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NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCH State University of New York at Buffalo A STUDY OF RADIATION DAMPING AND SOIL-STRUCTURE INTERACTION EFFECTS IN THE CENTRIFUGE by Karen Weissman Supervised by: Jean H. Prevost Department of Civil Engineering and Operations Research Princeton University Princeton, New Jersey 08544 Technical Report NCEER-88-0013 May 24, 1988 This research was conducted at Princeton University and was partially supported by the National Science Foundation under Grant No. ECE 86-07591.

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  • NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCH

    State University of New York at Buffalo

    A STUDY OF RADIATION DAMPING AND SOIL-STRUCTURE INTERACTION EFFECTS

    IN THE CENTRIFUGE

    by

    Karen Weissman

    Supervised by: Jean H. Prevost Department of Civil Engineering and Operations Research

    Princeton University Princeton, New Jersey 08544

    Technical Report NCEER-88-0013

    May 24, 1988

    This research was conducted at Princeton University and was partially supported by the National Science Foundation under Grant No. ECE 86-07591.

  • NOTICE This report was prepared by Princeton University as a result of research sponsored by the National Center for Earthquake Engineering Research (NCEER). Neither NCEER, associates of NCEER, its sponsors, Princeton University, or any person acting on their behalf:

    a. makes any warranty, express or implied, with respect to the use of any information, apparatus, method, or process disclosed in this report or that such use may not infringe upon privately owned rights; or

    b. assumes any liabilities of whatsoever kind with respect to the use of, or for damages resulting from the use of, any information, apparatus, method or process disclosed in this report.

  • PB89-1!H703

    111 11---------

    A STUDY OF RADIATION DAMPING AND SOIL-STRUCTURE INTERACTION

    EFFECTS IN THE CENTRIFUGE

    by

    Karen Weissmanl

    Supervised by Jean H. Prevost2

    May 24,1988

    Technical Report NCEER-88-0013

    NCEER Contract Numbers 86-2032 and 87-1312

    NSF Master Contract Number ECE 86-07591

    1 Graduate Student, Department of Civil Engineering and Operations Research, Princeton University

    2 Professor, Department of Civil Engineering and Operations Research, Princeton University

    NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCH State University of New York at Buffalo Red Jacket Quadrangle, Buffalo, NY 14261

    REPRODUCED BY U.S. DEPARTMENT OF COMMERCE

    NATIONAL TECHNICAL INFORMATION SERVICE SPRINGFIELD, VA 22161

  • 50272 -101 3. Recipient's Accession No. REPORT DOCUMENTATION 11. REPORT NO.

    PAGE . NCEER-88-0013 (' , .. '- ';' .:\ ,_ :,._ i, I 4. Title and Subtitle 5. Report Date

    A Study of Radiation Damping and Soil-Structure I nter-action Effects in the Centrifuge 6.

    May 24, 1988

    7. Author(s) S. Performing Organization Rept. No:

    Karen Weissman and supervised by Jean H. Prevost 9. Performing Organization Name and Address 10. Project/Task/Work Unit No.

    National Center for Earthquake Engineering Research State University of New York at Buffalo

    6-2032 & 87-1312 11. ~ntract(C) or Grant(G) No.

    Red Jacket Quadrangle Buffalo, NY 14261 (C) ECE 86-07591

    ~ 12. Sponsoring Organization Name·and Address 13. Type of .Report & Period Covered

    Technical Report

    14.

    15. Supplementary Notes

    This research was conducted at Princeton University and was partially supported by the National Science Foundation under Grant No. ECE 86-07591.

    16. Abstract (Limit: 200 words)

    This report describes the experimental phase of an ongoing research project on dynamic soil-structure interaction effects. The details of an in depth experimental study of radiation damping and dynamic soil-structure interaction performed in the Princeton University Geotechnical Centrifuge are reported. The experiments were designed to create a data pool which demonstrates the influence of the frequencies of the structure, the foundation embedment and the foundation shape on radiation damping and soil-structure interaction effects for a structure on a finite layer of soil during an earthquake. A total of 37 test cases are examined which include structures with surface and embedded circular, square, rectangular and strip footings and a variety of natural frequencies. The results are presented in the form of plots and qualitative observations. At this stage, the emphasis is on the experiments themselves and the wealth of data they provide. The data is meant for use in the validation of existing and newly developed analytical models. This work is currently in progress at Princeton University and will be reported subsequently.

    17. Document Analysis a. Descriptors

    b. Identifiers/Open-Ended Terms

    EARTHQUAKE ENGINEERING SOIL STRUCTURES RADIATION DAMPING CENTRIFUGE TESTS

    c. COSATI Field/Group

    IS. Availability Statement

    Release Unlimited

    (See ANSI-Z39.1S)

    SOIL STRUCTURE INTERACTIONS EMBEDDED FOUNDATIONS SURFACE FOOTINGS EMBEDDED FOOTI NGS

    19. Security Class (This Report) I 21. No. of Pages I-------'U_n._c_l_a_s_s_if_ie_d ____ --1----'--O _~ __ -----I

    I 22. Price I.. hi A 11'~~/,9s)'.56. 9

  • PREFACE

    The National Center for Earthquake Engineering Research (NCEER) is devoted to the expansion and dissemination of knowledge about earthquakes, the improvement of earthquake-resistant design, and the implementation of seismic hazard mitigation procedures to minimize loss of lives and property. The emphasis is on structures and lifelines that are found in zones of moderate to high seismicity throughout the United States.

    NCEER's research is being carried out in an integrated and coordinated manner following a structured program. The current research program comprises four main areas:

    • Existing and New Structures • Secondary and Protective Systems • Lifeline Systems • Disaster Research and Planning

    This technical report pertains to Program 1, Existing and New Structures, and more specifically to geotechnical studies, soils and soil-structure interaction.

    The long term goal of research in Existing and New Structures is to develop seismic hazard mitigation procedures through rational probabilistic risk assessment for damage or collapse of structures, mainly existing buildings, in regions of moderate to high seismicity. The work relies on improved definitions of seismicity and site response, experimental and analytical evaluations of systems response, and more accurate assessment of risk factors. This technology will be incorporated in expert systems tools and improved code formats for existing and new structures. Methods of retrofit will also be developed. When this work is completed, it should be possible to characterize and quantify societal impact of seismic risk in various geographical regions and large municipalities. Toward this goal, the program has been divided into five components, as shown in the figure below:

    Program Elements:

    Seismicity, Ground Motions and Seismic Hazards Estimates

    Reliability Analysis and Risk Assessment

    Expert Systems

    iii

    Tasks: Earthquake Hazards Estimates, GroWld Motion Estimates. New GroWld Motion Instrumentation. Earthquake & Ground Motion nata Bue.

    Site Response Estimates, Large Ground Defonnation Estimates. Soil-Structute Interaction_

    Typical Structures and Critical Structural Components: Testing and Analysis; Modem Analytical Tools.

    Vulnerability Analysis, Re1iability Analysis, Risk Assessment, Code Upgrading.

    An:hitectural and StnlcIUIal Design. Evaluation of Existing Buildings.

  • Geotechnical studies, soils and soil-structure interaction constitute one of the important areas of research in Existing and New Structures. Current research activities include the following:

    1. Development of linear and nonlinear site response estimates. 2. Development of liquefaction and large ground deformation estimates. 3. Investigation of soil-structure interaction phenomena. 4. Development of computational methods. 5. Incorporation of local soil effects and soil-structure interaction into existing codes.

    The ultimate goal of projects in this area is to develop methods of engineering estimation of large soil deformations, site response, and the effect that the interaction of structures and soils have on the resistance of structures against earthquakes.

    This study represents one step in a sequence of investigations carried out by NCEER in the field of soil-structure interaction. The authors present the results of an extensive series of centrifuge tests on radiation damping and soil-structure interaction. The data generated from these tests will be applied to existing and newly developed analytical models.

    iv

  • ABSTRACT

    This report describes the experimental phase of an ongoing research project on dynamic soil-structure

    interaction effects. The details of an in depth experimental study of radiation damping and dynamic soil-

    structure interaction performed in the Princeton University Geotechnical Centrifuge are reported. The

    experiments were designed to create a data pool which demonstrates the influence of the frequencies of

    the structure, the foundation embedment and the foundation shape on radiation damping and soil-

    structure interaction effects for a structure on a finite layer of soil during an earthquake. A total of 37 test

    cases are examined which include structures with surface and embedded circular, square, rectangular and

    strip footings and a variety of natural frequencies. The results are presented in the form of plots and qual-

    itative observations. At this stage, the emphasis is on the experiments themselves and the wealth of data

    they provide. The data is meant for use in the validation of existing and newly developed analytical

    models. This work is currently in progress at Princeton University and will be reported subsequently.

    v

  • TABLE OF CONTENTS

    SECTION TITLE PAGE

    1 Introduction ..................................................................................................................... 1-1

    2 Experimental Setup ......................................................................................................... 2-1

    3 Structure With a Surface Footing ................................................................................... 3-1

    4 Effects of Embedment. .................................................................................................... 4-1

    5 Effects of Foundation Shape ........................................................................................... 5-1

    5.1 Square .................................................................................................................... 5-1

    5.2 Rectangular (LengthlWidth=2) ............................................................................. 5-2

    5.3 Rectangular (LengthlWidth=4) ............................................................................. 5-3

    5.4 Strip (LengthlWidth=8) ........................................................................................ 5-3

    6 Summary and Conclusions ............................................................................................. 6-1

    7 References ....................................................................................................................... 7-1

    vii

  • TABLE

    2-1

    2-11

    LIST OF TABLES

    TITLE

    Fixed Base Frequencies and Damping Ratios

    Summary of Test Cases

    ix

    PAGE

    2-5

    2-8

  • LIST OF ILLUSTRATIONS

    FIGURE TITLE PAGE

    2-1 Horizontal Acceleration of Free Field Soil Deposit 2-2

    2-2 Dimensions of Structure 2-4

    2-3 Accelerometer Configuration for Soil-Structure System 2-7

    2-4 Schematic of Structure with Surface Footing 2-10

    2-5 Schematic of Structure with Embedded Footing 2-11

    3-1 Horizontal Acceleration of Top Mass Plotted Against Earthquake Input 3-4

    Acceleration Time Histories and their Fast Fourier Transforms

    3-2 System with Surface Circular Footing (f str = 1.66Hz) 3-5

    3-3 System with Surface Circular Footing (f str = 4.05Hz) 3-7

    3-4 System with Surface Circular Footing (f str = 4.69Hz) 3-9

    3-5 System with Surface Circular Footing (fstr = 5.27Hz) 3-11

    4-1 System with Embedded Circular Footing (f str = 1.66Hz) 4-3

    4-2 System with Embedded Circular Footing (fstr = 2.98Hz) 4-5

    4-3 System with Embedded Circular Footing (fstr = 3.12Hz) 4-7

    4-4 System with Embedded Circular Footing (fstr = 4.69Hz) 4-9

    4-5 System with Embedded Circular Footing (f str = 5.27Hz) 4-11

    5-1 System with Surface Square Footing (fstr = 1.66Hz) 5-5

    5-2 System with Surface Square Footing (fstr = 2.98Hz) 5-7

    5-3 System with Surface Square Footing (fstr = 3.12Hz) 5-9

    5-4 System with Surface Square Footing (fstr = 4.69Hz) 5-11

    5-5 System with Surface Square Footing (fstr = 5.27Hz) 5-13

    5-6 System with Embedded Square Footing (f str = 1.66Hz) 5-15

    xi

  • FIGURE TITLE PAGE

    5-7 System with Embedded Square Footing if str = 2.98Hz) 5-17

    5-8 System with Embedded Square Footing if str = 3.12Hz) 5-19

    5-9 System with Embedded Square Footing if str = 4.69Hz) 5-21

    5-10 System with Embedded Square Footing if str = 5.27Hz) 5-23

    5-11 System with Surface Rectangular (LIW=2) Footing if str = 1.66Hz) 5-25

    5-12 System with Surface Rectangular (LIW=2) Footing if str = 2.98Hz) 5-27

    5-13 System with Surface Rectangular (LIW =2) Footing if str = 4.69Hz) 5-29

    5-14 System with Embedded Rectangular (LIW =2) Footing if str = 1.66Hz) 5-31

    5-15 System with Embedded Rectangular (LIW=2) Footing if str = 2.98Hz) 5-33

    5-16 System with Embedded Rectangular (LIW=2) Footing ifstr = 4.69Hz) 5-35

    5-17 System with Surface Rectangular (LIW=4) Footing if str = 1.66Hz) 5-37

    5-18 System with Surface Rectangular (LIW=4) Footing if str = 2.98Hz) 5-39

    5-19 System with Surface Rectangular (LIW=4) Footing ifstr = 4.69Hz) 5-41

    5-20 System with Embedded Rectangular (LIW=4) Footing if str = 1.66Hz) 5-43

    5-21 System with Embedded Rectangular (LIW=4) Footing ifstr = 2.98Hz) 5-45

    5-22 System with Embedded Rectangular (LIW=4) Footing ifstr = 4.69Hz) 5-47

    5-23 System with Surface Strip (L/W=8) Footing if str = 1.66Hz) 5-49

    5-24 System with Surface Strip (L/W=8) Footing if str = 2.98Hz) 5-51

    5-25 System with Surface Strip (L/W=8) Footing if str = 4.69Hz) 5-53

    5-26 System with Embedded Strip (L/W=8) Footing ifstr = 1.66Hz) 5-55

    5-27 System with Embedded Strip (L/W=8) Footing ifstr = 2.98Hz) 5-57

    5-28 System with Embedded Strip (L/W=8) Footing (fstr = 4.69Hz) 5-59

    xii

  • SECTION 1

    INTRODUCTION

    This report contains the details of an in depth experimental study of radiation damping and dynamic soil-

    structure interaction performed in the Princeton University Geotechnical Centrifuge. The repeatability in

    the simulated earthquakes demonstrated in an earlier report [1] is exploited in order to examine the

    response of various types of structures to the same earthquake. The simulated earthquake is generated

    using the hammer-exciter plate method [1]. Standing waves which could occur due to the confinement of

    the model container are absorbed by lining the walls with Duxseal. This method of standing wave

    attenuation was developed by Coe [4] and Coe, Prevost and Scanlan [5] and its effectiveness was further

    demonstrated in centrifuge experiments performed by the authors [1].

    As elastic theory dictates, if a structure is built on a shallow layer over bedrock, radiation damping does

    not occur unless the natural frequencies of the structure are greater than the fundamental frequency of the

    site. With this in mind, the experiments were designed to create a data pool which demonstrates the

    influence of

    1. the frequencies of the structure

    2. the foundation embedment, and

    3. the foundation shape

    on radiation damping and soil-structure interaction effects for a structure on a finite layer of soil during an

    earthquake. This report presents the results of the experiments in the form of plots and qualitative obser-

    vations. The emphasis is on the experiments themselves and the wealth of data they provide. All the

    tests described herein were performed in a centrifuge at a centrifugal acceleration of 100g; thus the model

    is constructed to 1I100th of the prototype scale. To emphasize that the model really represents a system

    that is 100 times larger, all measurements in this report are given in prototype scale unless otherwise indi-

    cated.

    1-1

  • SECTION 2

    EXPE~ENTALSETUP

    In all of the following experiments the model system consists of a single building-like structure on a hor-

    izontal soil stratum over "bedrock". The "bedrock" in the model is actually the exciter plate which pro-

    vides the source of excitation. Previous experiments reported in Reference [1] have demonstrated that the

    same simulated earthquake can be repeatedly generated. Therefore, by keeping the soil depth constant

    the earthquake input to the structure can be kept constant in the following experiments. This way the

    responses of a variety of independently tested structures may be directly compared as they are subjected

    to the same earthquake (i.e. the same amplitudes and frequencies of shaking). The soil deposit is a

    27.08ft layer of Monterey-O sand. The horizontal accelerations at various points in the model soil deposit

    for the simulated earthquake are shown in Figure 2-1. This represents the free field response as the struc-

    ture has not yet been added to the system.

    Similar structures are used in all of the experiments. They consist of a rigid base supporting a stem and a

    top mass. All components are made out of brass and, in all cases, the base is massive with respect to the

    superstructure. To vary the natural frequency of the superstructure the top mass can be moved up and

    down along the stem. Figure 2-2 depicts the dimensions of the structures. The 16.40ft dimension of the

    base represents the diameter in the case of a circular footing and the width in the cases of square, rec-

    tangular and strip footings. In all cases, the superstructure remains the same (except for the position of

    the top mass along the stem).

    Each structure can be viewed as having two translational degrees of freedom, one associated with the hor-

    izontal motion of the superstructure and the other associated with the horizontal motion of the base. In

    order to explore the dependence of radiation damping on the frequencies of the structure relative to the

    frequency of the soil layer, it is desirable to vary at least one of these two frequencies above and below

    2-1

  • FREE FIELD, 14.58 ft. BELOW SURFACE.

    t:l 2.40 of 1. 80

    rl I 1.20 0 rl 0.60

    ~~ f\ M.M X 0.00 ~V \'

    w

    Z -0.60 0 H -1.20 E-< ~ -1. 80

    ;:J -2.40 W U -3.00 U .:x: -3.60

    0.00 0.50 1. 00 1. 50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

    TIME X 10 O)SEC

    FREE FIELD, SOIL SURFACE TO THE LEFT OF CENTER.

    t:l 2.40+-----~-----+-----+----~~----~----+-----~----~-----+-----+~

    1. 80 rl I 1. 20 o rl 0.60 A

    >< o. oo+----"*ItttHlltfd.lllooC\fI...Io."tf'rrA.-I."'~_._."'-_-..... __ ---________ _I_ Z -0.60 I~V vv o ~ -1.20

    ~ -1.80

    ;:J -2.40 W U -3.00 U .:x:-3.60~ ____ ~----_+----_+----~~----~----+_----~----1-----~-----+~

    0.00 0.50 1. 00 1. SO 2.00 2.50 3.00 3.50 4.00 4.50 5.00

    TIME X 10 O)SEC

    FIGURE 2-1: Horizontal Acceleration of Free Field Soil Deposit.

    2-2

  • FREE FIELD, CENTER OF SURFACE.

    t9 2.40

    1. BO .--< I 1. 20 o

    .--< 0.60 \~i\ A X O.OO+-------~H+~\I~~~V~~~~~--~~--~-------------------------+ z -0.60 I o H -1.20 b

    ~ -1. BO ~-2.40 ~ U -3.00 U ~ -3.60~----_r----~------+_----1_----_+------~----+_----_r----~------~

    0.00 0.50 1. 00 1. 50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

    TIME X 10 O)SEC

    FREE FIELD, CENTER OF SURfACE.

    3.60

    3.20 N I 2.80 0 .--<

    2.40 X

    2.00

    ::;: 1. 60 4<

    (j) b 1. 20

    0:: 0.80 D 0 0.40 4<

    0.00 0.00 0.40 O. BO 1. 20 1. 60 2.00 2.40 2.BO 3.20 3.60 4.00

    FREQUENCY X 10 1

    FIGURE 2-1: Horizontal Acceleration of Free Field Soil Deposit. (Cont'd)

    2-3

  • 25.76 ft

    .1'--10.0 ft---,t

    "f 4.17 ft Mmass l~~~...1

    16 i ft

    L-- 16 •• It -----1

    Mbase = 1.71xl04 f Ib 2 t Isec

    Mmass = 5.37x103 f Ib 2 tlsee

    Msrem = 9.33x102 f /b 2 I sec ("aled 10 prototype)

    FIGURE 2-2: Dimensions of Structure.

    2-4

  • the fundamental frequency of the soil layer (which remained constant). The structure is designed

    so that its fundamental frequency which is associated with the superstructure (henceforth denoted

    f str ) could be varied while the higher order frequency associated with the base if b) remains the

    same. It is, therefore, necessary to detennine approximate values of f str and f soil. These values

    only need to be exact enough to provide, a priori, an appropriate range of values of f str which

    span the value of fsoiZ. This is done as follows:

    f str - The fixed base natural frequency of the structure is determined experimentally from

    a measurement of the free vibration acceleration of the top mass while the base is

    clamped. A material damping ratio (~) is also estimated from this free vibration response

    ~ = an -an+m X 100% 21tman+m

    where an and a n+m are the amplitudes of the nth and the n+mth cycles of acceleration respec-

    tively. Table 2-1 shows the results of these fixed base experiments for a variety of positions of the

    top mass. Each of these configurations is used in at least one of the experiments to be described in

    the next three sections.

    TABLE 2-1 FIXED BASE FREQUENCIES AND DAMPING RATIOS

    HEIGHT OF f str ~ TOP MASS (ft.) (Hz.) (% of critical)

    18.75 1.95 0.37 12.50 2.98 0.32 9.90 3.12 0.80 9.38 4.05 0.53 7.81 4.69 0.24 6.25 5.27 0.36

    f soil - The cutoff frequency above which radiation damping will occur is determined by the fun-

    damental frequency of the site in the horizontal direction. This is because the dynamic excitation

    provided by the exciter plate consists primarily of vertically incident shear waves and, since the

    2-5

  • bottom-heavy structure is not inclined towards rocking, it can be assumed that the structure will

    respond to these shear waves predominantly in the swaying mode. This value off str is calculated

    form the formula

    fsoil = ~ = 4.90Hz where Vs is the shear wave velocity in the soil at a depth equal to half the cross sectional dimen-

    sion of the base of the structure (531ft/sec) and d equals the depth of the layer. A shear column

    model such as the one presented in Reference [3] would account for the variation of shear wave

    velocity with depth in the calculation, giving an average value of f str for the stratum. However,

    the accuracy of this method is beyond the accuracy to which the shear modulus is known as a

    function of depth, so the extra effort involved in such a calculation is not worth while in this case.

    It should be noted that the rigid base is associated with a higher order structural frequency and should act

    almost independently of the fundamental mode regardless of the value of f str. It is, therefore, not neces-

    sary to have an a priori estimate of f b as the value does not change and is most likely greater than f soil.

    Hence radiation damping is expected to occur at the base for all cases tested.

    Uniaxial accelerometers are used to measure the response at various points in the system. Figure 2-3

    shows the configuration of these transducers. There are horizontally oriented accelerometers placed at the

    soil surface, 14.5ft below the surface, the base of the structure and the mass of the structure. Vertically

    oriented accelerometers are placed on opposite ends of the base to detect rocking as well as vertical

    motion. The accelerometers in the soil are enclosed in cases to prevent erroneous readings due to the

    pressure of the sand. The output is recorded on a NORLAND 300 1 digital processing oscilloscope and

    stored on the Micro V AX for future analysis.

    2-6

  • 27.08 ft

    FIGURE 2-3: Accelerometer Configuration for Soil-Structure System.

    2-7

  • Table 2-1I is summary of the 37 tests cases studied.

    TABLE2-ll SUMMARY OF TEST CASES

    FOOTING SURFACE/ FREQUENCY OF FIGURE SHAPE EMBEDDED SUPERSTRUCTURE (Hz) Circular Surface 1.95 3-2

    " " 4.05 3-3 " " 4.69 3-4 " " 5.27 3-5 " Embedded 1.95 4-1 " " 2.98 4-2 " " 3.12 4-3 " " 4.69 4-4 " " 5.27 4-5

    Square Surface 1.95 5-1 " " 2.98 5-2 " " 3.12 5-3 " " 4.69 5-4 " " 5.27 5-5 " Embedded 1.95 5-6 " " 2.98 5-7 " " 3.12 5-8 " " 4.69 5-9 " " 5.27 5-10

    Rectangular (L!W=2) Surface 1.95 5-11 " " 2.98 5-12 " " 4.69 5-13 " Embedded 1.95 5-14 " " 2.98 5-15 " " 4.69 5-16

    Rectangular (L!W=4) Surface 1.95 5-17 " " 2.98 5-18 " " 4.69 5-19 " Embedded 1.95 5-20 " " 2.98 5-21 " " 4.69 5-22

    Strip (L/W=8) Surface 1.95 5-23 " " 2.98 5-24 " " 4.69 5-25 " Embedded 1.95 5-26 " " 2.98 5-27 " " 4.69 5-28

    2-8

  • The next three sections, in which the results of these tests are described, are organized as follows. First,

    the response of a structure with a surface footing is examined in detail, particularly for the influence of

    f str and f b on radiation damping and soil-structure interaction effects. Figure 2-4 shows a schematic

    diagram of a typical structure with a surface footing, where f str is dependent on the height of the top

    mass above the base (h). Next, the response of a similar structure with an embedded footing is presented

    for comparison. Figure 2-5: shows a schematic diagram of a typical structure with an embedded footing.

    Lastly, responses of structures with surface and embedded foundations of various shapes are discussed.

    2-9

  • h

    . . ~ . -' .. -~ -- '. / .. ", .• - r f ' SAND

    I . \. / 27.08 ft I •

    l .. .'"

    I ._. - --

    '.. L I - , .(,. j' " -

    - < . . /

    FIGURE 2-4: Schematic of Structure with Surface Footing. Frequency of Superstructure Varies with Height of Top Mass (h).

    2-10

  • h

    " . .... - , -

    I t . :.- , "-

    SAND -, , , /

    27.08 ft ,

    ~: ' I

    '.,/

    /--\ I • .:.-Jr-•

    FIGURE 2·5: Schematic of Structure with Embedded Footing.

    2-11

  • SECTION 3

    STRUCTURE WITH A SURFACE FOOTING

    In the first set of experiments, the structure with a circular base is placed on the surface of the soil deposit.

    The height of the mass is moved down or up to induce or inhibit radiation damping respectively. Four

    values off sfr were tested:

    (a) 1.66Hz < fsoil

    (b) 4.05Hz < f soil

    (c) 4.69Hz "'" f soU

    (d) 5.27Hz > fsou.

    Case (a) represents a situation where we anticipate no radiation damping. Case (d) represents a situation

    where radiation damping is expected to occur. Cases (b) and 4(c) fall in between these two extremes. In

    all cases, radiation damping is expected to occur at the base. Figures 3-1 through 3-5 show the accelera-

    tions recorded at various points in the soil-structure system along with their Fast Fourier Transforms.

    Many observations can be made from looking at this first set of results. First of all, it should be noted that

    the earthquake at 14.58 ft below the soil surface is similar for each case and, therefore, provides a con-

    sistent datum to which the structural response may be compared. Figure 3-1 shows the absolute accelera-

    tion of the top mass plotted with the earthquake recorded below the soil surface for cases (a) through (d).

    It can be seen from this comparison that in case (d) the response of the top mass dies out with the earth-

    quake excitation while in case (a) the top mass is still accelerating after the earthquake has finished. This

    implies that for case (a) energy is trapped in the structure and not allowed to radiate away, thus radiation

    damping is small of nonexistent. Figures 3-1 (b), (c) and (d) show that as f sfr is increased above f soil the

    amount of radiation damping increases. The concept derived from linear elastic theory that f soil is a cut-

    off frequency perhaps suggests a more drastic jump between the occurrence and nonoccurrence of radia-

    tion damping than actually exists.

    3-1

  • From Figures 3-2 through 3-5 it can also be seen that the response of the top mass to the strong motion

    part of the earthquake varies in frequency much more than amplitude. This motion is damped out within

    about the first second of the earthquake for all four values off str .

    In contrast to the top mass, the horizontal motion of the base is very similar for all four frequency values

    and dies out with the input earthquake. The Fast Fourier Transfonns of these signals indicate that the

    base is responding with a dominant frequency of about 7.82Hz which is above the fundamental frequency

    of the soil layer. Thus, the heavy base is essentially acting independently of the superstructure and radia-

    tion damping occurs for this degree of freedom regardless of the height of the top mass.

    The vertical accelerations recorded at opposite ends of the base are also quite similar for all four values of

    f str· The signals on the right and left side are out-of-phase indicating that some rocking does occur.

    However, the vertical accelerations die out with the earthquake indicating that rocking does not contribute

    to the trapped energy observed in the superstructure when f str > f soil. The amplitudes of the two verti-

    cal accelerations are slightly unequal indicating that some purely vertical motion exists as well.

    Finally, in addition to these observations on the soil-structure system, an important conclusion can be

    drawn about the ability of the bounded model to represent a layer of infinite extent. The fact that radia-

    tion damping can be observed in the centrifuge model means that the Duxseal lining the containment

    walls is indeed preventing waves from being reflected back into the system. This fact is crucial to the

    study of soil-structure interaction in the centrifuge.

    3-2

  • --EARTHQUAKE INPUT -----HORIZONTAL MASS (fstr ~1.9SHz)

    t9 1. 60 = 1. 54 1. 20 (a)

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    --EARTHQUAKE INPUT ---HORIZONTAL MASS (fstr =4. OSHz)

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    TIME X 10 O)SEC

    FIGURE 3-1: Horizontal Acceleration of Top Mass Plotted Against Earthquake Input For Structure with Surface Circular Footing.

    3-3

  • --EARTHQUAKE INPUT

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  • SECTION 4

    EFFECTS OF EMBEDMENT

    In the next set of experiments the structure with the circular footing used in Section 3 is embedded up to

    the top of the base (see Figure 2-5). The depth of embedment, therefore, is 4.89ft. Sand is now glued to

    the side of the base as well as the bottom to ensure bonding between the side walls of the footing and the

    soil. Based on the results of the first set of tests it was decided that f str should be increased more gradu-

    ally in order to get a broader picture of the behavior of the structure (previously three out of the four cases

    had values of f str close to or above f soil). The new range of frequencies is as follows:

    1.66Hz < fsoil

    2.98Hz

  • around 11Hz and 21Hz. Assuming this free field motion approximates the earthquake input at the base of

    the structure, it can be concluded that the embedded structure sees resonance effects from these peaks as

    f str is varied whereas the surface structure does not.

    The horizontal motion of the base behaves somewhat differently for the embedded case as well. First, the

    dominant frequency of the response, as seen from the Fast Fourier Transforms, is slightly larger for the

    embedded structures (10Hz) than for the surface structures (7.8Hz). Thus the stiffness at the base-soil

    level is larger for the embedded structure. Second, the damping associated with this peak frequency is

    also larger for the embedded structure. The third difference is that the base and the mass no longer act

    completely independently as they did for the surface structures. This can be seen most obviously when

    f str = 1.66Hz (Figure 4-1) where the horizontal acceleration of the base exhibits a ringing at the end of

    the signal which vibrates at the same frequency as the ringing of the superstructure.

    The vertical motions on opposite sides of the base are similar for all five values of f str and are again out-

    of-phase and of unequal amplitude. However, the vertical accelerations are smaller for the embedded

    structure than the surface structure. This is quite reasonable as the embedment provides some resistance

    to rocking, and the bonding of the sides of the foundation to the soil restricts vertical motion.

    4-2

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