing piles, called Case PR,

(2) a piled raft foundation, called Case PR, (3) a raft foundation with unconnected piles

installed in a soil under the raft, called Case RU, and (4) a raft foundation with no piles,

called Case RF.

3

OUTLINE OF THE TESTS

Figure 2 shows a schematic illustration of the test apparatus for Case RU. The model

consists of a soil and a structure supported by a raft foundation with unconnected piles

installed in the soil under the raft. This model is the same as the one for Case PR, which is

described elsewhere (Mano and Nakai 2004), except that there is a small gap of 5 mm (150

mm in the prototype scale) between the raft and the piles. In Case PF, the raft and the piles

are firmly connected and there is a gap of 5 mm between the raft and the soil. In Case RU,

there are no piles installed in the soil. A centrifuge acceleration of 30 G was applied in all

four cases. Table 1 summarizes the properties of the model.

Foundation Foundation

Soil Pile

Foundation

Soil

Foundation

Soil Pile

Soil Pile

Case PF: Piled Foundation Case PR: Piled Raft Foundation

Case RF: Raft Foundation Case RU: Raft w/ Un-connected Piles

Figure 1. Foundation types considered in this study

The structure and the raft are made of aluminum and a total mass is 9.05 kg (244 t in the

prototype scale). Piles are brass tubes of 12 mm diameter and 1 mm thickness. A total of

nine piles with the embedment length of 180 mm and the center to center spacing of 72 mm

were installed in Case PF, PR and RU. Four of the piles, called Pile-A, B, C and D, are

instrumented to measure bending stresses during loading.

Dry Toyoura sand with the relative density of over 90% was used for the model ground.

Special equipment called bending elements was installed in the soil in order to measure the

shear wave velocity of the soil during the application of centrifugal acceleration. According

4

to the results measured by this equipment prior to vibration, the shear wave velocity, Vs, of

the soil can be correlated with the overburden pressure, ′ σ v , by:

Table 1. Properties of model and prototype

Properties Model Prototype

Width × Length 204 mm × 204 mm 6.24 m × 6.24 m

Mass 9.05 kg 244 t Raft and Structure

Weight 88.7 N 2395 kN

Diameter 12 mm 360 mm

Length 180 mm 5.4 m Pile

Bending rigidity 3.01 × 10−5 kNm2 24.4 kNm2

Thickness 400 mm 12.0 m Soil

Density 1.63 t/m3 1.63 t/m3

400

180

450

100

750

105

120

204

72 72

450

170

50

80

49

100

100

100

7272

5

Toyoura Sand

Raft

Floor

BenderElement

Bender Element

Section

Plan

Pile (f12, t0.5)

Pile (w/ Strain Gauge)

DisplacementTranceducer

Accelerometer

Raft

AG1

AG2

AG3

AG4

AG0

Core

A

B

C

D

Figure 2. Schematic illustration of test apparatus for Case RU

5

Vs = 70 ⋅ ′ σ v( )0.25 (1)

The test apparatus shown in Figure 2 was placed on a shaking table that was set up in the

centrifuge test package. An artificial earthquake wave with the amplitude of 180 cm/s2 in the

prototype scale was used as an input to the shaking table. Maximum accelerations of actual

input recorded at the shaking table were 178.7, 187.0, 215.8 and 223.5 cm/s2 for Case PF,

PR, RU and RF, respectively.

0

10

20

30

40

50

0 5 10

Raft

Case PFCase PRCase RUCase RF

Am

plifi

catio

n

Frequency (Hz)

0

10

20

30

40

50

0 5 10

Floor


Am

plifi

catio

nFrequency (Hz)

0

10

20

30

40

50

0 5 10

Ground (AG4)


Am

plifi

catio

n

Frequency (Hz)

0

10

20

30

40

50

0 5 10

Core


Am

plifi

catio

n

Frequency (Hz)

(a) Raft (b) Floor

(c) Ground Surface (AG4) (d) Core Figure 3. Transfer functions at various points with respect to the bottom of the soil, AG0

TEST RESULTS

Figure 3 shows the transfer function at various points with respect to the bottom of the

soil, obtained from the so-called sweep test which is basically a small amplitude steady-state

vibration but its frequency changes gradually. As can be seen in Figure 3 (c), the first natural

frequency of the soil is about 3.2 Hz and the second is about 9.2 Hz. The natural frequencies

of the raft and the floor are 5.8 Hz and 2.6 Hz, respectively. That of the core seems much

higher and is not seen in Figure 3. The figure also indicates that test results are a little noisy

6

in the higher frequency range. Comparison among all four cases indicates that the response

of the structure is reduced considerably by introducing the contact between the raft and the

soil.

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PF / Core-Top : Amax

=-754.4 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PR / Core-Top : Amax

=550.3 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RF / Core-Top : Amax

=-686.6 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RU / Core-Top : Amax

=541.3 cm/s2

(a) Acceleration at the top of Core

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PF / Raft-Top : Amax

=-538.2 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PR / Raft-Top : Amax

=371.4 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RF / Raft-Top : Amax

=407.9 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RU / Raft-Top : Amax

=403.9 cm/s2

(b) Acceleration at the top of Raft

Figure 4. Comparison of acceleration time history

7

0 20 40 60

0

1

2

3

4

5

Pile APile BPile C

Max Bending Moment (kN�m)

Dep

th (m

)Case PF

0 50 100 150

0

1

2

3

4

5

Pile APile BPile C

Max Shear Force (kN)

Dep

th (m

)

Case PF

0 20 40 60

0

1

2

3

4

5

Pile APile BPile CPile D


Dep

th (m

)

Case PR

0 20 40 60

0

1

2

3

4

5

Pile APile BPile CPile D


Dep

th (m

)Case PR

0 20 40 60

0

1

2

3

4

5

Pile APile BPile C


Dep

th (m

)

Case RU

0 20 40 60

0

1

2

3

4

5

Pile APile BPile C


Dep

th (m

)

Case RU

(a) Case PF

(b) Case PR

(c) Case RU Figure 5. Comparison of bending moments and shear forces

Figure 4 shows the accelerograms at the top of the core and on the raft. Note that actual

input waves slightly differ from case to case in terms of the maximum amplitude, as

mentioned earlier. It is found from the figure that the acceleration of the raft of Case PF is

significantly larger than that of other three cases. This tendency corresponds to the result of

8

the transfer function and the reduction of the response is due to the contact between the raft

and the soil. The fact that the response at the top of the core of Case RF is larger than Case

PR and RU, however, indicates a dominant rocking motion for Case RF, hence the vibration

mode is slightly different. It is worthy of note that piles are not connected to the raft in Case

RU but that they have significant contribution to the dynamic soil-structure interaction.

Figure 5 shows the distribution of maximum bending moments and shear forces along the

piles. Since a structure is supported only by piles in the case of a piled raft foundation, Case

PF gives the largest response. It is again worthy of note that piles of Case RU that are not

connected to the raft carry a fairly large amount of load. This is considered to reduce the

input to the structure.

SIMULATION ANALYSIS OF MODEL TESTS

Before going on to a numerical analysis-based parameter survey, a simulation analysis of

the centrifuge model tests has been performed for Case PR and RU. The analysis is basically

a three dimensional finite element analysis in which a dynamic substructure method is

effectively utilized. A computer code ACS SASSI was used and the analysis was made in

the frequency domain.

ANALYSIS MODEL

Figure 6 shows the finite element mesh layout used in the analysis for Case PR. The

mesh layout for Case RU is the same as Figure 6 except that topmost elements of the piles are

replaced with soil elements in order to simulate a gap between the raft and the piles. The

shear wave velocity of the soil was determined by reducing the value computed from Eq. 1

by one third, in order to account for soil nonlinearity during loading.

Piles are often modeled as beams in the finite element analysis due to their flexural

characteristics. However, since beams do not occupy any volume in the three dimensional

space, the direct use of beam as a pile in conjunction with solid elements as soils is not

appropriate in the dynamic soil-structure interaction analysis. The reason is because a pile

modeled by a beam has very small diameter hence it tends to have small resistance.

According to the authors’ experience, it is confirmed that the beam element modeling

underestimates impedance functions and overestimates foundation input motions. Based on

this, piles are modeled by solid elements in this paper, as shown in Figure 6. The bending

9

moment and shear force of the pile can be obtained by superposing very soft beam elements

on the center of each pile and extracting resulting stresses.

Sym.

6120

2400

5400

1470

3600

2925

6120

3810.89

Pile B

Pile

Soil Column

Soil Column

Sand

Base

Pile A

Structure

Floor

Raft

Core

Figure 6. Finite element mesh layout

COMPARISON BETWEEN ANALYSIS AND MODEL TEST

Figure 7 demonstrates a comparison of transfer functions between analysis and sweep test

results of Case PR. From the figure, it can be seen that the natural frequencies of the soil (3.2

Hz) and the floor (2.6 Hz) are well predicted by the analysis although the computed peaks are

a little higher than the test results. Computed transfer functions in the higher frequency range

give larger amplification for the soil and smaller amplification for the structure when

compared with test results. This suggests that the variation of the soil stiffness along the

depth assumed in the analysis may differ from the actual one.

Figure 8 shows acceleration time histories for Case PR and RU observed at various

locations during earthquake excitation. The fact that computed values are significantly

smaller than measured values is resulted from low amplification of the computed transfer

function in the high frequency range.

10

0

10

20

30

40

50

0 5 10

RaftTest: Case PRAnalysis: Case PR

Ampl

ifica

tion

Frequency (Hz)

0

10

20

30

40

50

0 5 10

FloorTest: Case PRAnalysis: Case PR

Ampl

ifica

tion

Frequency (Hz)

0

10

20

30

40

50

0 5 10

Ground Surface (AG4)Test: Case PRAnalysis: Case PR

Ampl

ifica

tion

Frequency (Hz)

0

10

20

30

40

50

0 5 10

CoreTest: Case PRAnalysis: Case PR

Ampl

ifica

tion

Frequency (Hz)

(a) Raft (b) Floor

(c) Ground Surface (AG4) (d) Core Figure 7. Comparison of transfer functions between analysis and centrifuge model test (Case PR)

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PR / Core-Top : Amax

=265.8 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RU / Core-Top : Amax

=280.9 cm/s2

(a) Acceleration at the top of Core

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case PR / Raft-Top : Amax

=234.4 cm/s2

-1000

-500

0

500

1000

0 10 20 30 40

Acc

eler

atio

n

Time (s)

Case RU / Raft-Top : Amax

=256.7 cm/s2

(b) Acceleration at the top of Raft Figure 8. Comparison of acceleration time history

11

Figure 9 gives a comparison of maximum bending moments and shear forces along the

piles during earthquake excitation. A similar discussion to the above can be made on this

comparison, i.e. computed stresses of the piles are smaller than measured ones especially in

their deeper portion.

The above mentioned discussion suggests that further reduction of the soil stiffness and

increase of the damping corresponding to the strain level of the soil during earthquake

excitation, may improve the agreement between analysis and test results.

0 20 40 60

0

1

2

3

4

5Pile APile B

Max Bending Moment (kNm)

Dep

th(m

)

Case PR

0 20 40 60

0

1

2

3

4

5Pile APile B


Dep

th(m

)

Case PR

0 20 40 60

0

1

2

3

4

5Pile APile B

Max Bending Moment (kNm)

Dep

th(m

)

Case RU

0 20 40 60

0

1

2

3

4

5Pile APile B


Dep

th(m

)

Case RU

(a) Case PR

(b) Case RU Figure 9. Comparison of bending moments and shear forces

EFFECT OF PILE-RAFT CONNECTION CONDITION

AND SUPLEMENTARY SHORT PILES

In this section, the effect of pile-raft connection conditions on the behavior of a structure

during an earthquake is studied first based on the three dimensional finite element analysis.

12

The effect of supplementary short piles is then examined from the viewpoint of the load

bearing characteristics, i.e. how much of the inertial force of a structure is transferred to the

soil either from the base of the raft or from the piles.

ANALYSIS MODEL

The analysis method is the same as the one used in the previous section. In the analysis,

the soil is assumed to be an elastic half space. The foundation including a raft and piles are

modeled by solid elements while a superstructure which is a five storey building is modeled

by beam elements.

Analysis parameters considered in the study include:

• Piled foundation (PF) and piled raft foundation (PR)

• Fixed condition (CF) and hinged condition (CH)

• Supplementary short piles (Yes) and no short piles (No)

In addition, the following cases have been considered for comparison:

• Raft foundation with unconnected piles (RU) and raft foundation with no piles (RF).

Figure 10 summarizes the cases that were considered in the analysis.

Fixed HeadPiled Foundation

Piled Raft Foundation

Gap = B/2

Hinged Head

(Long) Piles

(Long) Pilesw/ Short Piles

Type of Foundation Type of Connection Extra Short Piles

Type of Connection (Cont'd)

B

B/2

Gap = B

B

B

Raft Only Figure 10. Analysis cases

13

Figure 11 shows a finite element mesh layout for Case PR-CF. The hinged condition

between a raft and a pile is implemented by placing a small gap between them and by

connecting both with a beam. A superstructure with a natural frequency of 2 Hz was

considered. El Centro 1940 NS accelerogram with the amplitude of 342 cm/s2 was used as

an input wave defined at the ground surface.

5 m

2.5 m

15 m

2.5 m

3 m

3 m

1 m

PilesShort Piles

Soil Elements Pile

Raft Foundation(Rigid)

SmallGap

Rigid Beam

Figure 11. Finite element mesh layout (Case PR-CF)

EFFECT OF PILE-RAFT CONNECTION CONDITION

Table 2 summarizes maximum accelerations, maximum shear forces and maximum over-

turning moments of the superstructure. From this table, it is seen that differences of the

response among the analysis cases is not very large.

If we further look into the results, however, the following discussions can be made:

• The difference between fixed (CF) and hinged (CH) conditions is very small for both

piled (PF) and piled raft (PR) foundations.

14

• Piled rafts (PR) give about 5 % smaller base shears, 12 % smaller over-turning

moments and 20 % smaller accelerations over piled foundations (PF). This can be

resulted from larger soil-structure interaction in piled rafts over piled foundations.

• If piles are not connected to the raft (RU), then the response becomes slightly larger

compared with piled rafts (PR). The response is also larger than that of raft

foundations (RF) except the maximum accelerations that are slightly smaller than

those of raft foundations.

• From the viewpoint of adding piles to a raft foundation, it increases base shears,

slightly increases over turning moments and decreases maximum accelerations.

Table 2. Maximum response

Maximum Response Type of

Foundation Connection Condition

Short Piles

Base Shear

[kN]

Over-turning Moment [kNm]

Acceleration

[m/s2]

Inertial Force [kN]

No 1000 10981 13.62 1092 Fixed (CF)

Yes 1025 11130 13.60 1130 No 989 10846 13.82 1180

Piled Foundation

(PF) Hinged (CH) Yes 998 10873 13.65 1160

No 960 9769 11.03 1212 Fixed (CF)

Yes 958 9748 11.01 1203 No 960 9660 10.84 1230

Piled Raft Foundation

(PR) Hinged (CH) Yes 960 9654 10.86 1228

No 1009 10602 12.79 1215 Gap = 0.5B (B: width) Yes 1011 10622 12.78 1219

No 1002 10704 13.24 1172

Raft w/ Un-connected

Piles (RU)

Gap = 1.0B (B: width) Yes 1005 10724 13.23 1176

Raft Found. - - 825 9627 13.49 1003

EFFECT OF SUPPLEMENTARY SHORT PILES

An additional study was made on the effect of supplementary short piles added to the

piled and piled raft foundations. A short pile of 3 m length with the same width as the

existing pile of 15 m length (called a bearing pile, hereafter) is taken as a standard short pile.

Half and double lengths were considered and half and double cross sectional areas were also

considered.

15

0

500

1000

1500

No Yes

Case PF-CFCase PF-CHCase PR-CFCase PR-CH

(kN�m)

Short Piles

PiledFoundation

Piled RaftFoundation

0

500

1000

1500

No Yes

(kN)

Short Piles

PiledFoundation

Piled RaftFoundation

Figure 12. Change of the stress of bearing piles due to the addition of short piles

0

0.2

0.4

0.6

0.8

1

0.5 1.0 2.0

Case PF-CFCase PF-CHCase PF-CFCase PF-CH

Bea

ring

Rat

io

Sectional Area of Short Pile

Bearing Piles

Short Piles

0

0.2

0.4

0.6

0.8

1

0.5 1.0 2.0

Case PR-CFCase PR-CHCase PR-CFCase PR-CH

Bea

ring

Rat

io


Bearing Piles

Short Piles

(a) Effect of Sectional Area of Short Pile

0

0.2

0.4

0.6

0.8

1

0.5 1.0 2.0

Case PF-CFCase PF-CHCase PF-CFCase PF-CH

Bea

ring

Rat

io

Length of Short Pile

Bearing Piles

Short Piles

0

0.2

0.4

0.6

0.8

1

0.5 1.0 2.0


Bea

ring

Rat

io


Bearing Piles

Short Piles

(b) Efect of Length of Short Pile

Figure 13. Effect of the size of short piles on the load bearing ratio

16

0

200

400

600

800

1000

0.5 1.0 2.0

[kN�m]


Case PF-CFBearing Piles

Case PF-CFShort Piles

Case PF-CHBearing Piles

Case PF-CHShort Piles

0

200

400

600

800

1000

0.5 1.0 2.0


[kN�m]


Bearing Piles

Short Piles

Bearing Piles

0

200

400

600

800

1000

0.5 1.0 2.0

[kN�m]

Lengh of Short Pile

Case PF-CFBearing Piles

Case PF-CFShort Piles

Case PF-CHBearing Piles

Case PF-CHShort Piles

0

200

400

600

800

1000

0.5 1.0 2.0


[kN�m]


Bearing Piles

Short Piles

Bearing Piles

(a) Efect of Sectional Area of Short Pile

(b) Efect of Length of Short Pile Figure 14. Effect of the size of short piles on maximum bending moments

Figure 12 shows the change of maximum bending moments and shear forces due to the

addition of short piles. Figures 13 and 14 show the effect of the size of short piles on the

load bearing ratio and the maximum stresses of piles. Here, the load bearing ratio was

computed by averaging over the duration time the ratio between the shear force at the pile

head and the inertial force of the structure. The inertial force of the structure means the sum

of a base shear at 1st floor and the mass of the foundation multiplied by its acceleration.

From these figures, the following points are made:

• Supplementary short piles reduce shear forces and bending moments of bearing piles,

especially in the case of piled foundations (PF).

17

• The change of the size of short piles has a relatively small influence on the load

bearing ratio.

• However, forces and moments acting on the piles are greatly changed by the size of

the short piles.

The above discussion suggests the effectiveness of supplementary short piles for the

seismic resistance of a structure.

CONCLUSIONS

In this paper, the effect of the connection condition between piles and a raft on the

dynamic characteristics of a structure supported by a piled raft foundation has been studied

extensively by conducting a series of dynamic centrifuge model tests and simulation

analyses. It was found from the study that:

(1) The dynamic response of a structure is reduced considerably by introducing the

contact between the raft and the soil.

(2) The effect of pile head connection conditions on the response characteristics of a

superstructure is fairy small when compared to the type of foundation.

(3) However, the connection condition affects the load bearing characteristics of piles.

(4) The existence of piles installed in the ground below the raft has a significant influence

on the response characteristics of a superstructure.

The last conclusion suggests the possibility of using piles as ground improvement even

for seismic design.

REFERENCES

ACS SASSI-C, 1998. An Advanced Computational Software for 3D Dynamic Analysis Including

Soil-Structure Interaction, Advanced Computational Software, Inc.

Horikoshi, K. et al., 2003. Performance of Piled Raft Foundations Subjected to Dynamic Loading, Int.

J. of Physical Modeling in Geotechnics, 2, 51-62.

Mano, H. and Nakai, S., 2000. An Approximate Analysis for Stress of Piles in a Laterally Loaded

Piled Raft Foundation, Journal of Structural Engineering, 46B, 43-50.

Mano, H. and Nakai, S., 2004. Stress of Piles in a Piled Raft Foundation during Earthquake, 11th

International Conference on Soil Dynamics and Earthquake Engineering, Vol. 1, pp. 726-733.

18

Poulos, H.G, 1994. An approximate numerical analysis of piled-raft interaction, Int. J. for Numerical

and Analytical Method in Geomechanics, 18 (2), 73-92.

Randolph, M. F., 1994. Design Methods for Pile Groups and Piled Rafts, Proc. 13th Int. Conf. on Soil

Mechanics and Foundation Engineering, Vol. 5, pp. 61-82.

Sugimura, Y., 2001. Pile Head Connection for the Performance-based Design, Foundation

Engineering and Equipment, 29 (12), 5 (in Japanese).

Wada, A. et al., 2001. Shaking Table Tests for Interaction of Soil and Structure on Short-Stiff-Piles

and Long-Flexible-Piles, Proc. 15th AIMETA Congress of Theoretical and Applied Mechanics,

Taormina, Italy.

Yamada, T. et al., 1998. An Example of Piled Raft Foundation in Building Design, Foundation

Engineering and Equipment, 26 (5), 100-103 (in Japanese).

Yamashita, K., 1998. Analyses of Piled raft Model Provided by ISSMGE TC-18 Part2 : Estimation

by three-dimensional finite analysis, ISSMGE TC18 JGS member ﾕ s meeting on Piled rafts.

1

Study on the Dynamic Characteristics of an Actual Large Size Wall Foundation by Experiments and Analyses

Masanobu Tohdoa)

The dynamic behavior of a large size wall foundation supporting a 54-story building is

studied in this paper. The contents are on a response analysis with soil-foundation-

superstructure interaction (SSI) applying SSI elements evaluated by a method proposed by

the author and a vibratory experiment conducted after the construction of foundation. The

method to evaluate SSI elements from soil consists of 4 steps : an equivalent linearlization of

soil against a design earthquake, formulation of force-displacement relationship among nodal

points for the wall based on the Thin Layer method (TLM), condensation of the relationship

to match with a beam model of the foundation, and an evaluation of SSI elements of a

Winkler type derived from LSM. From the experiment it is found that the wall foundation

has a high rigidity and the wave dissipation to soil increases with frequency. The simulation

analyses for the experimental results verify the validity of the method to evaluate SSI

elements.

INTRODUCTION

A 54-story reinforced concrete building is now under construction at Tokyo bay area

where deep soil deposits exist. The building is supported by a large size wall foundation with

46.5-meter square, 53-meter depth and 1.8-meter thickness.

For the seismic design of this building, the seismic safety had been verified by earthquake

response analyses considering the effect of a soil-foundation-superstructure interaction (SSI).

This paper presents on response behavior of the wall foundation during a design earthquake

ground motion applying a SSI model based on the Thin Layer method proposed by the

author.

a) Head of Structural Division, Technical Research Institute, Toda Corporation, [email protected] 5-34, Akasaka-8, Minato-ku, Tokyo, Japan


2

Just after the construction of foundation , a vibratory experiment had been conducted by

using a vibration generator. The experimental results on amplitudes and impedances are

discussed in comparison with the results of a simulation analysis.

THE OBJECTIVE BUILDING AND FOUNDATION

As shown in Fig.1, the objective is a 54-story reinforced

concrete residence building of 174 meters high and the

plan of 46.5 meters square with inner void space. This

building is constructed by members composed of high

strength material of concrete of 100MN/mm2 and steel bar

of 685MN/mm2 and others and applies a steel damper

column of low yielding stress of 225MN/mm2 for response

control to earthquake excitations. The foundation is

constructed by a reinforced concrete wall of boxed type and

piles shown in Fig.2 and supported by the depth of 53

meters from ground surface. Figure 3 shows the profile of

surrounding soil deposit which has deep soft soil layers

because the building is located at Tokyo bay area.

SEISMIC DESIGN

In the seismic design, various earthquake response analyses against a few input motions

had been performed : 1) a push-over analysis of the super-structure to evaluate the

RCframewithsteeldamper

wallfoundation

Figure 1. Skeleton view of the objective building

46.5m

46.5m

1.8m

46.5m

1.8m44m

9m Basement

- 100

- 80

- 60

- 40

- 20

00 300 600

Vs, Vp(m/ s)

Dep

th　

(m)

VsVp(× 10)

Figure 2. (a) Plan and (b) section of wall and piles foundation Figure 3. Soil profile

3

relationship between story shear force and story drift, 2) response analyses of the super-

structure based on a 3-dimensional frame model including a vertical input excitation, 3)

response analyses of soil-wall foundation-

superstructure interaction system , and 4) a dynamic

analysis due to an input excitation with phase

difference i.e. a traveling seismic wave. This paper

presents the response analysis of a soil-wall

foundation-superstructure interaction system (SSI) of

the analyses described above.

Figure 4 is the analytical model for the SSI which

is composed of the super-structure with a main

structure and a steel damper column, the wall

foundation and supporting soil elements. The super-

structure are modeled into an equivalent beam with

flexural-shear deformation converted from the push-

over analysis of the frame which has a nonlinear

restoring force characteristics on the basis of structural

experiments.

A METHOD FOR MODELING OF SOIL AND WALL FOUNDATION

INTERACTION SYSTEM

In order to perform earthquake response analyses of soil-wall foundation-superstructure

interaction (SSI) system, the soil and wall foundation are modeled into a kind of the beam

on continuous springs as the Winkler type. The wall foundation is modeled into a beam with

flexural-shear deformation using FEM explained later. The modeling makes possible to

perform nonlinear response analyses of a SSI system.

The analytical steps to convert a soil medium into springs connecting with a beam of

wall foundation are as follows and the schematic view is illustrated in Fig.5.

Step.1 : To perform an earthquake response analysis of a soil deposit only considering

strain dependency of soil i.e. nonlinearity and obtain the equivalent soil rigidity and

hysteresis damping of soil due to equivalent linearlization.

Ka

Kb

Kr

WallFoundation

EI,GA

SuperStructure

SteelDamperColumn

Figure 4. Model for response analyses of soil-wall foundation- superstructure system

4

Step.2 : To evaluate the relationship at a frequency excited by the function of tie ω

between forces and displacements among any nodal points within the equivalent soil

medium shown in Fig.5(a) where the objective wall foundation is settled, by applying 3-

dimensional Thin Layer method called as TLM (Tajimi 1980).

{ } [ ]{ }t*tt PfU = (1)

in which tP and tU are nodal forces and displacements with the freedoms of nodal points

multiplied by 3D, respectively and [ ]*tf is a full flexibility matrix in complex .

Step.3 : To make the condensation of the relationship of Eq.(1) in step.2 into the

freedoms of translation and rotation in x-y-z of planes which are assumed to move as rigid-

body shown in Fig.5(b) and locate at the same depth with the points discretizing wall

foundation. Using the displacements, rU representing the movement of plane, the

displacements, tU can be expressed as { } [ ]{ }rt UAU = , therefore the condensed relationship

becomes as follows.

{ } [ ]{ } [ ] [ ] [ ] [ ]AfAK,UKP *t

T*sfr

*sfr

1−== (2)

Nodal pointswithin soil

CL

CL

CL

一Rigidplane

w

w

GAEI

Wall K a

K b

K r

(a) Step.2 Relationship of tt UP − (b) Step.3 Condensation by (c) Step.4 .Winkler in soil by 3D-TLM rigid plane assumption type modeling Figure 5. Procedure to evaluate spring and dashpot constants of interaction elements represented by Winkler type based on the 3D-Thin Layer method for nonlinear response analyses

5

where [ ]*sfK is a full stiffness matrix in complex. The Eq.(2) might be a rigorous expression

based on the TLM.

Step.4 : To evaluate spring constants (includes dashpots) of the Winkler type as shown in

Fig.5 (c). We assume that the springs in horizontal response with rotation consist of aK ,

bK and rK for axial, shear and rotational deflection of soil, respectively and those are

vertically in vertical response. Using the springs, the relationship between forces and

displacements is expressed as

{ } [ ]{ }r*

swr UKP = (3)

in which the stiffness matrix is given by

]K[]K[]K[]K[ *rb

*a

*sw ++= (4)

where [ ]*aK and [ ]*

rK are diagonal matrixes in complex and [ ]bK is a tri-diagonal one

without damping. The spring constants of the Winkler type are estimated from [ ]*sfK of

Eq.(2) in the following.

Let us consider the condition that a wall foundation, the dynamic stiffness of which is

represented by [ ]*wK , is subjected by external forces, { }wF and soil responses in free field,

{ }sU . Under the condition, the equation of motion of the wall foundation, { }wU is

expressed as follows.

( ) }F{}U{}U{]K[}U]{K[ wsw*sw

*w =−+ (5)

in which [ ]*sK indicates [ ]*

sfK in Eq.(2) or [ ]*swK of Eq.(4) . The reaction forces of soil due

to { } { }00 ,,,QF Tw ⋅⋅⋅= of wall top force and { }sU are formulated by

})U{}U]({K[}R{},U]{K[}R{ swG*ssGwQ

*ssQ −== (6)

where { }wQU and { }wGU are the solutions due to { }wF and { }sU , respectively. When

{ }wF and { }sU are given, the solutions of { }fwQU and { }f

wGU are obtained using the

6

rigorous stiffness [ ]*sfK in Eq.(2), that are converted into { }f

sQR and { }fsGR by Eq.(6). Here

we consider on { }wsQR and { }w

sGR expressed by using the unkown stiffness of [ ]*swK in Eq.(4)

and substituting { }fwQU and { }f

wGU into Eq.(6). The square errors between { }wsLR and { }f

sLR ,

L=Q and G, can be expressed as follows.

( ) ( )}R{}R{}R{}R{w *fsL

*wsL

T

G,QL

fsL

wsLL −−=ε ∑

=

2 (7)

in which Lw is weighting factors and the superscript of (*) indicates the conjugate complex

values. The Eq.(7) leads to a least square method (LSM) for the unknown spring and dashpot

constants of *aK and bK as:

bi*aii

iKandKofxanyin

xmin, 0

22 =

∂ε∂

→ε (8)

Consequently, the unknowns of *aK and bK in Fig.5(c) can be estimated. Here we obtain

*rK for rotation from reaction moment in Eq.(2) due to independently given rotation before

the procedure described above.

The method to evaluate spring constants from TLM solutions described above can be

applied for pile foundations as well (Tohdo 2002).

AN EARTHQUAKE RESPONSE ANALYSIS

An earthquake ground motion is synthesized for the verification of seismic performance

of the objective structure shown in Fig.1. The design earthquake is assumed to be a Kanto

earthquake shown in Fig.6 which has the seismic moment of cmdyne. ⋅⋅ 271067 and the fault

plane of kmkm 70130 ⋅ . The procedure to estimate earthquake ground motions is a semi-

empirical wave synthesis method using observed accelerograms by a small event (Tohdo et al.

1992). Figure 7 is the acceleration wave forms of horizontal and vertical earthquake ground

motions at an engineering bed-rock at the site.

7

In order to model the wall foundation shown in Fig.2 into a beam, an analysis by FEM is

carried out, the condition of which is taking the pure wall foundation of boxed-type without

soil and a support fixed at bottom as shown in Fig.8(a). The total displacement distribution,

tδ due to a top force is shown by a solid line in Fig.8(b) and the shear-like displacement, sδ

by a dashed line which is obtained under the condition of web-wall only and restriction

vertically at top. The shear and flexural rigidities of the modelled beam are determined from

sδ and stf δ−δ=δ , respectively. It is noted here that pile foundations shown in Fig.2 are

Horizontal Comp. (303 gals, 38cm/ s)

- 400

0

400

Gal

Vert ical Comp. (187gals, 17cm/ s)

- 400

0

400

0 20 40 60 80 100Time (sec.)

Gal

Figure 7. Accelerations at engneering bed-rock for design earthquake synthesized by a fault model

Fault Planefor Kanto Earthquake

Site

dip angke 34 degree

cmdyne106.7 27 ⋅⋅

km70km130 ×

oM

WL ×

Figure 6. Desgin earthquake

fix support -50

-40

-30

-20

-10

00 10 20 30

Deflection

Dep

th (m

)

)MN/m(µ

tδsδfδ

Figure 8. (a) Mesh and (b) deflection of FEM analysis of the pure wall foundation to model into a beam with flexure-shear deformation

8

ignored in the SSI analysis because we find the fact derived from the FEM analysis of a wall-

pile-soil model that piles share less than 10% of stresses against a top force.

The step.1 analysis of soil shown in Fig.3 against the base-rock input of Fig.7 is carried

out applying a modified R-O model for restoring force characteristics of soil. The relative

displacement and acceleration are shown in Fig.10.

The spring constants of SSI elements due to equivalent linearlized soil are evaluated on

the basis of the method explained in step.2 through step.4. In the step.4, the conditions are

assumed : 1) { }sU shown in Fig.10(a) and some top Q of { }wF , and 2) weighting factors of

Qw and Gw as to be { } { }max

fsGGmax

fsQQ RwRw ⋅⋅ = by Eq.(6). The real part of of *

aK and

bK and the imaginary part of *aK are analyzed at the frequency of almost 0, i.e. statically,

and the 1st frequency of SSI system, respectively. The results are shown in Fig.9, which are

normalized by shear rigidity of soil and element thickness in discretization. The real parts are

spring constants and the imaginary parts are converted into dashpots.

- 50

- 40

- 30

- 20

- 10

00 10 20

Dept

h (m

)

RealImag

)HG/(K sa ∆

- 50

- 40

- 30

- 20

- 10

00 500 1000

Deph

t (m

)

Real

)HG/(K sb ∆

(a) aK for axial spring (b) bK for shear spring Figure 9. Spring constants for interaction elements connecting with wall foundation against design earthquake ground motions shown in Fig.7

9

At first, the pure wall foundation is subjected to earthquake ground motions due to the

input in Fig.7 which in free field are the time histories of response acceleration at base-rock,

and velocity and displacement of surface soil ground from top to bottom. Here the vertical

response analysis of soil is carried out by assuming P-wave traveling in surface soil (Tohdo et

al. 1998). The maximum response displacements and accelerations of wall vary little at depth

as shown in Fig.10. Figure 11(a) is maximum shear by horizontal input and axial stress by

vertical input which are normalized by weight of wall itself summed from top to the depth.

The shear stresses are strongly affected by the difference of response displacement between

wall and soil as shown in Fig.10(a). Figure 11(b) shows response spectra by the response

acceleration at wall top to be a foundation input motion, and the free field motion at ground

surface. The effect of high rigidity of wall foundation appears that the foundation input

motions at the period less than fundamental period of soil ground become smaller than free

field motions.

-50

-40

-30

-20

-10

00 2 4 6 8 10

Displacement　(cm)

Dep

th (m

)

WallSoil

-50

-40

-30

-20

-10

00 100 200 300 400

Acceleration (gal)

Dep

th (m

)

WallSoil

Figure 10. (a) Maximum displacements and (b) accelerations of wall foundation and soil due to response analyses against horizontal earthquake ground motions shown in Fig.7

10

The earthquake response analysis of the soil-wall foundation-superstructure interaction

system is performed. The results of maximum

story drift are shown in Fig.12 in comparison with

the results by the input of free field surface

acceleration. It is recognized in this analysis that

the response of the structure becomes fairly small

due to the SSI effect, that is, the structure has such

seismic performance against this design

earthquake.

VIBRATORY EXPERIMENT

An investigation by microtremor observation

in free field at the site had been carried out to

clarify the elastic wave velocity profile of the soil

ground. The spectral ratios of horizontal

components to vertical one of microtremors (H/V

spectrum) are shown in Fig.13., which have the

-50

-40

-30

-20

-10

00 0.5 1 1.5 2 2.5

Shear and axial stress coefficients

Dep

th (m

)

shearaxial stress

1

10

100

1000

0.01 0.1 1 10Period (sec.)

ｐＳ

ｖ (c

m/s

)

Hor. at WFHor. at GLUD at WFUD at GL

ｈ＝５％

Figure 11. (a) Maximum shear and axial stresses of wall foundation normalized by wall weight, and (b) response spectra obtained by accelerations at the top of wall and free field surface, due to horizontal and vertical earthquake ground motions shown in Fig.7

0 0.005 0.01Story drift angle(rad.)

overall SSI analysisFixed model by GL input

Figure 12. Maximum story drift angles of super-structure due to horizontal earthquake ground motion shown in Fig.7

11

peak amplitude at frequency of about 0.9Hz and the low amplitude around 2Hz. Using the

soil profile obtained from P-S loggings shown in Fig.3, an analysis derived from the Rayleigh

surface wave theory is done and its H/V spectrum due to the fundamental mode is shown by

a dashed line in Fig.13. Comparing the spectrum by the theory with one by observation, both

of the spectrum have similar variation in terms of frequency, that is, the soil profile shown in

Fig.3 is accurate.

A vibratory experiment had been conducted just after construction of the foundation by

using a vibration generator with unbalanced masses shown in Photo 1 which have the

maximum force of 0.03MN and is settled at .the 1st floor. The accelerogragh sensors of

horizontal and vertical components are arranged on the wall. Since the order of observed

vibration is 1 micron meter, the sensitive vibration of wall foundation is extracted by

analyzing the correlation between the signal of excitation and vibratory measurement.

The circle marks in Fig.14 show the amplitudes and phase differences taken out for

horizontal translation and Figure 15 is the rotational ones obtained from vertical

measurement on the web of wall. These amplitudes are converted for excitation force as to

be 1MN. It is found in these results that the horizontal and rotational amplitudes are so small

and do not have evident resonance, it seems the characteristics of wall foundation with high

rigidity, and the phase differences increase gradually as frequency becomes large, that is, the

wave dissipation from wall to surrounding soil increases.

0

2

4

6

0 1 2 3 4Frequency (Hz)

Am

plitu

de

Microtremors

Rayleigh wavetheory

Figure 13. H/V spectrum due to microtremors Photo 1. Vibration generator and Rayleigh wave theory based on the soil profile shown in Fig.3

12

A simulation analysis against experimental results is conducted on the basis of the

method described in the above section. Applying the condensed stiffness in Eq.(2) based on

the TLM, the movement of wall foundation can be written by

( ) }F{}U{]K[]K[ ww*sf

*w =+ (9)

From Eq.(9), the impedance function between forces and displacements at the top of the wall

foundation is obtained as follows.

Θ

=

U

RRRH

HRHH

KK

KKMP

(10)

where RHHR KK = . Therefore the displacements due to a force, P of the generator are

expressed by

0

50

100

150

0 1 2 3 4Frequency　(Hz)

Am

plitu

de

ExperimentAnalysis

-45

0

45

90

135


Phas

e di

ff. (D

egre

e)

ExperimentAnalysis

Figure 14. (a) Amplitude and (b) phase difference of horizontal displacement subjected to a lateral force at the top of wall

0

50

100

150

200


Am

plitu

de(×

10^-

6rad

/MN

) ExperimentAnalysis

-45

0

45

90

135


Pha

se d

iff.

(Deg

ree)

ExperimentAnalysis

Figure 15. (a) Amplitude and (b) phase difference of rotational displacement subjected to a lateral force at the top of wall

13

=

Θ

−

0U

1P

KK

KK

RRRH

HRHH (11)

The solid lines in Figs.14 and 15 are the simulated results by Eq.(11) which agree well with

the observed results.

Next, we discuss on the impedance functions derived from the observed data. It is noted

here that the unknown 3-components of the impedance can not be obtained directly from

observed data, because the excitation by generator is horizontal only, i.e. the equations are

composed of 2-unknowns only with shortage. So we assume the relationship of Eq.(12)

which is obtained using the analytical impedance of Eq.(10).

RRHH

HRK KK

Kr = (12)

Using this relation, the diagonal terms of impedance can be obtained by

-250

255075

100125


Rea

l(K

HH) (

MN

/mm

)

ExperimentAnalysis

-250

255075

100125


Imag

.(KH

H) (

MN

/mm

)

ExperimentAnalysis

Figure 16. (a) Real and (b) imaginary parts of horizontal translation impedance, HHK

-202468

10


Rea

l(KR

R)

(×10

^10M

N ・m

m/r

ad)

ExperimentAnalysis

-202468

10


Imag

.(KR

R)

(×10

^10M

N ・m

m/r

ad)

ExperimentAnalysis

Figure 17. (a) Real and (b) imaginary parts of rotational impedance, RRK

14

211

KHH

rUPK

−= , 2

2

2 1 K

KRR

rrPUK−Θ

= (13)

in which P is a excited force, and U and Θ are observed displacements. The resulted

impedances are shown by circles in Figs.16 and 17 in comparison with the analytical

impedance. Although RRK has rather differences because of the indirect part due to

horizontal excitation, both of HHK have well agreement.

From these comparisons between observed data by experiments and the analytical results,

it is recognized that the method applied here on the basis of TLM is appropriate for SSI

analyses in seismic design.

CONCLUSIONS

The study on the dynamic behavior of a large size wall foundation supporting a 54-story

building was presented, which considers the effect of a soil-foundation-superstructure

interaction (SSI). The contents are summarized as follows.

From an earthquake response analysis of the SSI system in the seismic design, it is

recognized that the structure is strongly influenced by SSI effects such that the response

displacements of the wall foundation are remarkable smaller than those of soil ground in free

field, and a foundation input motion into the super-structure is suppressed, consequently the

response of the super-structure becomes small.

A vibratory experiment for the wall foundation has made clear the dynamic

characteristics such that horizontal and rotational amplitudes at the top of wall are so small

and do not have evident resonance and the phase differences increase gradually with

frequency, that is, the wave dissipation from wall to surrounding soil increases. The results

are simulated well by the method which was applied for the earthquake response analysis.

This might show that the method applied for SSI analyses in seismic design is appropriate.

ACKNOWLEDGEMENT

The author would like to thank Dr.Izumi of chief structural designer of this building for

collaboration in the seismic design and my colleagues of the Technical Research Institute for

cooperation of the experiment.

15

REFERENCES

Tajimi H., 1980, A contribution to theoretical prediction of dynamic stiffness of surface foundations,

Proceedings of the 7th World Conference on Earthquake Engineering, pp.105-112

Tohdo, M., 2002, Study on earthquake response behavior of wall foundation, Proceedings of the 11th

Japan Earthquake Engineering Symposium, 233(CD ROM) (in Japanese)

Tohdo M., Chiba O., Fukuzawa R., 1992, Estimation of Earthqauke ground motions during large

earthquakes by superposing the element waves due to small events with stochastic parameters,

Journal of Structural Engineering, Vol.B, AIJ, pp.85-92 (in Japanese)

Tohdo M., Hatori, T., Chiba O., Takahashi K., Kobayashi Y., 1998, A role of sedimentary layers for

the wave propagation of vertical seismic motions, The effects of Surface Geology on Seismic

Motion, Balkema, pp.371-378

1

Field Method for Estimating Soil Parameters for Nonlinear Dynamic Analysis of Single Piles A. Anandarajah1, J. Zhang2 and C. Ealy3

Use of in situ soil properties increases the reliability and accuracy of numerical predictions. The problem of interest here is the nonlinear dynamic behavior of pile foundations. It is shown in this paper that soil parameters needed for simplified dynamic analysis of a single pile may be back-calculated from the dynamic response of the pile measured in the field. A pile was excited by applying a large horizontal dynamic force at the pile-head level, and the response measured. In this paper, two different (simplified) methods of modeling the dynamic response of the pile are considered. One of the methods is based on the Winkler foundation approach, with the spring constant characterized by the so-called nonlinear p-y springs. The second method is based on the equivalent linear finite element approach, with the nonlinearity of shear modulus and damping accounted for by employing the so-called degradation relationships. In the latter, the effect of interface nonlinearity is also considered. Starting with best estimates of soil parameters, the experimental data on the response of pile is used to fine-tune the values of the parameters, and thereby, to estimate parameters that are representative of in situ soil conditions. The soil parameters calibrated by the method can be applied to earthquake problems when the pore pressure build-up due to free-field response is not very high.

KEYWORDS piles, dynamics, soil, soil-pile system, soil-structure interaction, finite element method, Winkler method, nonlinear analysis.

INTRODUCTION The behavior of a deep foundation depends on a set of complex factors such as the nonlinear constitutive behavior of soils including the effect of pore water pressure, soil-pile-superstructure interaction including slip and separation at the pile-soil interface, characteristics of the loading, superstructure compliance, etc. When the amplitude of loading is large, most of these factors control the behavior. Accuracy and reliability of the predicted behavior depend not only on the analysis method employed, but also on the accuracy with which the model parameters (or soil properties) are determined. In cases 1 Professor, 2 Graduate student, Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, 21218, [email protected] 3 Geotechnical Engineer, Federal Highway Administration


2

where good quality undisturbed samples can be obtained, most of the required properties can be determined by testing them in a laboratory. Due to unavoidable sample disturbance during sampling, transportation, and preparation during testing, in situ methods are preferred over laboratory methods. However, heterogeneity of natural soil deposits and approximations implied in analysis methods cannot be compensated by any of the above measures. This is, in fact, the reason that the static capacity of piles are in most cases determined directly from pile load tests performed in the in situ soil. A similar approach is highly desirable in the design of piles subjected to dynamics loads. It is shown that parameters for simplified analysis methods such as the Winkler foundation method and the equivalent linear finite element method may be determined from measured response of the pile subjected to a large-amplitude dynamic load applied at the level of the pile head. Experiments were conducted in a uniform granular soil deposit, filled in a test pit available at the test site, Turner-Fairbank Highway Research center (TFHRC), Federal Highway Administration, McLean, Virginia.

Fig. 1. A Photograph of the Field Test Setup

EXPERIMENTS The tests were conducted in a 20 feet deep (6.1m) pit with a plan area of

8′1×8′1 (5.5m×5.5m). The pit was filled with a uniform sand in loose to medium dense state about an year prior to the time the tests were conducted (for a different purpose). During this time period, the sand was subjected to rain several times. At the time the tests were conducted, the water table was below the level of the pile tip. The sand within the depth of the pile was damp due to capillary action. A 4-in (0.1m) diameter, 12.3-feet (3.75m) long, pipe pile was driven into the soil to a depth of 9.2 feet (2.8m), with an overhang of 3.1 feet (0.95m). A weight of 122 lbs (0.54 kN) was attached to the pile at the pile head. The loading was to be applied by the Statnamic device (Middendorp, et al., 1992). The Statnamic device produces a single-pulse, impact loading. In order to extract more cycles of vibrations from a single-pulse

3

impact loading, a spring-mass oscillator was attached to the pile head, and the Statnamic load was applied in the horizontal direction to the pile at the pile-head level through this spring-mass oscillator. The test setup is shown in Fig. 1. As a shot is fired from the Statnamic device, the projectile latches onto the spring (which is attached to the pile head), and oscillates along with the pile head. Three tests were conducted, each time with

a spring of different spring constant. Fig. 2. Comparison Normalized Ground-Level Displacement Versus Time Histories of the Pile From the Three Tests. The load experienced by the pile head was measured directly by a load cell attached between the pile head and the excitation setup. The horizontal displacement response of the pile was measured using 2 LVDTs (Linear Variable Displacement Transformers), one attached at the pile-head level and the other at the ground level. In addition, the horizontal pile-head acceleration was measured with the aid of an accelerometer. Fig. 2 presents a comparison of the ground-level horizontal displacement-time histories of the pile from the three tests. The peak displacements from the 3 tests were 0.8in, 1.5in, and 0.9in (2.0cm, 3.8cm, and 2.3cm) respectively. Except for the differences in the amplitudes, the frequency responses are almost the same. Only the results of the first test (Test 1, which has a peak amplitude of 0.8in) are used in the subsequent discussions and analyses. The load-time history is presented below along with numerical results.

ANALYSES BY THE FINITE ELEMENT METHOD Details of the Method The analyses presented in this paper are performed using HOPDYNE (Anandarajah, 1990), which is a finite element computer program with capabilities to model soil (linear and nonlinear), foundations, superstructure (linear) and soil-structure problems. The primary features of HOPDYNE that are used in the present study are

4

• 8-noded solid isoparametric element to model the soil • 2-noded beam bending element to model the pile • 4-noded three-dimensional slip elements to model the soil-pile interface • Equivalent-linear approach to account for the nonlinearity of the soil

Details of these features can be found in published literature, and will not be repeated here. The soil properties needed for equivalent linear finite element analysis are (for each soil type): maxG , minβ , G versus effγ relation and β versus effγ relation. The pile is characterized in terms of xxI , yyI , zzJ , pA , E and ν , where xxI , yyI and zzJ are the second moment of inertias about −x , −y and −z axes respectively (with the pile axis taken along the −z axis), pA is the cross sectional area of the pile, E is the Young’s modulus and ν is the Poisson’s ratio. In addition, mass densities of the soil and pile are also required. While the properties of the pile are known and fixed, the properties of the soil are to be back calculated. To initiate the iterative process, starting estimates are required. The empirical equation suggested by Seed and Idriss (1970) is used to obtain a starting estimate for maxG :

21= /max

ˆmKG σ (1)

where K is a density-dependent constant, and mσ is the mean normal pressure. As the value of the coefficient of earth pressure at rest is unknown, it is assumed to be 1.0. With this assumption, mσ becomes equal to the vertical effective stress. For a loose sand, with

mσ expressed in lb/ft2 (or psf), 00040= ,K . The density of the sand was about 110 lb/ft3 (17.3 kN/m3). As the soil is homogeneous, and the water table is not within the depth of the pile, Eq. 1 becomes:

21621 10×420=11000040= //max .)(,ˆ hhG psf (2)

where h is the soil depth. The optimal value of maxG is then taken as

maxmax GFG 1= (3) where 1F is a multiplier, to be established iteratively by matching the experimental response to the theoretical response. The value of minβ was found to have a negligible influence on the overall response. On this basis, a value of 0.005% is assumed in the analyses reported here. The G versus effγ relation and β versus effγ relation are function of the soil types. As the soil type is known, the empirical relations proposed for this soil type (sand) by Seed and Idriss (1970) are used, and assumed to be fixed. Thus, the only parameter that is sought by the back-calculation process is 1F .

5

Fig. 3. Deformation of a Portion of the Domain Analyzed Analysis and Results The problem of interest is complex and three-dimensional. Three-dimensional finite element analyses can be computationally intensive, even in the case of a total stress based equivalent linear analysis such as the one of interest here. Equivalent linear analyses amount to a few (3 to 10) linear analyses. When pore water pressure effects are to be considered (which is the natural extension of total stress analyses), the computational efforts can be overwhelming to the point where the analyses can no longer be performed within a few minutes on a PC. Thus, from the point of view of using the analyses for practical design purposes, it is of interest to explore approximations that may yield results with acceptable accuracy.

Fig. 4. Plain-Strain Approximation of Gazetas and Dobry (1984)

6

First, we consider a regular mesh with no approximations. As the problem is symmetric about the vertical plane that contains the pile and the direction of applied loading, only half the domain needs to be discretized. This cylindrical mesh, which contains 2824 nodes, 2240 soil elements, and 18 bending elements, provides accurate results for the problem. The outer boundary of the cylindrical domain is placed at a radius of 30 feet (9.15m). There are 14 layers of elements in the vertical direction. The deformation is pretty much confined to the region near the pile. To show the details a little better, deformation of the domain (at a given time) within a window around the pile is shown in Fig. 3. Then two specific approximations are considered. In the past, several approximations have been developed for obtaining analytical solutions in the frequency domain (e.g., Gazetas and Dobry, 1984) and for approximate finite element solutions (e.g., Wu and Finn, 1997). We will use some of these as guidelines for our finite element analyses. In particular, Gazetas and Dobry (1984) developed models based on plain-strain approximations. In this, a slab of soil, extending to infinity in the radial direction, is assumed to have no displacements in the direction normal to the plane of the slab. At the center of the slab is a square-shaped pile segment undergoing a horizontal dynamic motion. The slab is divided into four quarters. As shown in Fig. 4, the energy that radiates away from the pile into the soil is assumed to take place in two distinct ways: (1) in the form of a compressional wave through two of the quarters, and (2) in the form of a shear wave through the other two quarters. It was shown that the radiation damping calculated from this approximate plane-strain model closely matched that radiation damping calculated from the plane strain solution of Novak, et al. (1978). The 14 plain-strain slabs, each with 4 quarters, are attached to the pile. In the radial direction, the slabs are fixed at 30 feet (0.915m) from the center. The slabs are not bonded in the vertical direction; i.e., each slab can undergo horizontal motions independently of each other.

Fig. 5. Deformed Configuration Using Approximate, Coupled Mesh

7

The effect of bonding the plain-strain slabs in the vertical direction is examined using the mesh shown in Fig. 5, where, owing to symmetry, only half the domain is discretized. Primary difference between the coupled and uncoupled meshes are that the horizontal slabs are not bonded (i.e., uncoupled) to each other in the uncoupled mesh whereas they are in the coupled mesh. To further cut down the number of degrees of freedom, the vertical degree of freedom was suppressed in all of the analyses presented; its effect is examined next.

t (sec)

Dis

p.-P

ileat

G-L

evel

(in)

0 0.5 1

-0.2

0

0.2

0.4

uz=0, XO=30'uz=0, XO=15'Non-zero uz, XO=15'

Fig. 6. Effect of Radial Domain Size and Vertical Degree of freedom Fig. 6 presents a comparison of ground-level displacement-time histories obtained with the full mesh under the following conditions: (1) 0′3=0X and 0=zu , (2) 5′1=0X and

0=zu and (3) 5′1=0X and 0≠zu , where 0X is the radial distance at which a fixed vertical outer boundary is placed, and zu ’s are the vertical degrees of freedom. It is seen that the differences in the results are very slight, indicating that the vertical response of the soil and the pile is negligible in the present case, and the radial distance of 30 feet is far enough to place a fixed vertical boundary.

t (sec)

Dis

p.-P

ileat

G-L

evel

(in)

0 0.5 1-0.8-0.6-0.4-0.2

00.20.40.60.8

Full meshPlane strain mesh560 elem.coupled mesh

Fig. 7. Comparison of Results From Full, Uncoupled Plain-Strain and Coupled Meshes Fig. 7 presents a comparison of ground-level displacement-time histories obtained with the three different meshes described earlier: (1) the full mesh, (2) the plain-strain mesh, and (3) the coupled mesh. While the results are not equal to each other, the approximate models appear to give acceptable results for practical use.

8

t (sec)

P(t)

(lbs)

0 0.5 1

-2000

-1500

-1000

-500

0

500

Measured

t (sec)

a(t)

(g)

0 0.5 1

-5

0

5

10Measured

t (sec)

a(t)

(g)

0 0.5 1

-5

0

5

10

CalculatedFE (560 elem) with 0.5Gmax

t (t)

Dis

p.-P

ileat

G-L

evel

(in)

0 0.5 1

-0.5

-0.25

0

0.25

0.5

0.75

MeasuredCalculatedFE (540 elem) with 0.5Gmax

Fig. 8. Comparison of Calculated (Using Full Mesh and max. G150 ) and Measured Results It should be noted that these are not general results, and the outcome might differ from problem to problem, depending on the frequency of loading, natural frequencies of the system, etc. However, the results do indicate that for a given problem, it is worth exploring these approximations so that subsequent analyses (e.g., parametric study or a

9

more systematic probabilistic study, where the analyses need to be repeated several times) may be performed using one of these approximate models. After a few trial runs, a reasonably good match is found for 150=1 .F . A comparison between the finite element results (using the full mesh) with 150=1 .F (Eq. 3) and the experimental results are shown in Fig. 8. The first plot in Fig. 8 presents the measured pile-head load versus time history, which is used as input to the finite element analysis. The 2nd and 3rd plots present the measured and calculated pile-head acceleration time histories respectively. The 4th plot presents a comparison between the measured and calculated ground-level displacement time histories. All of the above quantities are horizontal components. In view of the fact that the soil is actually an elasto-plastic material, whereas it is represented by a form of a nonlinear viscoelastic model in the finite element analysis, the quantitative comparison shown in Fig. 8 is considered to be reasonably good. In both cases, the response dies out in about 3 cycles. The rate of decay of the displacement amplitude is predicted reasonably well.

t (sec)

Dis

p.-P

ileat

G-L

evel

(in)

0 0.5 1-0.8-0.6-0.4-0.2

00.20.40.60.8

560 elem. coupled mesh560 elem. coupled meshwith slip elements

Fig. 9. Comparison of Calculated Responses with and without Slip Elements and

max. G150

t (sec)

Dis

p.-P

ileat

G-L

evel

(in)

0 0.5 1-0.8-0.6-0.4-0.2

00.20.40.60.8

560 elem. coupled mesh560 elem. coupled meshwith slip elements

Fig. 10. Comparison of Calculated Responses with and without Slip Elements and

max. G200 In the analyses described so far, the soil has been bonded to the pile, preventing any gapping or slipping to take place at the soil-pile interface. Using the 560-element coupled mesh (Fig. 5), an analysis is conducted with slip elements placed between the pile

10

elements and the soil elements. The calculated ground-level displacement time histories with and without the slip elements are shown in Fig. 9. It is noted that the use of slip elements renders the response softer, yielding larger pile displacements. These results were obtained with 150=1 .F . Then 1F is varied until a good match is obtained. The numerical results with 200=1 .F and with slip elements are compared in Fig. 10 with numerical results using 150=1 .F and without slip elements. The results from the both analyses are virtually identical, indicating that the soil stiffness doesn’t need to be reduced as much when slip elements are employed, since the use of slip elements makes the system softer by allowing slip and separation at the pile-soil interface. It should be noted that the consequence of allowing slip and separation may be more dramatic in other problems, and thus having the capability to use slip elements is desirable.

WINKER FOUNDATION METHOD Details of the Method

Fig. 11. Winkler Foundation Approach: Springs and Dashpots to Represent the Effect of Soil In the Winkler foundation approach (Fig. 11), the primary member analyzed is the pile. The influence of the surrounding soil on the pile is introduced through a series of nonlinear springs (in the case of static problems). The most widely used spring force-displacement relationships are the so-called p-y curves of Matlock (1970) for clays and Reese, et al. (1974) for sands. In extending this static method to problems involving dynamic loads such as that from earthquakes, ship collisions, etc., methods are needed for accounting for damping – both material and radiation damping. Several researchers have worked on this problem (Kagawa, 1980; Berger, et al., 1977; Wang, et al., 1998; Boulanger at al., 1997; Loch et al., 1998; Badoni and Makris, 1996; Abghari and Chai, 1995, Nogami , et. al., 1992, Gazetas and Dobry, 1984, Sen et al., 1985; Trochanis, et al., 1991). These studies indicated that there are some major difficulties to be resolved.

11

Firstly, the most appropriate spring/dashpot model to use is not clear. For instance, Wang, et al. (1998), after comparing results with series (spring and dashpot in series) and parallel (spring and dashpot in parallel) models, determined that the parallel model leads to a very stiff system, with the damping force over-dominating the system response. In either case, the material damping needs to be considered as well. The appropriate model to use is thus yet to be identified. Secondly, the issue concerning a suitable value to use for the coefficient of damping has not been resolved. For instance, if one uses Berger’s model (1977) to represent the radiation damping, where it is assumed that radiation of energy away from the pile takes place in the form of p- and s-waves through a volume of soil of constant cross section (like a one-dimensional rod), the damping coefficient becomes frequency independent, and is given by

dVVCCC spsp ρ)( +=+= (4) where pV is the p -wave velocity and sV is the shear (s-) wave velocity, ρ is the mass density and d is the diameter of the pile. Here C is the coefficient of damping per unit length of the pile. Wang et al. (1998) found that the value of C calculated using the above equation was too large. They arbitrarily assumed dVC s ρ2= . There is no consensus among researchers as to the most suitable model and the most appropriate equation for computing C. Berger’s model is approximate. The manner in which the energy radiates away from the pile is complex, and the p- and s-wave portions cannot be easily separated out as is done in Berger’s model. The cross section of the portion of the soil that carries the radiation energy is not constant. But analyses with non-uniform cross sections lead to frequency-dependent damping parameters (e.g., Gazetas and Dobry, 1984), making it difficult to apply them in a time-domain analysis. A frequency has to be arbitrarily selected for computing a value for C to use in a time-domain analysis such as that involved in the beam of nonlinear Winkler foundation method (BNWF). When the pile is shaken with a large amplitude loading – the problem of interest here - the material damping is more important than the radiation damping (Brown and O’Neill, 2001), and there is no rational method of calculating a value for the damping coefficient. There are yet other factors that cannot be properly accounted for at the present time. For instance, the softening that takes place at the soil/pile interface due to slipping and gapping is difficult to model. Also, the pore water pressure build up during a cyclic loading such as the earthquake loading cannot be accurately modeled. All of the above difficulties associated with the use of nonlinear Winkler foundation methods point to the need for a site-specific, field calibration of the method. In the specific Winkler foundation model used here, the soil is replaced by a series of elements involving a spring and a dashpot in parallel (i.e., without a second series dashpot shown in Fig. 11). The coefficient of damping is calculated according to Eq. 4, but with a modifier cF , as follows:

dVVFCCFC spcspc ρ)()( +=+= (5)

12

Estimated values of pV and sV are 738 ft/s (225 m/s) and 492 ft/s (150 m/s), and the mass density is 3.42 lb-sec2/ft4 (1.76 kN-sec2/m4 or 1.76 g/cm3). The spring constant is represented by the p-y relation suggested by Reese, et al. (1974) for sands. Parameters of the p-y relation depend on whether the loading is static or cyclic; here the cyclic parameters are used. The entire curve is a function of ),( 1kd,′,γφ , where φ is the friction angle of the soil, γ ′ is the effective density of the soil, d is the diameter of the pile, and 1k is the slope of the initial straight line. The value recommended for 1k for loose to medium dense sand is 60 lb/in3 (16225 kN/m3). Except for d , all other parameters can assume different values than our initial estimates. Let us, therefore, introduce multipliers with each parameter as:

*φφ φF= (6a)

*γγ γ ′=′ F (6b) *11 = kFk k (6c)

The estimated value of the friction angle for this soil is 350, and the density is 110 lb/ft3 (17.3 kN/m3). Analysis and Results HOPDYNE (1990) has the capability to consider nonlinear, discrete springs and dampers. The beam bending elements available in HOPDYNE is used to model the pile. The soil deposit is divided into 14 layers, and a parallel spring/dashpot elements is attached to the pile in the middle of each of these 14 layers. After several trials with different values for γφ FFFc ,, and kF , it is found that most matching results are obtained with 1=50=1= γφ FFFc ,., and 1=kF . In other words, changing only the value of φ not only is adequate, but gives the most optimal results. It may, however, be necessary to change some of the other parameters for best results in other problems. The comparison between numerical and experimental results is presented in Fig. 12, where the plots at the top and middle are the measured and calculated pile-head horizontal acceleration-time histories, and the plot at the bottom is a comparison between numerical and experimental ground-level horizontal displacement-time histories. It is seen that the comparison is as good as the one with the finite element results (Fig. 8), indicating that both the equivalent linear finite element method and the beam of nonlinear Winkler foundation method are equally capable of representing the dynamic response of the single pile under study here.

13

t (sec)A

cce.

-Pile

Top

(g)

0 0.5 1

-5

0

5

10Measured

t (sec)

Acc

e.-P

ileTo

p(g

)

0 0.5 1

-5

0

5

10Caculated by BNWF

t (sec)

Dis

p.-P

ileG

-Lev

el(in

)

0 0.5 1-0.6

-0.4

-0.2

0

0.2

0.4

0.6

MeasuredCalculated by BNWF

Fig. 12. Comparison Between Calculated (by BNWF Method with 5.0=φF ) and Measured Results

CONCLUSIONS A series of large amplitude dynamic tests was conducted on a single pile driven into a homogeneous sandy deposit. The pile was subjected to a horizontal impact load with the aid of a Statnamic device. The pile underwent a cyclic motion involving about 3 cycles. The pile-soil system was modeled using two different numerical methods: (1) Equivalent linear finite element method, and (2) beam of nonlinear Winkler foundation method with nonlinear p-y curves to represent the stiffness and Berger’s model to represent the damping. The objective was to back-calculate from the experimental results site-specific soil properties. The study indicates that both numerical methods are equally capable of representing the nonlinear dynamic response of the pile-soil system, and that the relevant soil parameters for these methods may indeed be back-calculated from the experimental data. While the beam of nonlinear Winkler foundation is simpler and computationally

14

more efficient than the finite element method, the latter has the advantage of having the capacity to consider the interface slip and separation, and the effect of pore pressure (not considered in the present study).

ACKNOWLEDGEMENT The research was supported by the U.S. National Science Foundation under grant No. CMS0084899 and by the Federal Highway Administration. The cognizant program director of NSF is Dr. Richard Fragaszy. These supports are acknowledged.

REFERENCES Abghari, A. and Chai, J. (1995). ``Modeling of soil-pile superstructure interaction in the design of bridge foundations,'' Geotechnical Specialty Pub. No. 51, Performance of Deep Foundations Under Seismic Loading, ASCE, John Turner (ed.), 45-59. Anandarajah, A. (1990). HOPDYNE: A finite element computer program for the analysis of static, dynamic and earthquake soil and soil-structure systems. Civil Engineering Report, Johns Hopkins University. Berger, E., Mahin, S.A. and Pyke, R. (1977). “Simplified Method for Evaluating Soil-Pile Structure Interaction Effects.” Proc. 9th. Offshore Technology Conference, OTC Paper No. 2954, Huston, Texas, pp. 589-598. Boulanger, R.W., Wilson, D.W., Kutter, B.L., and Abghari, A. (1997). ``Soil-Pile Superstructure Interaction in Liquefiable Sand.'' Transportation Research Record 1569. Brown, D. A., and O’Neill, M.W. (2001). “Static and Dynamic Response of Pile Groups”. NCHRP Study (report not available yet). Gazetas, G. and Dobry, R. (1984). “Simple Radiation Damping Models for Piles and Footings.” J. Engrg. Mech., ASCE, 110(6), pp. 937-956. Hilber, H.M., Hughes, T.J.R. and Taylor, R.L. (1977). Improved numerical dissipation for time integration algorithms in structural mechanics. Int. J. Earthquake Eng. And Structural Dynamics. 5:283-292. Idriss,, I.M., Lysmer, J., Hwang, R. and Seed, H.B. (1973): Quad4: A computer program for evaluating the seismic response of soil structures by variable damping finite element procedure, University of California, Berkeley Report No. EERC 73-16. Kagawa, T. (1980).``Soil-Pile Structure Interaction of Offshore Structures During an Earthquake.'' Proc. 12th. Annual Offshore Technology Conference, Huston, Texas, OTC 3820.

15

Matlock, H. (1970). “Correlations for Design of Laterally-Loaded Piles in Soft Clay.” OTC Paper No. 1204, Huston, Texas. Matlock, K., Foo, S.H. and Bryant, L.L. (1978). “Simulation of Lateral Pile Behavior.” Proc. Earthquake. Engrg. Soil Dyn. ASCE, July, pp. 600-619. Middendorp, P., Bermingham, P. and Kuiper, B. (1992). “Statnamic Load Testing of Foundation Piles.” Proc. 4th. Intl. Conf. Application of Stree-Wave Theory to Piles, The Hague, The Netherlands, pp. 581-588. Novak, M., Nogami, T. and Aboul-Ella, F. (1978). Dynamic soil reactions to pile vibrations. J. Eng. Mechanics Division, ASCE, 104(EM4):1024-1041. Nogami, T., Otani, J., Konagai, K. and Chen, H-L. (1992). ``Nonlinear Soil-Pile Interaction Model for Dynamic Lateral Motion.'' J. Geotech. Eng., ASCE, 118(1):89-106. Reese, L.C., Cox, W.R., and Kooper, F.D. (1974). ``Analysis of Laterally-Loaded Piles in Sands.'' Proc. 6th. Annual Offshore Technology Conference, Huston, Texas, OTC 2080. Seed, H.B. and Idriss, I.M. (1970). Soil Moduli and damping factors for dynamic response analyses. University of California, Berkeley Report No. EERC 73-16. Sen, R., Davis, T.G. and Banerjee, P.K. (1985). “Dynamic Analysis of Piles and Pile Groups Embedded in Homogeneous Soils.” Intl. J. Earthquake Engrg. Soil Dyn., 13:53-65. Trochanis, A.M., Bielak, J. and Christiano, P. (1991). “Simplified Model for Analysis of One or Two Piles.” J. Geotech. Engrg., ASCE, 117(3):448-466. Wang, S., Kutter, B.L., Chacko, M.J., Wilson, D.W. and Boulanger, R.W. (1998). ``Nonlinear Seismic Soil-Pile Structure Interaction.'' Earthquake Spectra, 14(2):377-396. Wu, G. and Finn, W.D.L. (1997). Dynamic nonlinear analysis of pile foundations using finite element method in the time domain. Canadian Geotechnical J. 34:44-42. Zienkiewicz, O.C. and Taylor, R.L. (1989). The finite element method. Vol I, 4th Edition, MacGraw-Hill.

1

Soil Profile Confirmation through Microtremor Observation Yuzuru Yasuia) and Tatsuya Noguchib)

It was shown first that the H/V spectrum method is useful in an examination

of a two layered soil structure model presumed. Then on a site having an

intermediate support layer, microtremor observation was conducted for about 5

months, and it was shown that the peak frequencies of the H/V spectrum appear

between two predominant frequencies corresponding to the shallower surface

layer and the deeper one. Furthermore, another site where soil velocity structure

model was made in detail based on logging survey data was taken up. It was

shown that discrepancies between soil amplification characteristics calculated by

the soil model and observed ones led to a correction of the model. The

microtremor array observation method was successfully used to revise the soil

model.

INTRODUCTION

A discussion of the Soil-Structure Interaction effect requires the clarification of the

circumference ground soil velocity structure for the building foundation concerned. To

discuss kinematic interaction effects especially, a soil structure model to a depth of a certain

hard support layer and a width to some lateral extent is required. The soil structure model is

commonly based on pinpoint logging data or/and on a limited number of boring data. The

present paper shows the usefulness of applying the microtremor measuring method to

confirm the presumed soil structure model, including supporting case notes.

The horizontal-to-vertical (H/V) spectrum method is one of the microtremor observation

methods used for soil structure surveys. The relevance of the H/V spectrum ratio and

underground soil structure has been pointed out (Nogoshi and Igarashi 1971) and

examinations of the applicability of this method to soil structure surveys have been

performed by many researchers. Studies have put forth that the multiple reflection of a body

wave can explain the formation of H/V spectrum peaks (Nakamura and Ueno 1986), that a a) Fukui University of Technology, Gakuen 3-6-1, Fukui 910-8505, Japan b) Kyoto University, Gokasho, Uji, Kyoto 0611-0011, Japan


2

surface wave motion may produce the peaks (for example, Wakamatsu and Yasui 1995) and

that the mode ratio of the surface wave can also explain the generation of the peaks (for a

recent example, Arai and Tokimatsu 2004). Those causes being set aside, the H/V spectrum

shows peaks at the predominant frequency, if the contrast of the surface layer to the lower

layer is strong, and it has been used successfully as an aid in soil structure investigation.

The microtremor array observation method was first advocated by Aki (1957), an

alternative method was proposed by Capon (1969), and the development towards utilization

was made by Horike (1985) and Okada and Matsushima et al. (1990). According to the array

observation method, the soil velocity structure, fitted for the obtained dispersion curve of

surface wave’s phase velocity, can be directly searched through inverse analysis. The H/V

spectrum method and the array observation method are economical and good in mobility, and

it is extremely important to use the exact application conditions.

The present paper shows that the H/V spectrum method is effective in confirming the soil

structure model based on the boring data, being applied in a line of this model. Then, a site

with an intermediate support layer is considered, the features of the H/V spectrum at a site

that does not have a gradually increasing velocity structure is described, and the limits of

model applicability are shown. Examination of the microtremor observation results and

earthquake observation results is performed for a point where earthquake observation is

conducted both on the ground surface and directly under ground, demonstrating that

correction of the soil velocity structure based on logging data is needed, and that the H/V

spectrum method and the array observation method play important roles in the process of

these examinations.

CONFIRMATION OF SOIL PROFILE MODEL

The target area is the Fukui plain, where a magnitude 7.1 earthquake occurred in 1948,

and 3,769 people were lost. The Fukui prefecture government produced a soil structure

model with every 500 m mesh based on existing boring data, and performed earthquake

damage evaluations using this model. Since this soil model was created with a limited

number of unevenly distributed data, examination needs to be completed using certain

methods. In this chapter, the examination example based on the H/V spectrum method is

described (Yasui 2003).

3

The target map and measured points of the area are shown in Figure 1. Microtremor

observation was conducted for 32 points distributed every 500 m on the cross line, the center

of which is Itagaki town (ITG) where there is Point FKI003 of K-NET that is the only

observatory station in Fukui plain. Where, K-NET and KiK-NET, to be mentioned later, are

earthquake observation systems covering all of Japan and are served by the National

Research Institute for Earth Science and Disaster Prevention

The microtremor measurement direction is horizontal, 2 components, and vertical, 1

component, which intersect perpendicularly. Measurements were collected for 5 minutes

using 100 Hz sampling frequencies, the H/V spectrum was calculated using 30,000 digit data.

The spectra of the microtremor records’ horizontal 2 components are compounded as the

horizontal spectrum (H), divided by the spectrum of the vertical component (V), resulting in

the H/V spectrum, with a Parzen Window bandwidth of 0.2 Hz.

The H/V spectrum of the N-9 point is shown in Figure 2 as an example. Two peaks are

seen in this spectrum (Wakamatsu and Nobata 1998). Table 1 shows the presumed Fukui

prefecture soil model at N-9. The lower peak is approximately 0.6 Hz, and is considered the

predominant frequency of the surface layer, upwards from the upper surface of the tertiary

rock ground. The higher peak is approximately 1.7 Hz, and is considered the predominant

frequency of the alluvium layer upwards of the diluvium upper surface.

Figure 3 shows a comparison about the two peaks between the peak periods of the H/V

spectrum, and the peak periods by the Fukui prefecture corresponding model along the NS

measured line. Although the observation value and the value by the assumption model are

generally in agreement, it may be necessary to reexamine the assumption model at the point

where the inconsistency is large. The peak periods according to the Fukui prefecture soil

model are the primary peak period of the soil amplification function over the tertiary upper

surface and the diluvium upper surface, calculated using SHAKE based on the assumption

soil column model at each measuring point, respectively.

In addition, research using the microtremor observation method, which examined the

Fukui plain, referring to the Fukui prefecture soil model for a 1 minute mesh was recently

reported (Kojima and Yamanaka 2004).

4

Figure 1. Measuring points in the south of Fukui plain

Figure 2. H/V Spectrum and soil amplification function (N-9)

0.1 0.2 0.5 1.0 2.0 5.0 10.0 0.0

2.0

4.0

6.0

8.0

Hz

Am

p. F

unc.

N-9 / H/V vs. Amp. Func.

H/VGL-20mGL-150m

5

Table 1. Fukui prefecture soil structure model at point N-9

Figure 3. Comparison of the H/V spectrum peak periods with ones from the Fukui

prefecture soil model

H/V SPECTRA OF SOIL WITH INTERMEDIATE HARD LAYER

The Doboku office observation point (DBK) in the Figure 1 map is one of a few points

for which the PS logging survey is performed in the Fukui plain. The H/V spectrum method

requires the soil velocity structure to be investigated precisely, thus, DBK point has been

used often as the reference point until now. The soil velocity structure of this point is shown

in Table 2, revealing a hard layer in the middle, and suggesting that the H/V spectrum peak

may have been influenced by this intermediate layer.

0

0.5

1

1.5

2

2.5

N12 N11 N10 N9 N8 N7 N6 N5 N4 N3 N2 N1 ITG S1 S2 S3 S4 S5 S6 S7 S8

TD（Calculated）TA（Calculated）TD（Observed）TA（Observed）

Peak

Per

iod

(sec

)

Measuring Point

Depth（m） Hi（m） ρ i

(ton/ m3)Vsi

（m/ sec）0 4 Clay- 1 1.6 1004 5 Sand- 1 1.8 1509 7 Clay- 2 1.7 15016 4 Sand- 2 1.9 20020 25 Gravel 2.1 50045 15 Clay 1.8 30060 15 Sand 1.9 40075 30 Gravel 2.1 500105 20 Clay 1.8 300125 10 Gravel 2.1 500135 10 Clay 1.8 300145 5 Gravel 2.1 500150 ー Tertiary Volcanic Rock 2.5 1,000

Diluvial

Geological Layer

Alluvial

6

Examples of the H/V spectra for this point are shown in Figure 4. Calculation of the H/V

spectrum is performed for the same conditions as the case shown in Figure 2. The soil

amplification functions using SHAKE are also shown in this figure with the H/V spectra on

October 21 (Date A), 2003 and February 25 (Date B), 2004. These soil amplification

functions are shown for the middle support layer in the GL-24 m case, and the downward

support of GL-150 m case. The peak frequency of 1.7 Hz on Date A corresponds to the

former peak (fA=2 Hz), and the peak frequency of 1.2 Hz on Date B corresponds to the latter

peak (fB=1 Hz), demonstrating that the peak frequencies change with measurement days. In

addition, although not shown in Figure 4, the peak value of the soil amplification function for

the GL-54 m base is approximately 3.50 with 1.35 Hz (=fC).

The observation period was approximately 5 months, with observations conducted at

15:00. Calculation of the H/V spectrum was made under the same conditions as in the Figure

2 case. The peak frequencies and peak values read from the H/V spectra are shown in Figure

5 (a) and (b). The peak frequencies corresponding to fA and fB did not alternate, but were

arbitrarily distributed between both values. The average value of peak frequency, 1.34 Hz

(with a standard deviation value of 0.2 Hz), is almost equal to fC. In contrast, the peak value

presents the aspect distributed from 3 to 12, making it difficult to be termed as stable, and the

average value is 6.41 (with a standard deviation of 1.64). This average value is close to the

peak value of the soil amplification function at fB (see Figure 4).

Table 2. Soil profile at DBK

Depth（m） Hi（m） ρ i

(ton/ m3)Vsi

（m/ sec）0 4 Fill 1.8 804 12 Fine- Medium Sand 1.7 15516 8 Sandy Clay 1.8 22524 8 Gravel 2.1 590

150 ー Tertiary Volcanic Rock 2.5 1,800

Geological Layer

Diluvial

Alluvial

290

660

32 22 Fine Sand 1.8

54 96 Gravel 2.1

7

Figure 4. H/V spectrum and soil amplification function (DBK)

Figure 5. (a) H/V Spectrum peak frequencies and (b) peak values

0

2

4

6

8

10

12

14

4/ 25 5/ 10 5/ 25 6/ 9 6/ 24 7/ 9 7/ 24 8/ 8 8/ 23

Month / Date

Peak

Val

ue

ObservedAverage (6.41)

0

1

2

3

4/ 25 5/ 10 5/ 25 6/ 9 6/ 24 7/ 9 7/ 24 8/ 8 8/ 23Month / Date

Peak

Fre

quen

cy （

Hz)

ObservedfA (2.0Hz)fB（1.0Hz）Average(1.34Hz)

0.1 0.2 0.5 1.0 2.0 5.0 10.0 0.0

2.0

4.0

6.0

8.0

10.0

Hz

Am

p. F

unc.

DBK / H/V vs. Amp. Func.

Date-ADate-BGL-24mGL-150m

8

INSPECTION OF LOGGING DATA

There are 11 K-NET and 7 KiK-NET earthquake observatory stations in Fukui prefecture.

The seismometers in the K-NET system are set only on the ground surface. In the KiK-NET

system, the sensors are set at the ground surface and the underground base rock. In the

current study, the Eiheiji station (FKIH01) of the KiK-NET system is the target and the

sensor is set at ground surface and GL-103 m. Earthquake records from this station could be

important data for the examination of the input earthquake motion on this plain because this

station is close to Fukui plain. The soil velocity structure of this point, based on the logging

survey, is shown in Table 3. Table 4 shows the dimensions of the four observed earthquakes

at the target site.

The Fourier spectrum ratios of earthquake records of the ground surface to GL-103 m are

shown in Figure 6. During the calculation, the total length of each datum is set as 120

seconds, containing the whole duration of a seismic wave with sufficient succession zero

portion, and sampling time is 0.005 seconds. As the observed spectra, eight spectrum ratios

of both NS and EW for the four earthquakes are written in piles. The soil surface

amplification functions over the E+F input in GL-103 m, calculated using SHAKE, are also

shown in this figure, which reveals that the calculation value and the observation values are

not in agreement.

The H/V spectra calculated from the earthquake records at ground surface are shown in

Figure 7(a). Figure 7(b) shows the H/V spectrum calculated based on microtremor

observations conducted near the earthquake observation station. The calculating conditions

are the same as in Figure 2 or 4. The soil surface amplification functions over 2E input in

GL-4 m, calculated using SHAKE, and GL-19 m are shown in this figure, which reveals that

the calculation value and the observation value are not in agreement.

The microtremor array observation was then performed using the SPAC method (Okada

and Matsushima et al. 1990) to examine soil velocity structure. The array radii are set at 3 m,

10 m, and 28 m. Figure 8 is the dispersion curve of the surface wave phase velocity obtained

from the array observation results, and the theoretical dispersion curve simulated by trial and

error is also written together. It became necessary to change the thickness of the top surface

layer into 9 m from 4 m as a result of this examination. The correction velocity structure is

shown in Table 5. The soil surface amplification function over the E+F input in GL-103 m of

the corrected soil model and the soil surface amplification functions over 2E input in GL-9 m

9

and GL-19 m are shown in Figure 9 and Figure 10, respectively. The calculated value and the

observed value are mostly in agreement.

Table 3. Original soil profile at FKIH01

Table 4. Dimensions of earthquakes examined

Figure 6. Calculated soil amplification function of GL m0± to GL-103m for (E+F) input

using original soil profile model compared with observed earthquakes

Year Month/ Date hr. : min : sec Latitude Longitude M △ (km) D(km) Amax(Gal)2003 6/ 5 23:14:00 36.3 136.3 4.1 24 10 36.32003 2/ 11 18:34:00 36.05 136.34 4.0 5 6 156.22002 9/ 8 0:11:00 35.97 136.57 3.9 23 10 45.22002 8/ 18 9:01:00 36.13 136.18 4.5 17 11 35.8

0

20

40

60

80

100

1 10 100Hz

Amp.

Fun

c.

Earthquake Calculated

Depth（m）

Hi（m） Geological Layer

ρ i

(ton/ m3)Vsi

（m/ sec）0 4 Sand 1.8 1504 2 Gravel 2.2 1,0006 6 Granite12 7 Andesite19 46 Granite 2.5 2,100

65 38Alternation ofGranite and

Andesite2.5 2,500

103 ー Andesite 2.5 2,500

2.2 1,650

10

Figure 7. H/V spectrum for (a) observed earthquake and (b) microtremor observation,

compared with calculated soil amplification functions of GL m0± to GL-4m and to GL-19m

for 2E input using original soil profile model

0

5

10

15

20

1 10 100Hz

H/V

and

Amp.

Fun

c.

Microtremor Calculated to GL-19m Calculated to GL- 4m

0

10

20

30

1 10 100Hz

H/V

and

Amp.

Fun

c.

Earthquake Calculated to GL-19m Calculated to GL- 4m

11

Figure 8. Obtained dispersion curve of phase velocity from microtremor array observation

compared with theoretical calculation

Table 5. Modified soil profile at FKIH01

Depth（m） Hi（m） Geological Layer ρ i

(ton/ m3)Vsi

（m/ sec）

10 3 Granite12 7 Andesite19 46 Granite 2.5 2,100

65 38Alternation ofGranite and

Andesite2.5 2,500

103 ー Andesite 2.5 2,500

0 9 Sand 1.8

2.2 1,650

150

0

100

200

300

400

500

600

0 5 10 15 20Hz

Phas

e Ve

loci

ty (m

/sec

)　　　　Observed

　　　Theory

12

Figure 9. Calculated soil amplification function of GL m0± to GL-103m for (E+F) input

using modified soil profile model compared with observed earthquakes

0

20

40

60

80

100

1 10 100Hz

Amp.

Fun

c.Earthquake Calculated

13

Figure 10. H/V spectrum for (a) observed earthquake and (b) microtremor observation,

compared with calculated soil amplification functions of GL m0± to GL-4m and to GL-19m

for 2E input using modified soil profile model

0

10

20

30

1 10 100Hz

H/V

and

Amp.

Fun

c.

Earthquake Calculated to GL-19m Calculated to GL- 9m

0

5

10

15

20

1 10 100Hz

H/V

and

Amp.

Fun

c.

Microtremor Calculated to GL-19m Calculated to GL- 9m

14

CONCLUSIONS

A possibility that the thickness of the alluvial and diluvial layer could be presumed

utilizing two peaks of the H/V spectrum was shown.

The peak frequency of the H/V spectrum of the site which has an intermediate support

layer showed the tendency to be arbitrarily distributed between the shallower predominant

frequency and the deeper one.

Confirmation of the soil structure by the H/V spectrum method even at the point where

detailed soil velocity structure was acquired by logging survey is recommended. When

making a revised soil model, the microtremor array observation serves as an effective

method.

REFERENCES

Aki, K., 1957: Space and time spectra of stationary stochastic waves with special reference to

microtremors, Bull. Earthq. Res. Inst. Tokyo University, 35,pp.415-456,

Arai, H., and Tokimatsu, K., 2004. S-wave velocity profiling by inversion of microtremor H/V

spectrum, Bulletine of the Seismological Society of America, Vol. 94, No. 1, pp. .53-63.

Capon, J.,1969. High-Resolution frequency-wavenumber spectrum analysis, Proc. Of the

IEEE,Vol.57,No.8,pp.1408-1418

Fukui Prefecture, 1997. Report on estimation of earthquake damage in Fukui Prefecture (in

Japanese).

Horike., M., 1985. Inversion of phase velocity of long-period microtremors to the S-wave-velocity

structure down to the basement in urbanized area, Journal of Phys. Earth 33, pp. 59-96.

Kojima, K., and Yamanaka, H., 2004. Estimation of quaternary structure of Fukui plain based on

microtremor observation, Journal of Structural Mechanics and Earthquake Engineering, Japan

Society of Civil Engineers, No. 752/Ⅰ-66, PP. 217-225(in Japanese).

Nakamura, Y., and Ueno, M., 1986. A simple estimation method of dynamic characteristics of subsoil,

Proceedings of 7-th Japan Earthquake Engineering Symposium, pp. 265-270(in Japanese).

Nogoshi, M. and Igarashi, T., 1971, On the amplitude characteristics of microtremor (Part2), Zishin 2,

24, pp.26-40 (in Japanese).

Okada, H., Matsushima, K., Moriya, T., and Sasatani, T., 1990, An exploration technique using

long-period microtremors for determination of deep geological structures areas, Geophys.

15

Explor., Vol.43, No.6, pp.402-417 (in Japanese).

Yasui, Y., 2003. Examination on the ground model in the southern part of Fukui plain using H/V

spectrum method, Summaries of Technical Papers of Annual Meeting Architectural Institute of

Japan, B-2, Structures Ⅱ, pp. 289-290(in Japanese).

Wakamatsu, K. and Nobata, A., 1998. Underground structure of Fukui plain and interpretation on the

damage of Fukui earthquake in 1948, Summaries of Technical Papers of Annual Meeting

Architectural Institute of Japan, B-2, Structures Ⅱ, pp. 227-228(in Japanese).

Wakamatsu, K., and Yasui, Y., 1995. Possibility of estimation for amplification characteristics of soil

deposits based on ratio of horizontal to vertical spectra of microtremors, J. Struct. Constr. Eng.,

AIJ, No. 471, pp. 61-70(in Japanese).

ACKNOWLEDGEMENTS

This paper is based on the graduation thesis in the 2002 and 2003 academic year. The

authors would like to express their gratitude to the graduate students. The research is

indebted also to the people of the Fire Defense and Disaster Prevention Division and Fukui

Public Works Office of the Fukui Prefecture Government. Moreover, the data of KiK-NET

was used and microSHAKE of Jishin Kougaku Kenkyusho Inc. was used in the analysis. And

more the program by Dr. Osamu Kurimoto of Obayashi Corporation was used for the

spectrum analysis of H/V. The authors would like to express their gratitude to all those

mentioned above.

1

Evidence of Soil-Structure Interaction from Ambient Vibrations - Consequences on Design Spectra

François Dunand,a,b) Pierre-Yves Bard,a,c) Jean-Luc Chatelain,a,d) and Philippe Guéguen a,c)

INTRODUCTION

The dynamic response of a structural system to dynamic loading is strongly controlled by

the amount of damping involved in each mode of vibration. At design stage, damping

characteristics of building structures are usually assumed to some "standard", predetermined

values, mainly because it is basically poorly known and very difficult to assess prior to

construction. In most cases, damping is thus assumed to have the same value for each mode,

and to be independent of the amplitude and frequency of the vibrations (Li 2002). But, as

observed by (Jeary 1986) and (Lagomarsino 1993), among others, actual damping values are

frequency and amplitude dependent.

In a first part, the Randomdec method is applied on a set of ambient vibration recordings

performed in 26 different reinforced concrete buildings, all founded on thick alluvium, to

derive their modal characteristics, including frequency and damping values for each

identified mode. Damping values do exhibit a clear correlation with frequency and aspect

ratio (i.e., ratio between the width of the building parallel to the excitation direction, and its

height, which is the inverse of the slenderness ratio). Then, in a second part, this correlation

is interpreted as due to soil-structure interaction (SSI) and the associated radiation damping,

through a simple SSI model using impedance functions derived from cone models

(Wolf 1994).

a) Laboratoire de Géophysique Interne et de Tectonophysique, France b) Bureau Veritas, France c) Laboratoire Central des Ponts et Chaussées, France d) Institut de recherche pour le développement, France


2

EXPERIMENTAL ANALYSIS

In the framework of a preliminary seismic vulnerability analysis within the city of

Grenoble (France), (Farsi 1996) performed an ambient vibration survey with broad band

velocimeters in a set of 26 buildings ranging from 3 to 28 story, and having a structural

system consisting in RC shear walls. As the Grenoble city is settled in a thick post-glacial

deposit valley, the soil geology under all these buildings is about the same, with a S-wave

velocity around 270 m/s at the surface, a Poisson’s ratio larger than 0.35, and a mass density

around 1.9 g/cm3, and a thickness exceeding 400 m everywhere (Cornou 2002).

The randomdec method (Caughey and Stumpf 1993, Ibrahim et al. 1998, Vandiver 1982)

has been applied on the ambient vibration records obtained at the roof or upper story, and

allowed to derive the frequency and damping for the fundamental modes in both transverse

and longitudinal directions. The frequency values (f0) range between 0.6 and 8 Hz, while the

damping values (ξ0) range from 0.7 % to 12 %. As displayed in Figures 1a and 1c, damping

values exhibit some correlation with the frequency and, though to a lesser extent, with the

aspect ratio L/H (inverse of the slenderness ratio H/L, L being the horizontal dimension of the

building in the mode direction and H the height of the building). A log-linear least-square fit

allows to derive the regression equation (1):

HLf 11.039.024.0)ln( 00 ++−=ξ with a standard error σ of 1.69 (1)

A log-linear equation has been chosen because it better fits to the data than a linear

regression. The error σ is defined as the exp of the standard deviation of ln(ξ0ι) to the ln of

the regression, as follows:

∑=

++−−

−=

n

i i

iii H

Lf

n 1

2

00 11.039.024.0)ln(1

1)ln( ξσ (2)

A similar result was obtained from same kind of survey in the city of Nice, where

sediments are thinner (maximum thickness is about 100 m), and slightly less stiff (Vs

between 200 and 250 m/s at the surface).

The damping ratio (ξ0) is indeed reflecting the energy loss of the structure over one

vibration cycle. This loss of energy is generally assumed in dynamic analysis to be mainly

due to the structural damping, which is generally not considered, at least in every day’s

practice and in the vast majority of construction codes, as frequency dependent. However,

3

another origin for the energy loss during the vibration of the structure comes from the back-

radiation of waves into the soil, associated to soil-structure interaction (Guéguen 2000). This

phenomenon is frequency dependent and at least partly explain our observations: we thus

checked this hypothesis with a simple numerical model.

(a)

0 2 4 6 8

100

101

102

Frequency (Hz)

Dam

ping

Rat

io (

%)

(b)

0 2 4 6 8

100

101

102

Frequency (Hz)

Dam

ping

Rat

io (

%)

(c)

0 1 2 3

100

101

102

Aspect ratio (L/H)

Dam

ping

Rat

io (

%)

(d)

0 1 2 3

100

101

102

Aspect ratio (L/H)

Dam

ping

Rat

io (

%)

Figure 1. Observations from Ambient vibrations data (Grenoble data set). Damping (ξ0) versus frequency (f0) (a) for the Grenoble data set, (b) following the regression of equation (1), which depend on frequency (f0) and aspect ratio (L/H) of buildings. The vertical lines are the standard error (σ). Damping (ξ0) versus aspect ratio (L/H) (c) for the Grenoble data set, (d) following the regression of equation (1), which depend on frequency (f0) and aspect ratio (L/H) of buildings. The vertical lines are the standard error (σ).

MODELLING

We used a single degree of freedom (SDOF) structural model accounting for soil

structure interaction (and radiation damping) through impedance functions estimated with the

cone model proposed by (Wolf 1994). This model, depicted in Figure 2, allows to derive the

impulse response of the whole [soil+structure] system, and thus their fundamental frequency

4

and damping values through the logarithmic decrement method (Clough and Penzien 1993).

This simple model has been applied to the set of Grenoble buildings taking into account their

actual size (height H, horizontal dimension L), and the soil mechanical properties. Figure 3

shows that a rather satisfactory agreement (standard error (σ) of 1.84) exists between the

model results and the observations: in particular, the computed damping exhibits a clear trend

to increase with frequency (corresponding to a more efficient soil-structure interaction and

therefore higher radiative damping, for stiffer buildings), and also some trend to increase

with the aspect ratio (although the scatter is large). We therefore infer that one possible

explanation for this frequency dependent damping is the soil-structure interaction.

Figure 2. The 1 DOF oscillator with soil-structure interaction.

0 1 2 3

100

101

Aspect ratio (L/H)

Sys

tem

Dam

ping

Rat

io (

%)

0 2 4 6 8

100

101

System Frequency (Hz)

Sys

tem

Dam

ping

Rat

io (

%)

Figure 3. Comparison of observed data and numerical simulation. Triangles: observed data, circles; numerical simulation.

5

CONSEQUENCES

Obviously, the damping values derived under ambient vibrations cannot be extrapolated

directly to the damping values under strong shaking: a lot of non-linear material degradation

phenomena occur in both the structure and the soil, which should most generally increase the

damping values of the whole [soil+structure] system at large strains. However, one may

consider that the frequency values derived from ambient vibration recordings are an upper

bound for the actual frequency values under stronger shaking, while, simultaneously, the

ambient vibration damping values are a lower bound for the actual damping for strong

motion.

Therefore, as the usual design practice is to consider one "standard" damping value,

generally associated only with the construction material (RC, steel, masonry, wood, ...)

and/or the structural system (frame, shear wall, ...), and never with the building height and

frequency, we propose that the damping is most generally underestimated for stiff structures

resting on soft or medium-soft soils. Therefore, their design is probably conservative, at least

more conservative than the design of taller buildings having lower fundamental frequencies.

As an example, Figure 4 is showing the design spectra corrected for the minimum damping

value (as measured from ambient vibration recordings), for the Grenoble area and thick soils

with medium stiffness (site category S3): the design spectra is modified only beyond 4 Hz,

since, according to equation (1), the damping value exceeds 4 % (the standard recommended

value for RC structures) for frequencies larger than 4 Hz. One may see that, at 10 Hz, the

response spectrum ordinate corresponding to the actual damping value is 56 % less than the

design spectrum.

6

10−1

100

101

0

0.5

1

1.5

2

2.5

3

Frequency (Hz)

Nor

mel

ized

acc

eler

atio

n

4

Figure 4. Consequences of the soil structure interaction on the design spectra. The black line represent the French design spectra for a S3 site category (Grenoble) and a damping ratio of 4 % (reinforced concrete structures). The dotted line represent the modification of the French design spectra by using the proposed damping correction of equation (1) if the corrected damping is greater than 4 %.

CONCLUSION

Estimation of 26 RC buildings modal frequencies and damping ratio from ambient

vibration recordings shows that their damping ratio is increasing with the structure modal

frequency, to the contrary of what is usually used in seismic codes. This dependency can be

explained by soil-structure interaction with radiation damping due to the back-radiation of

waves in the soil by structures. As our observations comes from ambient vibrations, the

damping values are a lower bound for the actual damping for strong motion. By introducing

our observed damping dependence to frequency in the French code it is shown that seismic

forces are overestimated in the code for high frequency structures (tall structures, f0 > 4 Hz)

at least for those that are founded on soft soil.

REFERENCES

T.K. Caughey and H.J. Stumpf, 1993. Transient response of a dynamic system under random

excitation. Journal of Applied Mechanics, pages 563–566, 1961.

R.W. Clough and J. Penzien, 1993. Dynamics of structures. McGraw-Hill,.

C. Cornou, 2002. Traitement d’antenne et imagerie sismique dans l’agglomération grenobloise (Alpes

françaises) : implication pour les effets de site. PhD thesis, University of Grenoble, France.

7

M.N. Farsi, 1996. Identification des structures de génie civil à partir de leurs réponses vibratoires.

PhD thesis, University of Grenoble, France.

P. Guéguen, 2000. Interaction sismique entre le sol et le bâti : de l’interaction Sol-Structure à

l’Interaction Site-Ville. PhD thesis, University of Grenoble, France.

S.R. Ibrahim, J.C. Asmussen, and R. Brincker, 1998. Vector triggering random decrement for high

identification accuracy. Journal of Vibration and Acoustics, 120: 970–975.

A.P. Jeary, 1986. Damping in tall buildings - a mechanism and a predictor. Earthquake Engineering

and Structural Dynamics, 14: 733–750.

S. Lagomarsino, 1993. Forecast models for damping and vibration periods of buildings. Journal of

Wind Engineering and Industrial Aerodynamics, 59: 131–157.

Q.S. Li, K. Yang, N. Zhang, C.K. Wong, and A.P. Jeary, 2003. Field measurments of amplitude-

dependant damping in a 79-storey tall building and its effects on the structural dynamic

responses. The Structural Design of Tall Buildings, 11: 129–153.

J.K. Vandiver, A.B. Dunwoody, R.B. Campbell, and M.F. Cook, 1982. A mathematical basis for the

random decrement vibration signature analysis technique. Journal of Mechanical Design, 104:

307–313.

J.P. Wolf, 1994. Foundation vibration analysis using simple physical models. PTR Prentice Hall,

Englewood Cliff, USA.

1

Effects of Soil-Structure Interaction at an Earthquake Observation Station Identified by Microtremor Measurement

Toshiro Maedaa)

For the 2000 Tottori-ken-seibu earthquake (Mj7.3), strong horizontal motion

more than 900gal was recorded at the KiK-net Hino station. We have done micro-

tremor observation at and around the station to find significant soil-structure

interaction effects around 8Hz for weak motion at the station floor. Then, a soil

coupled structure model for the station at a small strain level is constructed to

simulate transfer functions of the station floor to the free surface. Finally, we

evaluate horizontal motion at the ground surface during main shock by

eliminating the interaction effects with equivalent linear soil properties to indicate

that the interaction effects were not significant for strong motion during main

shock because of large damping due to soil hysteresis.

INTRODUCTION

For the 2000 Tottori-ken-seibu earthquake (Mj7.3), strong horizontal motion more than

900gal was recorded at the KiK-net Hino station. Several studies, e.g. Nagano et al. (2001),

Higashi and Abe (2002), and etc., tried to obtain reasonable bedrock motion with horizontally

layered models for aftershocks, as well as for the main shock, simulating vertical array

transfer functions of the station floor to GL-100m by the genetic algorithm; however, none of

them seemed successful to simulate the transfer function from 5 Hz to 10 Hz for aftershocks.

Speculating that the recorded acceleration could be different from the free-surface motion

because of soil-structure interaction of a station, we carried out simultaneous observations of

micro-tremor at the station terrace and nearby ground surface. We found that the motion at

the terrace was amplified around 8 Hz to the ground surface for micro-tremor and weak

motion of a small earthquake due to the soil-structure interaction (Hibino et al. 2003). These

soil-coupled dynamic characteristics were later identified by free vibration excited by

a) Dept. of Architecture, Waseda Univ., 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, JAPAN.


2

hammering at the station structure (Yoshimura et al. 2003). We also carried out micro-tremor

array observations for Rayleigh wave dispersion curves and found that shear wave velocity

just beneath the ground surface must be less than those of PS logging data (Maeda et al.

2003), which is in accordance with aforementioned studies simulating the vertical array

transfer functions.

In this paper, we will simulate the transfer functions of the station terrace to the nearby

ground surface with a soil-coupled structure model for the station, i.e. a rigid structure model

supported by horizontally layered soil model. Then, we compute the horizontal motion at the

free surface by eliminating the interaction effects from the record at the station floor during

the main shock with equivalent linear soil properties, observing that the interaction effects

were not significant for strong motion during main shock because of large damping due to

soil hysteresis.

STRUCTURE AND SITE OF HINO STATION

KIK-NET HINO STATION

KiK-net HINO station (NIED) is located at the lakeside in the mountainous area of the

western Japan. The station structure is one-story reinforced concrete building of 3.15m high

and 2.2m by 3.2m in plan, we designate horizontal axis of X (N53E) parallel to the longer

wall and Y (N37W) parallel to the shorter wall as shown in Fig. 1.

TERRACE

ELEVATI ON

31502450

NE

X

Y

PLAN

Ki k- netSei smogr aph

3200

2200

37deg.

2200

Figure 1. KiK-net Hino station.

3

The station has two sets of seismographs on the floor and at GL-100m, both of which

measure NS, EW, and UD components. Surface geology shows that the station sits on deposit

next to rock boundary, and PS logging data reveals stiff soil profile down to GL-100m, with

Vs=210m/sec for a top layer of 11 m thick classified as gravel underlain by granite as shown

in Fig. 2.

0

20

40

60

80

100

120

0 1000 2000 3000

[m/s]

dept

h[m

]

VpVs

gravel

granite

Figure 2. PS logging data at KiK-net Hino station.

TRANSFER FUNCTIONS TO GL-100M

Nagano et al. (2001) tried to evaluate bedrock motion with one-dimensional equivalent

linear soil models, which were constructed by simulating vertical array transfer function for a

main shock and aftershocks with GA, the genetic algorithm. The Vs structure of their model

for aftershocks, shown in Fig. 3, scarcely altered Vs of PS logging, exhibiting lower 1st

frequency and less amplitude around 6Hz compared to the averaged transfer function for four

aftershocks used in Nagano et al. (2001) as shown in Fig. 4. The lower evaluated 1st

frequency was attributed to horizontal layer modeling applied for the complex geology.

Higashi and Abe (2002) also constructed one-dimensional model with GA incorporating with

reflection survey data to put bedrock at GL-84m of about three times of Vs as PS logging

data as shown in Fig. 3, where damping factor was not explicitly described. The 1st frequency

for aftershocks was simulated well by Vs structure of Higashi and Abe with damping factor

of Nagano et al. assigned; however, the second frequency was higher and amplitude around

6Hz were underestimated as shown in Fig. 4.

4

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500 3000

[m/s]

dept

h[m

]

Nagano et al. Higashi and Abe

Figure 3. Shear wave velocity structures proposed by Nagano et al. (2001) and Higashi and Abe (2002).

0 5 10 15 20 1e-001

1e+000

1e+001

1e+002

Average for aftershocks

Higashi and Abe

Nagano et al.

Figure 4. Vertical array transfer functions of Vs structures proposed by Nagano et al. (2001) and Higashi and Abe (2002); aftershocks used for average transfer function are same as those in Nagano et al.; damping factors in Nagano et al. are applied for Vs structures of Higashi and Abe for this transfer function.

MICRO TREMOR OBSERVATION AND SIMULATION

ARRAY OBSERVATION AND DISPERSION CURVES

We carried out micro-tremor array observation near the station for dispersion curves of

Rayleigh wave phase velocities. Three circular arrays with different radii of 3m, 10m, and

20m comprise four three-component seismographs, one at the center and other three at the

circumference as shown in Fig.5. Those seismographs are over-damped velocity meter with

sensitivity of 1V/gal, sampling period of 0.005 sec., and low-pass filtered at 50 Hz. We have

5

applied the SPAC method (Aki 1957) on vertical components to obtain dispersion curves

shown in Fig. 6.

Array

Hino station

Figure 5. Array configurations (r=20m).

0

200

400

600

800

1000

0 10 20 30frequency[Hz]

[m/s

]

PSHigashi & Aber=3mr=10mr=20m

Figure 6. Dispersion curves.

Those dispersion curves are compared for Rayleigh wave fundamental mode computed

by the generalized transfer and reflection matrix method proposed by Luco and Apsel (1983).

Fig.6 shows that the top layer should have smaller Vs than PS logging data of 210m/s.

6

SIMULTANEOUS OBSERVATION

We speculated a possibility that acceleration records obtained on the floor were affected

by dynamic interaction, and we simultaneously measured micro-tremor at the station terrace

and the ground surface at several meters from the station. Transfer functions of the floor to

the ground surface are evaluated for X- and Y-components shown in Fig. 7. X-component

parallel to the longer wall shows a peak of 9Hz and Y-component to the shorter wall 8Hz.

Since Y-component of the transfer function to the ground surface looks simpler and vertical

component also shows a peak at 8Hz, we simulate Y-component in the following.

0 5 10 15 20 25 30 35 40 45 50 1e-002

1e-001

1e+000

1e+001

1e+002

ear t hquake

mi cr o- t r emor

f r equency[ Hz]

0 5 10 15 20 25 30 35 40 45 50 1e-002

1e-001

1e+000

1e+001

1e+002

ear t hquake

mi cr o- t r emor

f r equency[ Hz]

Figure 7. Transfer functions of station terrace to the ground surface, (upper panel) X-component parallel to the longer wall and (lower panel) Y-component parallel to the shorter wall.

7

Ground motion for a small earthquake of M3.9 in this region was obtained during micro

tremor measurement. Acceleration waveform low-pass filtered at 20Hz is shown in Fig.8.

Comparison of major part of the acceleration shows remarkable predominance of 8Hz to 9

Hz at the terrace as shown in Fig. 9, and transfer functions have similar properties observed

for micro tremor as shown in Fig.7. Thus, transfer functions of the station terrace to the

ground surface for micro tremor can be used to study soil-structure interaction for weak

motion during earthquakes.

0 10 20 30 40 50 -3.45

0.42

4.30

0 10 20 30 40 50 -3.26

0.06

3.38

X t er r ace

X GL

[ gal ]

0 10 20 30 40 50 -1.73

-0.06

1.62

0 10 20 30 40 50 -2.08

-0.11

1.85

Y t er r ace

Y GL

[ gal ]

Figure 8. Weak motion of small earthquake observed during micro-tremor measurement (upper two panels) X-component parallel to the longer wall and (lower two panels) Y-component parallel to the shorter wall.

8

8 9 10 11 12 13 -3.45

0.42

4.30

8 9 10 11 12 13 -3.26

0.06

3.38

X t er r ace

X GL

[ gal ]

8 9 10 11 12 13 -1.73

-0.06

1.62

8 9 10 11 12 13 -2.08

-0.11

1.85

Y t er r ace

Y GL

[ gal ]

Figure 9. Major part of weak motion of small earthquake, (upper two panels) X-component parallel to the longer wall and (lower two panels) Y-component parallel to the shorter wall.

MODELING OF THE STATION

The station is made of reinforced concrete, yet detailed specifications are not known. We

assume density of 2.4t/m3, projected roof thickness 0.3m for horizontal area, wall thickness

of 0.2m, and foundation thickness of 0.5m, 0.7m, and 1.0m. The superstructure is modeled by

two lumped mass of 7.6t at GL+2.8m and 11.0t, 14.4t, and 19.5t according to foundation

thickness at GL-0m. Preceding to the FEM analysis, we evaluated equivalent semi-infinite

soil model by specifying natural frequency of soil-coupled rigid structure of 8 Hz to ( )πω 2/1

shown in Eq. (1) from Tajimi (1976) with static stiffness of Eq. (2) for a square foundation

evaluated by average displacement from AIJ (1996).

−

++++=

20

20

2

20

2

20

20

20

2

20

20

222

221 411

21

//

ie

is

ie

is

ie

H

H ∓ωωωω

, (1)

2,1ω : 1st and 2nd soil-coupled natural frequencies,

9

mK HH /2 =ω , HR KKe /20 = , ,/2

0 mIi G=

where m stands for total mass, GI for inertia moment with regard to the gravity center, HK

for horizontal foundation stiffness, RK for rocking foundation stiffness, s for height of the

gravity center.

ν

π−

=22345.1 GBK H , (2a)

( )νπ−

=12

264.23GBK R , (2a)

where 2sVG ρ= stands for rigidity with 3/7.1 mt=ρ , ν for horizontal foundation stiffness

set equal to 0.4, B for half width of equivalent square foundation set equal to 1.3m. Fig. 10

shows that equivalent stiffness should correspond to the shear wave velocity of about

100m/sec for 8Hz peak, disregarding frequency dependence of soil impedances.

0

5

10

1520

25

30

35

50 100 150 200Vs [m/ s]

frequ

ency

[Hz]

Figure 10. Axisymmetric FE model for simulation.

Soil is modeled by axisymmetric FEM valid up to 20 Hz with an energy transmitting

boundary at the circumference and viscous boundary at the bottom, as shown in Fig. 11.

Since the top layer of the soil should have less shear wave velocity than that of PS logging

data, 210m/s, implied also from the preliminary study with static foundation stiffness, we

consult the shear wave velocity structure proposed by Higashi and Abe (2002) for soil-

structure interaction simulation, of which the top layer has Vs of 127m/s as shown in Table 1.

1st frequency

2nd frequency

10

Energytransmittingboundary

Viscousboundary

SeismographGL-100m

structureH-2.8mR=1.5m

z

r

soillayers

1

6

5

2

4

3

115m

R=4m

1

6

5

2

4

3

Figure 11. Axisymmetric FE model for simulation.

Table 1. Soil model parameters for soil-structure interaction

No.

Depth [m]

Thickness [m]

Density [t/m3]

Poisson ratio

Vs_init [m/s]

h_init Vs_eq [m/s]

h_eq

1 4 4 1.7 0.4 127 0.01 64 0.20 2 11 7 1.7 0.4 211 0.01 105 0.21 3 21 10 1.9 0.4 382 0.01 266 0.15 4 43 22 1.9 0.4 551 0.01 418 0.12 5 85 42 2.2 0.4 943 0.01 822 0.07 6 115 30 2.2 0.4 2487 0.01 2466 0.02

SIMULATION OF TRANSFER FUNCTION TO THE GROUND SURFACE

Fig. 12 compares amplitudes of the transfer functions evaluated by micro-tremor and

computed by FEM with different foundation thicknesses. With Vs structure proposed by

Higashi and Abe, Y-component of the transfer function of the terrace to the ground surface is

simulated well by the structure model with foundation of 0.7m thick, exhibiting a peak at

8Hz with amplification of around 2 and a trough at 9.5Hz with de-amplification of around 1/5.

11

Although the structure model is roughly assumed and we do not adhere to the foundation

thickness of 0.7m, we will use this in the following for a case strudy.

0 5 10 15 20 1e-002

1e-001

1e+000

1e+001

frequency[Hz]

Micro-tremo

FEM

0.5m0.7m1.0m

Figure 12. Comparison of transfer functions of the floor to the ground surface for weak motion.

GROUND MOTION EVALUATED FROM THE RECORDS

SIMULATION OF WEAK MOTION

We evaluate the ground motion from the records obtained at the terrace and compare that

with the records obtained at the ground surface for weak motion of a small earthquake.

Fourier amplitudes smoothed by the Parzen window of 0.2Hz are compared in Fig. 13, which

shows that dominated components around 8Hz at the terrace is removed, but higher

frequency components are not recovered to the observed level. In Fig. 14, acceleration wave

form shows less dominated components of 8Hz as compared with Fig. 8 and Fig. 9.

12

0 5 10 15 20 1e-002

1e-001

1e+000

1e+001

frequency[Hz]

Terrace Ycomp.

GL Ycomp.

0 5 10 15 20 1e-002

1e-001

1e+000

1e+001

frequency[Hz]

GL Ycomp.

GL simulated Ycomp.

Figure 13. Fourier amplitudes of weak motion of a small earthquake (Y-component), (upper panel) Records on the terrace and the ground surface and (lower panel) Record and simulation on the ground.

0 10 20 30 40 50 -1.34

0.08

1.51

[ sec]

[ gal ]

8 9 10 11 12 13 -1.34

0.08

1.51

[ sec]

[ gal ]

Figure 14. Simulated acceleration of weak motion at the ground surface (Y-component), (upper panel) Whole waveform and (lower panel) Major part of waveform.

13

SIMULATION OF STRONG MOTION

We evaluate Vs and damping factors in equivalent linear analysis by specifying

acceleration records at GL-100m of the model shown in Table 1. G-γ and h-γ curves shown

in Fig. 15, which are proposed for sand in Japanese national codes for buildings, are used for

layers other than bedrock. We take average of converged Vs and damping factors over sub

layers in each layer to define layer parameters as shown in Table 1. With these soil

parameters, transfer function of the floor to the ground surface during the main shock is

evaluated by axisymmetric FEM up to 20Hz.

0

0.2

0.4

0.6

0.8

1

0.00001 0.0001 0.001 0.01 0.1shear strain[γ]

G/G0-γ

h-γ

Figure 15. G/G0-γ and h-γ curves for equivalent linear model.

Comparison of impedance functions for strong motion with those for weak motion shown

in Fig. 16 exhibits remarkable decrease in real part and comparable imaginary part implying

dominated damping effect. The evaluated transfer function exhibits a wide and smooth peak

around 3Hz with amplitude a little larger than unity as shown in Fig. 17.

The acceleration record obtained at the floor is divided by this transfer function to give

acceleration time history shown in Fig.18 via inverse FFT. Comparison of the computed

motion at the ground surface and the records on the floor low-pass filtered at 20 Hz shows

little difference due to soil-structure interaction. This insignificant effect is attributable to

large damping factor around 0.2 evaluated by equivalent linear analysis. Vibration caused by

inertial soil-structure interaction should be died out quickly by large hysteretic energy loss in

the soil.

14

Figure 16. Comparison of impedance functions for weak and strong motion, (upper left) real part of horizontal impedance, (lower left) imaginary part of horizontal impedance, (upper right) real part of rocking impedance, (lower right) imaginary part of rocking impedance.

0 5 10 15 20 1e-002

1e-001

1e+000

1e+001

frequency[Hz]

Strong motionsimulation

Micro tremor Ycomp Weak motionsimultaion

Figure 17. Comparison of transfer functions to the ground surface for the main shock.

15

0 10 20 30 40 50 -555.14

-29.71

495.73recorded on the floor

0 10 20 30 40 50 -585.96

-74.63

436.71 si mul at ed on t he gr ound

[ sec]

[ gal ]

Figure 18. Strong motion records and evaluated ground motion during the main shock, (upper panel) Record in the station and (lower panel) Simulation on the ground surface.

CONCLUSIONS

Micro-tremor measurement was carried out to find soil-structure interaction effects on the

record of KiK-net Hino station during the 2000 Tottori-ken-seibu earthquake. Simultaneous

observation at the station terrace and nearby ground surface shows significant amplification

at the terrace around 8Hz revealing the interaction effects for micro-tremor and weak motion

of a small earthquake. We have simulated transfer function of the terrace to the ground

surface by axisymmetric FEM with a rigid structure model supported by horizontally layered

soil model to show a good agreement consulting soil parameters proposed for vertical array

simulation. Then we have evaluated acceleration waveform of the main shock on the ground

surface from the record obtained inside the station by adapting equivalent linear soil

parameters to the FE model to depict that soil-structure interaction effects on the record of

the main shock was insignificant due to large damping representing large plastic deformation.

We wish to express our gratitude to National Research Institute for Earth Science and

Disaster Prevention for allowing us to use KiK-net data.

REFERENCES

Architectural Institute of Japan (AIJ), 1996. “An Introduction to Dynamic Soil-Structural Interaction”,

Architectural Institute of Japan, 342 pp. (in Japanese).

Aki K., 1957. Space and Time Spectra of Stationary Stochastic Waves, with Special Reference to

Microtremors, Bulletin of the Earthquake Research Institute, Vol. 35, pp.415–457.

Hibino H., Maeda T., Yoshimura C., Kurauchi N., and Uchiyama Y., 2003. Estimation of bedrock

ground motion during 2000 Tottori-ken-seibu earthquake at KiK-net Hino considering effect of

observation house. Part 1 Effect of observation house obtained from microtremor and earthquake

16

observation, Summaries of Technical Papers of Annual Meeting Architectural Institute of JAPAN,

B-2, pp.165-166 (in Japanese).

Higashi S. and Abe S., 2002. Estimation of bedrock motions at KiK-net Hino site during the 2000

Tottori-ken Seibu Earthquake based on the results of seismic reflection survey, Proceedings of the

11th Japan Earthquake Engineering Symposium, pp. 461-464 (in Japanese).

Luco J. E. and Apsel R., 1983. On the Green’s Functions for a Layered Half-space Part 1, Bulletin of

the Seismological Society of America, Vol. 73(4), pp.909–929.

Maeda T., Kurauchi N., Hibino H., Yoshimura C., and Uchiyama Y., 2003. Phase velocity dispersion

curves around the Tottori-Hino KiK-net station by micro-tremor array observation, Programme

and abstracts, The seismological society of Japan 2003, Fall meeting, B043(in Japanese).

Nagano M., Kato K., and Takemura M., 2001. Estimation of bedrock motions near seismic fault

during the 2000 Tottori-ken Seibu Earthquake, J. Struct. Constr. Eng., AIJ, 2001, No.550, pp. 39-

46 (in Japanese).

National Research Institute for Earth Science and Disaster Prevention (NIED),

http://www.kik.bosai.go.jp/kik/index_en.shtml.

Tajimi, H., 1976. “Introduction to Structural Dynamics”, Corona Publishing Co., Ltd., 81 pp. (in

Japanese).

Yoshimura C., Hibino H., Uchiyama Y., Maeda T., Kurauchi N., and Aoi S., 2003. Vibration

characteristics of the observation house at KiK-net Hino, Abstracts 2003 Japan Earth and

Planetary Science Joint Meeting, (in Japanese).

1

A Study on Dynamic Soil-structure Interaction Effect Based on Microtremor Measurement of Building and Surrounding Ground Surface

Masanori Iiba a), Morimasa Watakabe b), Atsushi Fujiic), Shin Koyama a), Shigeki Sakai d) and Koichi Morita e)

Design and evaluation of building during earthquake is moved to be a

performance based one. For the performance based design, behaviors of buildings

are clarified more precisely based on data of earthquake motion observation. But

in general buildings, the earthquake motion observation is not popular, especially,

for purpose of soil structure interaction (SSI). Under a few points of

accelerometers, a detailed analysis for SSI phenomena is not easy and many

assumptions are needed. Here, the SSI effects of building are investigated based

on a microtremor measurement. The instruments were set in the building and on

the ground to evaluate the sway, rocking and torsional vibrations. The building is

7-storied residential one with flamed structure in longitudinal direction and pre-

cast walled structure in transverse direction. Through transfer functions of

buildings, predominant frequencies under sway, rocking mode and those of based-

fixed condition are calculated. The SSI effect is remarkable in transverse direction

due to predominant rocking mode. Also based on the random decrement

technique, the damping factor of buildings is obtained. It is founded that the

damping factors are around 5 to 6% under the microtremor level.

INTRODUCTION

Inertial forces of superstructure, that is, base shear, inertial forces of embedment and

overturning moments will be transferred to supported grounds (through piles when pile

foundations). When the supported grounds are soft, the base fixed condition is not satisfied.

a) National Institute for Land and Infrastructure Management, 1, Tatehara, Tsukuba, Ibaraki, 305-0802, Japan b) Toda Corporation, 8-5-34, Akasaka, Minato-ku, Tokyo, 107-0052, Japan c) Konoike Construction, 1-20-1, Sakura, Tsukuba, Ibaraki, 305-0035, Japan d) Hazama Corporation, 515-1, Karima, Tsukuba, Ibaraki, 305-0822. Japan e) Building Research Institute, 1, Tatehara, Tsukuba, Ibaraki, 305-0802, Japan


2

The phenomena of the displacement and rocking angle of foundations by the base shear

and overturning moment, so-called “soil structure interaction (SSI)” occur. The phenomena

are the “inertial soil structure interaction”. On the other hand, the effect of SSI related to

seismic input motions to the buildings is called the “kinematic soil structure interaction”. As

a result of the horizontal and rocking motions due to the SSI, characteristics of superstructure

are changed as follows;

1) Elongation of natural period (compared with base fixed condition)

2) Change of damping factor (compared with base fixed condition)

The Building Standard Law and its related enforcement and notices were revised for the

direction to the performance-based design from 1998 in Japan. The calculation method of

response and limit strength was provided for checking serviceability and safety of buildings.

The calculation procedure is based on the response spectrum method. The acceleration

response spectrum, and equivalent period and damping factor of 1st mode have to be

evaluated [Midorikawa, et al., 2000]. The amplified characteristics of surface ground and SSI

effects should be considered. A simplified method for incorporating SSI effects is proposed

in the calculation [Iiba, 2001].

In order to complete performance-based design, it is important that not only structural

characteristics and seismic behaviors of buildings but characteristics of earthquake motions

to buildings have to be made clear. Especially, the SSI and earthquake motions are influenced

by characteristics of surface ground. The evaluation including ground characteristics is

necessary.

The paper focuses fundamental predominant frequency and damping factor of residential

buildings through microtremor measurements to estimate the fundamental characteristics of

the SSI phenomena. The effect of SSI on a transverse (span) direction of the residential

buildings is remarkable due to many continuous walls in the direction. However, earthquake

motion observations of residential buildings are not popularly conducted. The microtremor

measurement is effective to evaluate the SSI effect on these buildings [Yagi, et al., 2002].

Using data measured in buildings and surrounding ground surface, transfer functions of

the systems are calculated which including characteristics of sway, rocking and building

modes. Based on the transfer functions, predominant frequencies of sway, rocking modes and

3

those of base fixed condition are compared. And the damping factors of the buildings are

evaluated through the random decrement method (RDM) [Tamura, et al., 1993].

OUTLINES OF BUILDINGS AND GROUND

A plan at ordinary floor and a section in the transverse direction of the buildings are

drawn in Fig. 1. A bird-eye view of the building is presented in Photo 1. The buildings,

which have 7-storied residential ones with central corridor at longitudinal direction, are

constructed in a central area of

Tsukuba, Japan. There are three and

nine spans in transverse and

longitudinal directions, respectively.

A ratio of transverse to

longitudinal widths is 1:3.2 and

ratios of width to height in both

directions are 0.46 and 1.47.

The buildings are composed of

girders of reinforced concrete (RC)

structure, columns of steel RC

structure and floors and walls of

pre-cast RC boards. The buildings

are supported by the individual

foundation with pre-stressed

concrete piles. The site map is

illustrated in Fig. 2. The same

buildings called A- and B-buildings

are constructed with distance of about

70 m between them. There is a main

load on the north side and a load on

the west.

The soil condition at the site is

drawn in Fig. 3. There is a loam layer

whose N values are about 5 within

Plan

Section

4,600 4,600 4,600 4,600 4,750 4,600 4,600 4,600 4,600

540

02

100

540

0

RF

7F

6F

5F

4F

3F

2F

1F270

02

775

270

270

02

702

702

700

Sensors Horizontal

Vertical

Fig. 1 Plan and section of building measured in microtremor, including the positions of velocity-type sensors in building and surrounding ground surface

Photo 1 Bird eye view of building

4

6.6 m in depth from ground surface. The N values of following layers increase to about 20 to

40. The sandy layers between 17 to 27 m in depth have N value more than 30. The sandy and

clayey layers are laminated in 28 to 41 m and in deeper depth gravel layers with more than 50

of N value can be found.

OUTLINES OF MEASUREMENT

Sources of the vibration of buildings are in the following;

a) Microtremor

The microtremors in the buildings and on the ground surface are measured. Periods of

measurement are 600 or 500 s and 7 or 8 sets of these periods are recorded. The interval

of records is 0.005 s.

b) Oscillation by human bodies

The forced vibration test is carried out. 6 to 7 persons exert their forces to columns in the

center at 7th floor. The forced vibration with near 1st predominant frequency and in 10 s

of period is repeated at several times.

Depth(m)

Soiltype Mark

56.6

10

11.913.0 Clay

15

20

25

27.629.1 Clay 30

34.035.4 Clay 3536.1 Sand

40

41.5

45

50.4 50

Sand

LoamClay

Sand

SandwithClay

ClaywithSand

Gravel

0 10 20 30 40 50

Ｎ Value

Fig. 3 Ground condition with soil types and standard penetration values (N-values)

0 10 20 30 40 50m

A- Bui l di ng

Main Road

B- Bui l di ng

N

11- St or y Bui l di ng

Fig. 2 Site situation of two building, which are the same

geometrical and structural conditions

5

Measuring points and their marks in transverse and longitudinal directions are shown in

Fig. 4. Three horizontal and two vertical sensors on the roof and 1st floor, one horizontal one

on the 4th floor are set in the buildings. Three horizontal sensors are installed on the ground

surface with 13m at both sides and 26m at one side far from the building. The sensor

arrangements are the same in both buildings.

Types of sensors are different between buildings. Velocity transducers with servo type

(VSE-15D, Tokyo Sokusin Co. Ltd.) and those with moving-coil type (Sindo Giken Co. Ltd.)

are used in the A- and B-buildings, respectively. The unit of measured data is velocity.

#01#04

RF#02

#05

#03

4F#06

#07 #12#10

1F#08

#11#09

Ｙ（西）

　Ｘ（北） #13Ｚ

#14

R8HSR8VW

R8HCR8VE

R8HN

4FHC

1FHS

1FVE1FHC

1FVWG1HE

1FHN

G2HE

G3HE

13.0m

19.2

5m

#01#04

RF#02

#05

#03

4F#06

#07 #12#10

1F#08

#11#09

Ｙ（西） #13

Ｚ　Ｘ（北）#14

R8HW

R8VS

R8HC

R8VS

R8HE

4CX

1FHW1FVS

1FHC1FVN*1

G1X

1FHE

G2HE

G3X

19.2

5m

37.4m*1

(21.0+16.4m)

a) Transverse direction b) Longitudinal direction Fig. 4 Locations and marks of sensors in building and ground surfaces in longitudinal and transverse

directions

EFFECTS OF SWAY AND ROCKING ON VIBRATION CHARACTERISTICS

In order to investigate effects of the SSI on the vibration characteristics of buildings,

relationships between input and response are clarified using the simplest vibration model

with one mass, sway and rocking stiffness. Based on the microtremor measurement data,

predominant frequencies are evaluated in transfer functions of response to input motion. The

comparison of predominant frequencies between longitudinal and transverse directions and

between two buildings is conducted.

Simple Sway and Rocking Model

The vibration system with surrounding ground is assumed to be the sway and rocking

model [Stewart, et al., 1998] shown in Fig. 5. Following systems are considered.

a) Sway and rocking model (SBR-system)

b) Rocking model (RB-system)

6

c) Building model with base fixed (B-system)

In each system, the relationship between input and response is presented in Table 1.

uf' uf''ug

ug + uf'ug

H･θ u

H

θRigid Foundation

without MassSurface Ground

Fig. 5 Definition among displacement at ground surface, sway and rocking displacements and building displacement

Table 1 Relationship between input and response based on displacements shown in Fig. 5

Input Output (Response)

1) SRB ug

2) RB ug + uf

3) B ug + uf + H･θ

ug + uf + H･θ + u

ug : Free Surface Ground Motionuf' : Foundation Input Motion

System

H : Height of Buildingθ : Rocking Angle at 1st Floor

uf '' : Swayuf : 1st Floor Motion Relative to Free Surface　 ( herein assumption to uf = uf' + uf'' )u : Top Response Relative to 1st Floor

Relationship between Input and Response in Measured Data

The measurement points and arranged data in buildings and on ground surface according to

relationships between input and response in Table 1 are expressed in Table 2. The

measurement points and marks are referred to information in Fig. 4. The arranged data are

calculated in time domain. In case that there are the plural data at the same levels, for

7

example, at the roof, averaged ones on the floor are used. The rocking angle at the 1st floor is

obtained by vertical data on the both ends of buildings. In the longitudinal direction, though it

is not clear that a rigid (uniform) rotation occurs, the displacement due to rocking is

considered.

Table 2 Measurement points and arranged data in buildings and on ground surface

Transverse Direction(A and B-building)

Longitudinal Direction(A-building)

Longitudinal Direction(B-building)

Output of SRB, RB, B ug+uf+Hθ+u (R8HC+(R8HN+R8HS)/2)/2

Input for SRB ug

Input for RB ug+uf (1FHC+(1FHN+1FHS)/2)/2

Input for B ug+uf+Hθ (1FHC+(1FHN+1FHS)/2)/2+H(1FVW-1FVE)/W

(1FHC+(1FHW+1FHE)/2)/2+H･1FVN/W1-H･1FVS/W2

(1FHC+(1FHW+1FHE)/2)/2+H(1FVN-1FVS)/W

Height : HRocking Span : W (W1+W2) 13.0m 37.4m

(21.0m+16.4m) 42.0m

(21.0m+21.0m)

Related Height andWidth

Input and Output for Analized System

(R8HC+(R8HW+R8HE)/2)/2

G2HE

(1FHC+(1FHW+1FHE)/2)/2

19.25m

Calculation of predominant frequency based on transfer function

Based on the relationships between input and response, transfer functions are calculated by

following equation.

)Sii()Sio()( ωωω =H (1)

where Sio and Sii are the cross spectrum of response and input and power spectrum of input

data, respectively. The real part of the transfer functions provides the amplitude of them. The

phase between response and input gives the phase difference of them.

The cross and power spectra are obtained through the Fourier spectrum converted from

8192 data of time history with interval of 0.005 s. The Fourier spectrum is calculated by

moving the first data with interval of 40 s. The overlapped duration is about 50 % of analyzed

one of the Fourier transform. All of the amplitudes of transfer functions obtained are

averaged. The average amplitude spectra of transfer functions are smoothed by Hanning

windows with eight times.

Predominant frequency of buildings

The example of time histories (10 s) of input and responses is drawn in Fig. 6. The data at

upper 4 axes are measured and another three ones are arranged.

8

Roof floor, Horizontal Data, 3-points

1st floor, Vertical Data, 2-points

1st floor, Horizontal Data, 3-points

Ground surface

ug+uf+Hθ+u and ug+uf

Hθ+u and Hθ

ug+uf+Hθ

a) Longitudinal direction

Roof floor, Horizontal Data, 3-points

1st floor, Vertical Data, 2-points

1st floor, Horizontal Data, 3-points

Ground surface, 1-point

ug+uf+Hθ+u and ug+uf

Hθ+u and Hθ

ug+uf+Hθ

b) Transverse direction

Fig. 6 Time histories of measured and arranged data

9

The time histories of horizontal data in the longitudinal direction at the same levels, that

is, roof and 1st floors are similar to each other, because of very nearly measured points. On

the other hand, in the transverse direction, a little difference of amplitude and phase are found

out. Based on the transfer functions of rotational vibrations, the horizontal data seem to

include torsional vibration of the buildings or phase difference of input motions. When the

horizontal amplitude in the transverse direction becomes large, the phases of vertical

vibrations at 1st floor are opposite and the rocking vibrations are observed. The amplitude

and phase have a good correspondence of time histories between at 1st (ug+uf) and roof floors

(ug+uf+Hθ +u). The data at 1st and roof floors have the relation between input and response

in the RB system. The phase difference becomes small with large amplitude of roof floor.

Compared between the data of relative response of roof to 1st floor (Hθ +u) and the data

rocking response (Hθ ), the effect of rocking vibration is remarkable and the amplitude of

rocking vibration is 50-90 %of that of relative response of roof to 1st floor in the transverse

direction.

The amplitude and phase difference spectra of the transfer functions with buildings and

their directions are shown in Fig. 7. The predominant frequencies obtained from amplitude

spectra are presented in Table 3. The amplitude spectra have simple one simple peak like a

transfer function of one-degree-of-freedom system. With comparison of amplitude at

predominant frequencies in three systems, there are the relations of SRB＞RB＞B-systems in

the transverse direction. On the other hand, the tendency is not so clear in the longitudinal

direction.

Table 3 Predominant frequencies of various systems and ratios to frequency of B system

System Direction Building SRB RB B S R

A-building 2.87 (0.70)

3.23 (0.78)

4.13 (1.00)

6.21 (1.50)

5.21 (1.26) Transverse

B-building 2.80 (0.68)

3.19 (0.77)

4.11 (1.00)

5.83 (1.42)

5.04 (1.22)

A-building 2.62 (0.78)

3.32 (0.99)

3.37 (1.00)

4.28 (1.27)

19.57 (5.81) Longitudinal

B-building 2.76 (0.75)

3.21 (0.87)

3.70 (1.00)

5.39 (1.46)

6.47 (1.75)

10

0123456789

101112

1 2 3 4 5 6 7 8Frequency(Hz)

Am

plitu

de

Ｓ

Ｒ

2.87Hz

3.24Hz

4.13Hz

A-buildingTransverse

-180

-135

-90

-45

0

45

90

135

180

1 2 3 4 5 6 7 8Frequency(Hz)

Phas

e D

elay

(deg

.)

ＳＲ

A-buildingTransverse

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8Frequency(Hz)

Am

plitu

de

Ｓ

Ｒ2.62Hz

3.37Hz

3.32Hz

A-buildingLongitudinal

-180

-135

-90

-45

0

45

90

135

180

1 2 3 4 5 6 7 8Frequency(Hz)

Phas

e D

elay

(deg

.)

ＳＲ

A-buildingLongitudinal

A-building

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8Frequency(Hz)

Am

plitu

de

ＳＲＢ

ＲＢ

Ｂ

B-buildingTransverse

2.80Hz

3.19Hz

4.11Hz

-180

-135

-90

-45

0

45

90

135

180

1 2 3 4 5 6 7 8Frequency(Hz)

Phas

e D

elay

(deg

.)

ＳＲＢＲＢＢ

B-buildingTransverse

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8Frequency(Hz)

Am

plitu

de

Ｓ

Ｒ

2.76Hz3.21Hz

3.70Hz

B-buildingLongitudinal

-180

-135

-90

-45

0

45

90

135

180

1 2 3 4 5 6 7 8Frequency(Hz)

Phas

e D

elay

(deg

.)

ＳＲＢＲＢＢ

B-buildingLongitudinal

B-building

Fig. 7 Transfer functions of SRB-, RB- and B-systems

11

The predominant frequencies of the 1st mode in different systems have the relation of

SRB＜RB＜B-systems in the transverse direction. In the longitudinal direction, the relation

of SRB ＜ RB ≒ B-systems or SRB ＜ RB ≦ B-systems is obtained. The predominant

frequencies for the sway (S) and rocking (R) systems shown in Table 3 are calculated by a

system with one mass and springs in series of sway, rocking and building itself. Based on

Table 3, the ratios of predominant frequencies of RB- and SRB-systems to those of B-system,

which is according to base fixed condition, are 0.77 – 0.78 and 0.68 – 0.70 in the transverse

direction. Compared with predominant frequencies of the S-, R-, B-systems, the frequencies

of B -system are smallest. However, since the predominant frequencies of the S-, R, B -

systems are similar, the effect of sway, rocking motion on the response of buildings are

remarkably large.

On the other hand, the ratios of predominant frequencies of RB- and SRB-systems to those

of B -system in the longitudinal direction are 0.87 – 0.99 and 0.75 – 0.78, respectively.

Compared with predominant frequencies of the S-, R- and B-systems, the frequencies of B -

system are smallest. In case of A-building, the predominant frequencies of the R- system are

quite large and this means there is very small rocking effect, that is, the rocking motion is

negligible. In the longitudinal direction, the effect of sway motion is remarkable.

The characteristics of two buildings except rocking motion in the longitudinal direction

are quite similar. When the rocking angles of the 1st floor are calculated, vertical data are

used. In the longitudinal direction, the distance between two vertical sensors is large and it is

necessary to evaluate whether the rocking motions will be estimated by two vertical sensors

and whether 1st floor is rigidly vibrating or not.

DAMPING FACTOR BASED ON RANDOM DECREMENT METHOD (RDM)

To obtain the damping factors of the buildings, the RDM is applied to the observed

microtremor data. Focused on the predominant frequency of fundamental vibration mode of

interaction system, the damping factors are calculated with two buildings and their directions.

To estimate the damping ratios of the buildings, there are methods of the 1/square root of 2,

the half power, curve fitting and phase gradient, as procedures based on data in frequency

domain. Here, using the data of time history, the damping factors under free vibration are

obtained based on the RDM.

12

Calculation Procedure by RDM

The observed data at the roof floor X(t) is assumed to be expressed to be sum of free

vibration D(t) and response due to forced vibration

R(t). Through superposing time histories which are

set to the maximum at time of zero, the response R(t)

gradually vanishes and the response D(t) remains

with superposition as shown in Fig. 8 [Tamura, 1993].

The superposed time histories ∑ )(tDi will be the

response of free vibration with the initial amplitude

∑Pi which is the sum of each random amplitude Pi

as expressed in the following;

))1(cos()exp()()( 02

0 ththPitDi ωω∑ ∑ −−= (2)

Where h is the damping factor and 0ω is fundamental

predominant frequency of the buildings.

The process to get the free vibration time histories

by RDM is shown in Fig. 9. The horizontal data

Fig. 8 Superposition of time histories

based on the RDM (refer to Tamura et al.)

Data of Microtremors

Treatment with Band-Pass Filter

Band Width of Band-Pass Filter2.0~4.0Hz

To use horizontal microtremors at the center at roof floor

Free Vibration（Damped Vibration）

Each Peak

t=0

Frequency

Overlapping each intervalfrom the peak for 5

seconds

Time

Time

Band-Pass Filter

Damping ratio was obtained by means of Least Squares Method

ａｅ－hω ｔ

ｆ0

( 6 data sets for each building )

Fourier Spectrum

To evaluate Natural Frequency f0 from Fourier spectra

Applying the Random Decrement Method

for 5 seconds

Time

Overlapping Each Section from Each Peak for 5 Seconds over the all data

Data of Microtremors

Treatment with Band-Pass Filter

Band Width of Band-Pass Filter2.0~4.0Hz

To use horizontal microtremors at the center at roof floor

Free Vibration（Damped Vibration）

Each Peak

t=0

Frequency

Overlapping each intervalfrom the peak for 5

seconds

TimeTime

TimeTime

Band-Pass Filter

Damping ratio was obtained by means of Least Squares Method

ａｅ－hω ｔ

ｆ0

( 6 data sets for each building )

Fourier Spectrum

To evaluate Natural Frequency f0 from Fourier spectra

Applying the Random Decrement Method

for 5 seconds

TimeTime

Overlapping Each Section from Each Peak for 5 Seconds over the all data

Fig. 9 Process to get the free vibration time histories by RDM

13

observed at the center of roof floor are used. The ensemble averages of the Fourier amplitude

spectra of the time histories with buildings and their directions are drawn in Fig. 10. When

the RDM is applied, the filtering with narrow frequency band called Butterworse type is

conducted.

0.0E+00

2.0E- 04

4.0E- 04

6.0E- 04

8.0E- 04

0.0 5.0 10.0 15.0Frequency (Hz)

Amp.

(kin

e*se

c)

301短辺M01

2.75Hz

0.0E+00

2.0E- 04

4.0E- 04

6.0E- 04

8.0E- 04

0.0 5.0 10.0 15.0Frequency (Hz)

Amp.

(kin

e*se

c)

303短辺M013.00Hz

0.0E+00

2.0E- 04

4.0E- 04

6.0E- 04

8.0E- 04

1.0E- 03

0.0 5.0 10.0 15.0Frequency (Hz)

Amp.

(kin

e*se

c)

2.80Hz301長辺M01

0.0E+00

2.0E- 04

4.0E- 04

6.0E- 04

8.0E- 04

0.0 5.0 10.0 15.0Frequency (Hz)

Amp.

(kin

e*se

c)

3.00Hz 303長辺M01

A-building

Transverse

A-bu ilding

Longitudinal

B-building

Transverse

B-building

Longitudinal

Fig. 10 Fourier amplitude spectra with buildings and their directions

A- buildingTransverse

M01

- 2.0

- 1.0

0.0

1.0

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time (sec)

Norm

alize

d am

plitu

de

B- buildingTransverse

M01

- 2.0

- 1.0

0.0

1.0

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time (sec)

Norm

alize

d am

plitu

de

A-building (Transverse) B-building (Transverse)

A- buildingLongitudinal

M01

- 2.0

- 1.0

0.0

1.0

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Time　(sec)

Norm

alize

d am

plitu

de

B- buildingLongitudinal

M01

- 2.0

- 1.0

0.0

1.0

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0時刻 (sec)

Norm

alize

d am

plitu

de

A-building (Longitudinal) B-building (Longitudinal)

Fig. 11 Free vibration responses by RDM and envelop curves by LSM

14

The predominant frequency of the velocity time histories is 2.75 to 3.0 Hz. The frequency

range of 2 to 4 Hz which includes the predominant frequency of buildings is kept. The

filtered spectra are converted to the time histories. After the times when maximum velocities

occur are set to be zero in time and the data of 5 seconds in period from that times are

superposed. The total measured records are used in the RDM, the number of superposition is

around 10,000 (refer to Table 4). The resulting time histories are normalized by the

amplitudes at time of zero and the damping factors are obtained, applied the least square

method (LSM) using 8 maximum data in time histories.

The results of free vibration response by the RDM and envelop curves by LSM with

buildings and their directions are shown in Fig. 11. The envelop curves show good

agreements with the free vibration response by the RDM. Table 4 summarizes whole results

of damping factors. The damping ratios are not so scattered. The average damping factors are

5.5 to 6.0 % and 6.5 to 6.9 %, in the transverse and longitudinal directions, respectively.

DAMPING FACTOR BASED ON HUMAN FORCED VIBRATION

The damping factors of the buildings are evaluated based on the data of free vibration due

to force vibration of building generated by human oscillator. The time history data are

arranged by band pass filter (2 to 4 Hz). Appropriate data according to the duration of free

vibration in all of the filtered data are picked up as presented in Fig. 12. The data in period of

55 to 60 s are selected in this case. The damping ratios are identified through the LSM based

on the data, using following equation.

Table 4 Damping factors of buildings by RDM

data set ｆ0 (Hz)*1 ｈ（%) N*2 data set ｆ0 (Hz)*1 ｈ　（%) N*2

A- TM01 2.75 6.51 1801 B- TM01 3.00 5.81 1472A- TM02 2.95 5.97 1796 B- TM02 2.75 5.04 1478A- TM03 2.85 5.82 1779 B- TM03 2.90 6.17 1485A- TM04 2.85 5.73 1771 B- TM04 2.75 5.04 1460A- TM05 2.85 5.10 1777 B- TM05 2.80 5.96 1469A- TM06 2.90 6.67 1796 B- TM06 2.80 5.32 1468average 2.86 5.97 1787 average 2.83 5.56 1472A- LM01 2.80 5.57 1785 B- LM01 3.00 7.48 1524A- LM02 2.90 5.07 1772 B- LM02 2.80 7.75 1519A- LM03 2.80 7.40 1792 B- LM03 2.80 7.45 1520A- LM04 2.95 7.27 1833 B- LM04 2.80 5.99 1505A- LM05 2.85 7.51 1833 B- LM05 2.90 6.16 1495A- LM06 3.10 6.46 1823 B- LM06 2.90 6.31 1515average 2.90 6.55 1806 average 2.87 6.86 1806

*1：natural frequency obtained by peak of Fourier spectrum*2：Number of overlapping for each data set

Longitudinal

A- building B- building

Transverse

15

))1(cos()exp( 02

00 ththDD ωω −−= (3)

Examples of time histories of observed free vibration and identified envelop curves are

drawn in Fig. 13. Since the time histories of free vibration have some dependency on

Selecting parts of free vibration data

[A-building Transverse（BPF : 2.0-4.0Hz）]

-0.015

-0.01-0.005

00.005

0.010.015

0 20 40 60 80 100Time(s)

Vel

ocity

(mki

ne)

[Period : 55-65 seconds]

-0.015-0.01

-0.0050

0.0050.01

0.015

55 57 59 61 63 65Time(s)

Vel

ocity

(mki

ne)

Fig. 12 Pick up of appropriate data from free vibration response

A-building, Transversef1=2.91Hz, h1=4.95%)

-1

-0.5

0

0.5

1

0.0 0.2 0.4 0.6 0.8 1.0Time（s）

Nor

mal

ized

Am

plitu

de

Velocity (normalized)y=exp(-h1*2π*f1*t)

A-building (Transverse)

A-building, Longitudinal(f1=2.75, h1=5.88%)

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1Time（s）

Nor

mal

ized

Am

plitu

de

Velocity (normalized)y=exp(-h1*2π*f1*t)

A-building (Longitudinal)

Fig. 13 Identified envelop curves of free vibration response

16

amplitude of vibration, identified damping ratios vary according to predominant frequency.

Table 5 shows representatives of damping factors with buildings and directions. In the

transverse direction, the damping factors by forced vibration are a little less than those by

microtremors. In the longitudinal direction, the damping factors by forced vibration are

smaller by 1 to 2 % than those by microtremors. Since the number of obtained damping

factors by forced vibration is very small, the quantitative evaluation is difficult.

CONCLUSIONS

In order to evaluate the fundamental characteristics of the SSI phenomena by means of

microtremor measurements are conducted. Through several methods, fundamental

predominant frequencies and damping factors of residential buildings are calculated. The

fundamental predominant frequencies are obtained from the transfer functions of the systems

including vibration modes of sway, rocking and buildings. The damping factors are evaluated

from microtremor and forced vibration data. The damping factors based on microtremor data

are got using the random decrement method (RDM).

The ratios of predominant frequencies of SSI systems to those of building with base fixed

condition are 0.75 – 0.78 in longitudinal direction. Effects of sway mode on the predominant

frequencies are founded. In the transverse direction, the ratios of predominant frequencies of

SSI systems to those of building with base fixed condition are 0.68 – 0.70. In the transverse

direction, the effects of rocking mode are remarkable.

The damping ratios by the RDM are not so scattered. The average damping factors are 5.5

to 6.0 % and 6.5 to 6.9 %, in the transverse and longitudinal directions, respectively. The

damping factors by forced vibration are a little less than that by microtremors. In the

longitudinal direction, the damping factors by forced vibration are smaller by 1 to 2 % than

those by microtremors. Since the number of obtained damping factors by forced vibration is

very small, the quantitative evaluation is difficult. More data are necessary to discuss the

damping factors and the effect of radiation damping.

Table 5 Damping factors of buildings by forced vibration

A-building B-building f1 (Hz) h1 (%) f1 (Hz) h1 (%)

Transverse direction 2.91 4.95 2.75 5.66 Longitudinal direction 2.75 5.88 2.72 4.90

17

ACKNOWLEGEMENTS

The research on soil structure interaction is conducted in the research group which treats

the theme of “Seismic behaviors of building and its near ground”. The research is conducted

under the Tsukuba Research Institute Council. The authors express their sincere thanks the

members of the research group for their help of microtremor measurements.

REFERENCES

Iiba, M. 2001. Performance-based Type of Provisions in Building Standard Law of Japan -

Introduction of Soil Structure Interaction in Calculation of Response and Limit Strength-,

Proceeding of 2nd U.S. Japan Soil Structure Interaction Workshop

Midorikawa, M., Hiraishi, H., et al., 2000. Development of Seismic Performance Evaluation

Procedures in Building Code of Japan, Proceedings of 12th World Conference of Earthquake

Engineering, Auckland, Paper no. 2215

Stewart J. P. and G. L. Fenves, 1998. System Identification for Evaluating Soil-Structure Interaction

Effects in Buildings from Strong Motion Recordings, EESD, 27, 869 pp.

Tamura, Y. and J. Sasaki and H. Tsukagoshi, 1993. Evaluation of Damping Ratios of Randomly

Excited Buildings Using the Random Decrement Technique, Journal of Structural and

Construction Engineering, No. 545, 29 pp. (in Japanese)

Yagi, S., N. Fukuwa and J. Tobita, 2002. Influence of Rotational Foundation Input Motion Due to

Rayleigh Wave on Transfer Function Estimation, Journal of Structural and Construction

Engineering, No. 552, 77 pp. (in Japanese)

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