NSF/CEE-81081

SEISMIC SOIL-PILE-STRUCTURE INTERACTION PILE GROUPS

Report to NATIONAL SCIENCE FOUNDATION

INFORMATION RESOURCES NATIONAL SCIENCE FOUNDATION

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Seismic Soil-Pile-Structure Interaction, Pile Groups August 19B1

--- ---------------------------------• AJr!h~",!!~

T "-- Kagawa -- ~~~~~!~..: O,...nization Name and Address

McClelland Engineers, Inc. P.O. Bo x 37321 Houston, TX 77026

06323(-) a. Performin, Oraanization Rept. No.

10. Project/Task/Work Unit No.

11. Contract(C) Or Grant(G) No.

(C) PFRB001503

(G)

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W • Ha k a 1 a, C EE Directorate for Engineering (ENG) National Science Foundation Was_~ington, DC 20550

i~- Supplementary Notes

Submitted by: Communications Program (OPRM) National Science Foundation Washi ngton, DC _205~Q.. __ ----------- ---

~~ ~~!-!!"!'~! n .. imit: 200 words)

14.

- ---------------------1

A parametric study is presented of dynamic pile-group effects for an idealized 50il­pile-structure system consisting of a lumped mass model of a superstructure and elastic piles fully embedded in a homogeneous, linearly elastic soil layer. The results are used to develop an approximate method, based upon a beam-on-Winkler foundation model, that can be used for dynamic response analyses of pile-groups in layered elastic soils. The approximate pile-group method is evaluated by comparing computed and observed seismic response data of a building supported by a group of piles. The comparison shows that the dynamic stiffness and damping characteristics of a pile group can be evaluated correctly using the procedure. The pile method was found to provide a rational tool to quantify and evaluate pile-group effects for the seismic response of complex pile-supported structures.

-----------------------------------------------------------------------------------~ H~ Document Analysis a. Descriptors

Earthquakes Earthquake resistant structures Structural analysis Seismic response

b. Identifiers/Open· Ended Terms

Ground motion T. Kagawa, IPI

Pile foundations Pile structures Soil s Mathematical models

c. COSATI Field/Group

---------------------------------------.-------------------~------------~ 21. No. of P.,aes .. u!l';~~~!~!~!" Statement 19. Security Class (This Report)

NTIS r---------------------~-----------------ZO. Security Class (This PaCe) 22. Price

------~_c_____------------------~-----------'I-------~ ~Z.:') See Instructions on Reverse OPTIONAL FORM 272 (4-77) (Formerly NTIS-35) Department of Commerce

SEISMIC SOIL-PILE-STRUCTURE INTERACTION

-PILE GROUPS-

by

Takaaki Kagawa, Ph.D., P.E. Engineering Consultant

McClelland Engineers, Inc.

This material is based upon work supported by the National Science Foundation under Grant No. PFR 80-01503.

Any opinions, findings, and conclusions, or recommendations expressed in the publication are those of the author and do not necessarily reflect the views of the National Science Foundation.

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SEISMIC SOIL-PlLE-STRUCTURE INTERACTION

-PILE GROUPS-

*' * *

by

Takaaki Kagawa

--1 I I, II

II

II ;

i I

I II,) II Grant No. PFR 80-01503 I'

!I /'

A Report on Research Sponsored by the National Science Foundation

1

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!I I * * * Ii Ii II

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'I II M c C L ELL AND ENG I NEE R S, INC. II

I Geotechnical Consultants

Houston, Texas

II August 1981 II

IL'=I ============= f'~cCl[LLAi\:1J ZNG1IIJEERS ====--==========:::::::'.111

CON TEN T S

ABSTRACT ............................................... .

I NTRODUCT I ON ........................................... .

Summary of Previous Work ........................... .

Scope of Study ..................................... .

Report Format ...................................... .

THEORETICAL PILE-GROUP EFFECTS IN IDEAL I ZED PILE GROUPS ................................ .

Analytic Model ..................................... .

System Parameters .................................. .

I II

Solution Procedure ................................. .

Response of Soil Layer ........................ . Responses of Piles ............................ . Soil-Pile Compatibility Conditions ............ . Boundary Conditions ........................... . Structural Response ........................... . Soil-Pile Interface Stress Patterns ........... .

Evaluation of Analytic Method ...................... .

Appropriate Soil-Pile Stress Patterns ......... . Comparison with other Solution ................ .

Pile-Group Effects ................................. .

Major Factors Affecting Pile-Group Effects .... . Directionality ................................ . Spring and Damping Constants of Pile Group .... . Shear and Moment Distributions ................ . Seismic Pile-Group Effects .................... . Soil-Pile Springs and Damping ................. .

Surnm.ary ........................................................................ .. II II S IMPLIF lED METHOD FOR PILE GROUPS ••••••••••••••••••••••.

Ii Introduction ....................................... .

il

I i

II

I I,

Analytic Model .................................................................. .

soil-Pile Spring for a Single Pile ................. .

Soil-Pile Springs for a Pile Group ................. .

Correction Factors for Pile-Group Effects ..... . Evaluation of Correction Factors .............. .

Numerical Procedure ................................ .

Ii

l'=11 ============== rc:eCL[lLA:cJD Er~GINEEnS , . r ,(

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1 II 1 II 2 II , 3 iI

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II 18 18 II 20 20

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24 I 25 II 26 II

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CON TEN T S (Cont.)

! Ij CASE STUDY ............................................................................. .. < i !

I l I

Ii H i I

II

Introduction ....................................... .

Earthquake Response Observation .................... .

Analysis Procedure ................................. .

Analysis Results ................................... .

Comparison for the 1974 Izu Event ............. . Comparison for the 1975 Ibaraki Event ......... .

Summary ............................................ .

I CONCLUD I Nt> COMMENTS •••••••••••••••••••••••••••••••••••••

II ILL U S T RAT ION S

II ,I I! I: Ii I) ['

I II :1 'I i

Analytic Model of a Pile-Supported Structure ........... . Ranges of Nondimensional Parameters for

Par ameter Study ...................................... . Soil-Pile Interface Stress ............................. . Soil-Pile Interface Stresses for Analysis .............. . Representation of a Pile Section by Discrete Elements .. . single-Pile Stiffness and Damping from Several Methods .. single-Pile Soil-Pile spring Coefficients from

Several Methods ...................................... . 2-Pile Interaction for Different Soil-Pile

Stress Patterns ...................................... . Comparison with Poulos' Group Deflection Factors ....... .

i Soil Motions due to Pile Vibration ..................... . i Effects of s/2r and Frequency on 2-Pile Interaction ... . J,ll Effects of H/2r~ on 2-Pile Interaction for

Later al Mode ......................................... . II:!I! Effects of H/2r o on 2-Pile Interaction for

Lateral Mode ......................................... . II Effects of H/2r on 2-Pile Interaction for , Vertical Modeo ........................................ .

I ,.

Effects of ~R on 2-Pile Interaction for Lateral Mode ... .

Effects of K on 2-Pile Interaction for Vertical Mode .. . Directional Rngle for 2-Piles .......................... .

Ii Directionality of 2-Pile Interaction .........•..........

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I I

Page Ii II

28 il I. iI

28 " 1I

29 1\ iI II

29 1I

31 II 31 31

32 II :

33

Plate 1 ! J i

1 11 Ii

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3 II 4 II 5 I

I , 6

Ii 7

i 8 ,

9

II 10 11

I,

12 II I' d

13

II 14 II 15

16 II 17

II 18

I Ii II II

II II r!cCLELU\i\lCi ENGfNEE7IS ==============='.1 , ",,/ :::.-

;$ 1 f!

ILL U S T RAT ION S (Cont.) , i

,i

I

II , Pile-Group Effects for 2x2 Group ....................... . II Pile-Group Effects for 3x3 Group ........................ . ill Comparison of Damping for Pile Groups

I and Surf ace Footings ................................. .

I Distribution of Pile-Head Shear ........................ . Distribution of Pile-Head Moment ....................... . Pile-Group Effects on Soil-Pile Spring Coefficients .... . Analytic Model of a Pile-Supported Structure ........... . Soil-Pile Spring and Dashpot ........................... . Average Soil-Pile Spring Coefficient for Lateral Mode .. . Average Soil-Pile Spring Coefficient for Vertical Mode .. Performance of Approximate Method ...................... . Numerical Schemes for Program PILES .................... .

I 14-Story Building for Case Study ....................... .

I Soil Conditions and Seismic Observational Points ....... .

I, Structural Properties for Case Study ................... . II Earthquake Motions at Pile-Tip Level II f or Case Study ....................................... . , computed and Observed Acceleration Time Histories

for Izu Event ........................................ . Computed and Observed Response Spectra

for I zu Event ........................................ . :j Computed and Observed Response Spectra II f or I bar aki Event ................•..•.................

II APPENDIX A: REFERENCES

'I I! !J

Ii '1 I, /1 ,i iI

I! II '/

i

i

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I

I I I II

Plate " \i

19 20

21 22 23 24 25 26 27 28 29 30 31 32 33

34

35

36

37

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:1

II II 'I

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1,.;1 ============== r,1cCU:LltiND ENGIN!CERS ==============~II IV

r I

H Ii ABSTRACT ii II Dynamic pile-group effects were studied parametr ically for an I; q idealized soil-pile-structure system. The system consisted of a il lumped mass model of a superstructure and elastic piles fully II embedded in a homogeneous, linear ly elastic soil layer. The re­'i II suIts were used to develop an approximate method, based on a III beam-on-Winkler foundation model, that can be used for dynamic Ii response analyses of pile-groups in layered elastic soils. " Ii Major findings from the parameter study for an idealized II soil-pile-structure system are itemized below.

I (1) Correct pile-soil-pile interaction can be assessed using

uniform soil-pile stress patterns over the width of a pile for a wide frequency range, although this assumption fails

I for a single pile at high frequencies. i (2) Pile-group effects are affected primarily by the nondimen-i sional frequency wr IV and the spacing ratio s/2r for flex-

I ible and compressib~e ~iles. other factors have oRly a minor influence on the pile-group effects.

II1I (3) 2-pile interaction is pronounced at spacing ratios less than 30 for the lateral vibration mode and about 20 for the verti­

II II cal vibration mode. ,

Ii (4) Group stiffness varies strongly with frequency. For a clus­

tered pile group, the group stiffness can be negative and can II be larger than a simple summation of static single pile I stiffnesses. Ii (5) Damping of a pile group also is frequency-dependent, and it II can be approximated by that of an equivalent surface footing Ij'l, at low frequencies, where the seismic soil-pile interaction

is important. Ii (6) Distr ibution patterns of shear and moment among piles depend j, largely on frequency. Center piles, for example, can be I' stiffer and carry a greater load than corner piles under i dynamic loading conditions than they do under static.

I, (7) Pile-group effects are strongly frequency-dependent. Pile- j

,i group eff iciency from static theory is not necessar ily ap- I Ii propr iate for designing a dynamically loaded pile foundation. II

II comp~~~ng a~~~~~~:~t:n~i!~~~~~~~ ::iZ~~~ ::!~~:~ ~:~a e~~l~a~~~l~: I

'I

ing supported by a group of piles. The compar ison showed that I I the dynamic stiffness and damping characteristics of a pile group 1

1

,1 can be evaluated correctly us ing the procedure. Thus, the method provides a rational tool to quantify and evaluate pile-group

!; effects for the seismic response of complex pile-supported

I II

I

structures.

1

INTRODUCTION

I Summary of Previous Work

I

I

I

!I I

Pile-supported structures have experienced significant damage

and failure during major earthquakes. For example, a number of

pile foundations for bridge structures suffered severe damage

during the Niigata and Alaska Earthquakes of 1964 (Fukuoka, 1966;

Kachadoorian, 1968), and many prestressed and reinforced concrete

piles for buildings were damaged during the 1978 Miyagi-Oki

Earthquake. The damage was caused by the failure of the founda­

tion soil due to liquefaction or by the sOil-pile interaction

generated by earthquake excitations. II

II

I

The dynamic response analysis of soil-pile-structure systems I

has been the subject of considerable interest and research in II

recent years. Design of pile-supported structures against . i

seismic loading requires character ization of soil-pile spr ings II that can be combined into the structural response analysis. The I

state-of-the-art on characterization of soil-pile springs under

seismic loading is in a formative stage of development, and

extensive work is needed to study the dynamic characteristics of

the lateral load-deflection relationships of piles.

Soil-pile springs may be represented analytically by the

11 discrete models such as the subgrade reaction theory (Ogata and ;r i Kotsubo, 1966; Yoshida and Yoshinaka, 1972; and Prakash and

I Chandrasekaran, 1973) and the Minlin's static solution (Parmelee, ! II Penzien, Scheffey, Seed, and Thiers, 1964; and Liou and Pensien,

111977) , by the continuous models such as the elastic solutions L II (Tajimi, 1969; Nogami and Novak, 1977; Kobori, Minai, and Baba,

Iii 1977 ; and Kagawa and Kraft, 1981), or by the semi-continuous

I models such as the finite element method (Blaney, KaJlsel, and

II Roesset, 1976; Kuhlemeyer, 1979 i Roesset and Angelides, 1979; and j I Kagawa and Kraft, 1980a). Most of these studies are based on I ! single pile systems.

!I I Studies on pile-group effects have been based mostly on

l!=::s=t=a=t=l=' c==c=o=n=s=i=d=e=r=a=t=l=' o=n=s=( PO:~~~:,,:,: :~G"::': ~:~ 9) =. _==D=y=n=am=i=C,=S=O=i=l-P He II

\ ~ Ii

... il

2 I ,

interaction effects were represented by the concept of "effective

soil mass" (Parmelee, Penzien, Scheffey, Seed, and Thiers, 1964).

I: In this procedure, a certain portion of the soil around piles is 11

II assumed to move together with piles, and the inertia effects of H ii soil dur ing pile vibration are approximated. No established I' II Ii

I: Ii

II

criteria

associated

to evaluate the effective mass and radiation damping

with soil-pile interaction, however, is available in

this method. Therefore, a rational procedure is needed to

evaluate the pile-group effects obtained from this procedure.

Recently, Wolf and von Arx (1978) solved a problem of a

footing supported by up to 100 vertical piles by first solving

!I the single pile problem for a visoelastic system using an axisym­

II metr ic finite element method. They constructed from this solu­

II tion, by superposition, the total complex flexibility matrix of

II !I

Ii the soil-pile system, and finally the corresponding impedance

matrix by inversion of the flexibility matrix. They illustrated

I the significance of the pile-soil-pile interaction effects; due

II to pile group effects, the stiffness of an average pile in a pile

Ii group may be substantially reduced and the radiation damping may

I

:; [I increase considerably compared to an isolated pile. The possible '

II wave scatter ing and generating of standing waves within a group \

I: of piles, however, were not fully accounted for in this study. II i'!"li The effect of the lack of standing waves in the solution on the !".,II'

Pile-group effect needs to be examined.

II II Scope of Study Ii :1 !i '; I;

It :! Consider ing the lack of our knowledge of dynamic pile-group ii II ::~::~:' o;e la~~::~ p~~::::~~:::~e ~::::::~::~IY A t::l:::::::~:~ I:

II :;::::ur:'d wa:he:::~ :::~t::1u::on:' w~::a~~:::e:~ i1 ;~~ 1: i::~~~::; ~ !]

I! the soil layer was assumed homogeneous and elastic. The effects

II of var iations of soil-pile interface stress patterns on pile

I responses were examined to study the significance of the possible I wave scattering and generating of standing waves within a group

of piles. Pile-group effects were studied in terms of: (1) dyna-

\1

II II iI II Ii II 'I

I' I' II Ii

II Ii !i

ii II 'i

,

3

mic group efficiency for horizontal stiffness of the pile group,

(2) dynamic load-deflection relationships of piles represented by

soil-pile springs and energy dissipation due to material and rad- 'j !I

iation damping rand (3) shear and moment distr ibutions among the :! II

piles.

An approximate, economical method was constructed, using the Ii II

results of the theoretical analysis, to study the pile-group II II

effects of complex sOil-pile-structure systems encountered in ,I ii

practice. The method is based on a linearly elastic beam-on- iI i Winkler foundation model of a pile group. Discrete soil-pile i,l,

springs and dashpots for the method were determined using the: :i equivalent soil-pile springs for single piles and correction fac- :j

tors for group effects. :1

i The approximate method was evaluated by comparing computed \ 1

and observed seismic response data of an apartment building sup- 'I III! I

II Ii ported by a group of piles. 'I

II I

1

1:

1

: Report Format II

i The report first presents a theoretical development of il 11 !I Ii sOil-pile-structure interaction of an idealized pile group and '1'1

'1'[ II II the results of a parameter study. This is followed by de- I: \1 d Ii scr iptions of the approximate method and the results of the II I Ii

'1'1 compar ison between computed and observed seismic response data. !' 1'\ Ii iii All illustrations follow the text, and citations of all reference Ii I: mater ial are included in Appendix A. II i ;j

jl THEORETICAL PILE-GROUP EFFECTS IN IDEALIZED PILE GROUPS

II

Analytic Model i

11

'\ I'

il :\ 'I 'I j\

I! I;

II il d II

"

A pile-supported structure was modeled by a linearly elastic ,i soil-pile-structure system, Plate 1. The superstructure is re­

presented by a lumped mass model that has translational degrees

of freedom only. Each of the identical, linearly elastic piles

has a uniform cross section and is fully embedded into the soil

layer. The soil layer of unif,orm thickness rests on a rigid base

at which a seismic excitation is applied. The pile-structure

'I II jl d 11 11

II II II Ii Ii l! Ij i! system is allowed to translate in the x-direction only and .rotate !I I!

==================~I

11

[

I':,: ar ound !i layer.. ~l

the y axis. The rigid pile-cap does not contact the soil

" i I: The major assumptions in our analytic model are: (1) the 'I

i' piles are fully embedded into the soil layer and are supported on ;1

Ii the rigid base, (2) the soil layer is homogeneous, linearly elas- i,., III

II tic with hysteretic material damping, (3) vertical soil motion '

:1 generated by the hor izontal vibration of a pile has only a minor il I! effect on the pile response and can be neglected, (4) horizontal II Ii soil motion generated by the vertical vibration of a pile can be Ii II neglected, (5) piles are perfectly bonded to soil, and (6) ver- ,1

tical shear forces at soil-pile interface do not influence the :\ "

lateral vibration of the pile. These assumptions are reasonable 'I il for studying the fundamental response characteristics of most ,i

':""1: single piles (Kagawa and Kraft, 1980a) r and are good also for ;,1

evaluating most pile-group effects. III '\ -I Ii System Parameters i

II Factors affecting the pile-group response in the present :1

:1:1' analytic model include il Ii Ii (1) Spacing ratio (=s/2r o )' i'

Ii (2) Frequency. II Ii (3) Pile slenderness ratio (=H/2r ). I: II 0 I'

il (4) Pile flexibility factor (RR = EI/EsH4). Ii Ii (5) Pile compressibility factor (R = EA/E H2). II ii c s ii

(6) Poisson's ratio of soil. 'i ii \i 1j (7)

;: 11

Pile-head fixity condition, and loading condition. ii :1 ii Effects of variations of these factors were studied. Plate 2 I ,1 'I

II summarizies the ranges of nondimensional parameters used in this

:1 study. Frequency is represented as the ratio between the excita-,

Ii tion frequency f and the fundamental resonance frequency of the

soil layer fro

Our study showed that the spacing ratio, excitation fre-! I quency, and pile slenderness ratio had a large influence on the

pile-group effects. Variations of other nondimensional )) Ii dynamic

parameters

effects.

on

The

Plate 2 had a small impact on the pile-group

pile-head fixity condition and loading condition II

II \1

had minor influences on the pile-group effects.

d il II Ii

:1 I[ I' II il Ii

II II II 'I ij q n 'I

5

Solution Procedure

in

Response of Soil Layer. When the structural base translates

the x direction and rotates at the ground level around the y

axis, the piles deform both in the lateral and axial directions.

Thus, the behavior of piles can be described by the superposition

of lateral and axial vibration modes, and the piles transmit

lateral and vertical forces into the soil. When piles exert soil­

pile forces Fi(Z) and Hi(z), response of the homogeneous, lin-

early elastic soil layer can be described as

(X*+G*) {~,~,~}A + Gs*V2cu,V,W} s s ax ay az

N i i iwt - E {f (x,y,z),O,h (x,y,z)}e i=l

u,v,W,=

I II

il 'I I, " I: 1:

displacements in the x, y, and z directions, G: = Gs (1+i2D), Gs - II shear modulus of soil, D = material damping of soil, i =~, ~:=!

2vG:/(1-2v), v = Poisson's ratio of soil, p = mass density of

soil, N = number of piles in the group, w e circular frequency

(=2"f), and the soil-pile interface stresses fi(x,y,Z) and i h (x,y,z) are defined as

pi(z) = f fi(x,y,Z) dxdy (2)

= f i h (x,y,z) dxdy

The relation between Fi(Z) and fi is illustrated on Plate 3, and

Hi(Z) and hi are defined in a similar manner. The integrals are

performed over the circumference of the pile ~t z.

To solve Eg. 1, we decoupled horizontal and vertical vibra-

tion modes: no vertical soil motion is involved in the hori-

zontal vibration, and no horizontal soil motion is considered for

the vertical iwt motion u e

o

vibration. We applied a horizontal rigid base

to the system. Soil displacements and soil-pile

forces were expanded into discrete Fourier series as

===~=il

6 il

II I {U,V,W} ! , I

,I Ii :1

(n=1,3,5, ... ) ... (3) :\ I' Ii 'I !I II where a = n71 12H, and H :; height of the soil layer. The summation II n

ii ,I

11 is taken for odd integer numbers of n. With Eg. 3, Eg. 1 can be

ii Ii

II 1

reduced to

a2 2 ___ {h u ,v ,w } +

ax 2 n n n

1

Ii :1 " !1

i[ :i I d ,I i

:1 il

il II = - '! H

·1,1 wher e h 2 s (VV J ' V pan: * s V s compr es s ion an~" ~~:ar ~:~e Ii

velocities of the soil, and the wave number is defined as k = Ii Ii Ii Ii IV I! ;1 W • Ii 'I s L I, To solve Eq. 4, we applied Four ier transforms to the soil "

II displacements and the soil-pile forces as I':,'

Ii il II : {u ,; ~ f i 0, hni} = C1 [un' v , w , f i 0, hi] I! it n n' n' n' J n n n' n ii

II cg ,I ilIff {un' Vn , Wn ' f~t 0, h~} ei(ax+PY)dxdy 'I II 271 ~ II Ii

:1 . . . . . . ( 5 ) i!

ii Also, we applied Fourier transforms to Eq. 4, and obtained the il,1

II solutions to Eq. 4 as I!

II II 'I Ii ;i 'i'll

ill

Ii Ii I' 'I

II ii !I ii

,,;':.1C::~L:~~L:\N~' Ei\lGj~·,:5:[K5 =====..::::== ~--=-:::;:,.~~~_~I

Ir--" ,i

I: Ii Ii H i: H U

(6 )

and is I! where 1/I'n = (a2+,B2+a~_k2){h2(a2+.82) + a~-k2}, :' Dirac r s delta function. Soil displacements are then solved by

Ii applying inverse Four ier transforms to Eg. 6 as

'I !i

1<:2 4u 4u

'I

II ;'

u r: [~ + 0 = n a 2_k2 n7r mr n

00 N + 1 fI~ (a2+,B2h2+a2_1<:2) r: fi e-i(ax+,BY)dad,B]

21TG* n . 1 n -00 'n 1= s

x sin anz

1 00

(h2-1) N fi e-i(ax+,BY)dadP V = -[ If ap r: sin anz

n 21TG* "n i=l n s -00

w = r: 1

n 21TG~ ,:

Ii

iwt e

iwt e

(7)

l 1

I

II I

1\ ~ ! ,( :1

II il

'1\ 11 j!

"

ii :1 Soil response can once il the soil-pile forces are II obtained be

il specified inEq. 7. ;'

I' il 1\ i ~ ~ i

I: Responses of Piles. When the i-th pile in a group receives ii

J

'I,',' the lateral soil reaction F i (z) and the vertical soil reaction Ii Hi(Z), the equations of motion of the pile can be represented as

il ;

1

a2

(wie iwt ) = az2

(8)

Ii !i

!i il II il II ii )1

il ========================~I

I I 8 I Ii Ii where u

i

Ii relative

and wi = horizontal and vertical pile displacements

to the horizontal rigid base motion u e iwt , m = mass ' o p ,I H per unit ,I

length of the pile, EI = flexural rigidity of the pile, :I

Ii and EA = axial stiffness of the pile. Reponse of the pile can be

I! determined once the unknown soil reactions Fi(Z) and Hi(Z) and I'

I! boundary conditions are specified. To solve Eq. 8, we expanded ! Ii the soil-pile forces into discrete Four ier ser ies as

!I {F i , Hi} = L {F

i Hi} sin a z n' . .. .. .. . .

'I

II II ;1

II II I: il II " :1 Ii p

With Eq.

u i =

wi =

n n n

9, general solutions to Eq. 8 are obtained as

Ai . s~np.z + BiCOSP.Z + Cisinhp.z + DiCOshp.z

2 i

+ L 4uow mp/n7T -F n

sin anz n

Ela4 2 - w m n p

Kisin;z i -Hi

L n sin + L cosp.z anz n EAa~-w2mp

. . . .. .. .

(9)

(10) d 4 2 - 2 Ii where p. .. w m lEI I P. il t t· p t t

iii i i Li are A ,B ,C ,D ,K , and

il in egr a ~on cons an s.

H Soil-Pile Compatibility Conditions. According to Eq. 7, the !i Ii hor izontal and vertical soil movements at the center line of the

i i Ii H

i-th pile, (x ,y ), can be represented as

11

i i 4u 4u k 2 N

oijF j } iwt U(x L {~ 0

+ E sin ,y ,z) = + a z e n n n n7r(a2 -k2) j=l n1T n II !l Ii

II (!

il :1

i i W(x ,y ,z) = E (11) n

'I I: These soil displacements equal the i-th pile displacements to II Ii maintain the soil-pile compatibility condition. Using Eqs. 10

!I and 11, we represented the condition as II

:i ~ ! :1

II H

.i

ii

II I

!i II i, I H !I

I if ,)

I

I

i I, 'l=:============== !:';;;c:,,"[!~~ .. ~Ii\jD iE)JGj;;J[[~S w~~_ ~=============='l

I'

I' Ii II \: 2 i

+ E 4uow mp/n7T- F n

sin a Z

Ela~ 2 n n - w m p

~+ 4UQ

k2 N oijFj } "" E { + E

n7T(a~-k2) n n

n7T j=l

Hi Kisin~z + Licos~z - L _____ n __ __

n

N = E { E r 1J H

j }

. 1 n n n J=

9

sin anz

. . . . . . .. ( 12)

:\ I

,I II 'I

I " When i' :1

we expand sin~z, cos~z, sinh~z,

il :1

cosh~z, s inp.z, and cosp.z 'I :1

i

II ii

into discrete

matrix form.

Fourier series, Eq. 12 reduces to the following II if

II I, ,. i·

1\ II i' :I 1/

11 !\ :1 " u Ii II i: j: :i II

n7T

.. M n + N n

a~:> [1] + En [::j + + I n t:j

i :1 II.

!I ..... .

\1 where the matrices [4> l n and ['I']n' and the Fourier coefficients Ii

(13a) :1 I,

:1 LEn' Fn' In' I n , Mn' and Nn are given as II

II II Ii i!

Ii II

Ii II Ii " ;1

;1

1 o

[4>] = [O~j] + 1 n 4 2

EIa -w m 0 n p 1

1 o

[it]n [r ij ] + 1 = n EAa~-w2mp 0 1

sin~z = L E sin anz, cos~z = L Fn sin anz n n n

sinh~z = L I sin anz, cosh~z = L J sin anz n n n n

sin~z = L n

Mn sin anz, COSIJ,Z = L N n n sin anz

Eq. l3a can be solved for Fi n and Hi

n as

Fi 4uo w2mp k2

N ~ij+

N _ .. = ( ) L E L 01J n

Ela~-w2mp a 2 _k2 n n. 1 n mT j=l J= n

N ~ijBj

N ~ijcj

N ~ij + F L + I L + J n L n n n n n

j=l j=l j=l

Hi N

;ij Kj N ;~j Lj = Mn L + Nn I: n n

j=l j=l

10

...... (13b) i

Aj

Dj

..... (14)

.1 ') ii

;: i

'J

d :; II Ii Ii ii II 'I il Ir II

where ~~j and ;~j are the (i,j) element of the inverse matrices !I of [4>]n and [it]n· With Egs. 10 and 14, the unknown soil-pile 'I

il

:/!

forces can be eliminated, and the pile displacements are II 'I II II Ii " !I i! :1 'i \1 !! LQ(;CL.[lL!U\:D ENG~N~:::RS ===============~

I' Ii Ii l'

Ui = Ai sin~z + Bi cos~z +

4uo /mT fw2mp + r: (

n Ela~-w2mp

N En ~ij

r: U.: n

j=l n 4 2 Elan-w mp

N I ~ij

L 0: n n

j=l n Ela4-w2m n p

11

Ci sinh~z + Di cosh~z

2 k

2 N _ .. w mp ) L OlJ} sin anz

4 2 a2 _k2 n

Elan-w mp j=l n

N F ~ij

anZ}Bj r: {r: n n sin

j=l n Ela~-w2mp

N J ~ij

anZ}Dj r: {r: n n sin

j=l n Ela4-w2m n p

12

1 2 N U (H) = U (H) = ...... = U (H) = Ub . . . . . . (16)

:~llz_H= :~2Iz=H = ...... = :~IZ=H = , ...... (17) Ii II I: where ; = pile-cap lateral displacement relative to the rigid

, = rotation of the pile cap. Also, the geometric

for the pile-cap rotation calls for additional N

i; base, Ii

!I :.

constraint

11 H II Ii

equations Wi(H) = _, xi (i=1,2, ... ,N) ...... (18)

" :1 where I'

is the arm-length of the i-th pile measured from the

II

I , i

I II Ii Ii II 'I [,

axis of rotation, Plate 3.

Finally the boundary conditions that specify the loading on

the pile cap yield

3 N N EltL { E Ai costLH + 1: c i coshtLH} = L

i=l i=l (19)

N (Xi)2 EAIJ, coslJ,H 1: = - M

i=l

II Eqs. 16 through 19 give 3N+l number of equations. Since we also i)

11 have i N 1 N 1 N

3N+l unknowns (A ,---, A , C ,---, C , K , ---, K , and '), ", ii all unknowns can be determined to obtain the pile-group response.

II' I, structural Response. Detailed procedures to evaluate the

I response of the superstructure on Plate 1 were presented by

li Kagawa and Kraft (1981). The method is based on the mode super­

II position procedure. Base shear and moment are obtained as a l! il function of pile-cap displacement and rotation as

(Am} and {Ar} are given as

KHR = 12Eln{Ar}n/(W2h~)-

6Eln{Ar}n/(W2h~) - 4Eln/hn·

{Am} = [~]{Tj(W) ([~]T{mS})j}

{Ar} = {~]{Tj(W) ([~]T(r})j}

(20)

(21)

i

I I

I

I

II II ;3 -II II II where ! j-th

[¢] = modal matrix,

mode defined by

T.(w) = dynamic magnification of J 2 2

W /[Kj{l-(w/w j ) +i2P j (w/W j )}], Kj=

the II

I j-th mode, w. = circular natural J i

generalized stiffness of the

frequency for the j-th mode, II T

Ii, mode, {ms } = (ml,···,mn ), and

Pj

= damping ratio for the j-th ! T 2 { r } ( 0 , ... , 0, 6E I /h ). Eq. 20 n n

, can be solved with Eqs. 16 through 19 to obtain the seismic II II

r

I I II II

response of the pile groups.

Soil-Pile Interface Stress Patterns. To study the pile-group

effects, we considered two types of soil-pile interface stress

patterns for the lateral pile vibration:

types, Plate 4. These stress patterns

uniform and Boussinesq i i

at x and yare de- I scribed by

-i fi sin I I I

II j

f (x,y,z) r: O(X-x i ) S (y_yi) anz (uniform) n n

I -I \1 q

= r: f1 n O(x-x i ) 2/11 sin a z (Boussinesq) n j i 2 2 n l-(y-y ) /r

0

II (22)

where S(y) = box function defined in the interval (y -ro ' y +r o )' II! i i

II Using Eg. 22, we can represent Eq. 2 as

I I

II ,I

il

I Ii II Ii II

f f i (x , y , z ) dxdy

(uniform and Boussinesq)

(23)

Also, the Fourier transform of Eg. 22 yields

(uniform)

-1 ~ fn ro J (n ) L.. -u 0 ~ro (Boussinesq) = n 11

(24) 11

II where J ( ) is the O-th order Bessel function of the first kind.

I I i ,

I I

I .1

II

I

I Foro vertical vibration, we considered a "cross-blade" type

I soil-pile interface stress pattern where each blade has a uniform I

II str ass pattern. ""'''L''D '"<;0""" II

14

i h (x,y,z) = E n

-i iii i hn {O(x-x )S(y-y ) + S(x-x )O(y-y )} sin anz

(25)

For this stress pattern,

hi are given as

Hi(Z) and the Fourier I

transform of II

II I i -i H (Z) = 4r E h sin a z

o n n n I j I 11

sin anz II n 1T a

(26)

Eqs. 23, 24, and 26 can be incorporated into Egs. 7 and 10 to

determine the pile-group response. The integrations in Eq. 7 I were evaluated numerically. i

Evaluation of Analytic Method II

Appropriate Soil-Pile stress Patterns. Soil stress distri- I bution patterns around piles depend largely on exciting frequency !

I Use of a soil-pile II and pile spacing ratios, among other factors.

stress pattern that is independent of these factors may result in ' I erroneous pile response. Therefore, the effects of variations of

sOil-pile stress patterns on pile response were evaluated in de-

tail for the lateral vibration mode to select a simple but rea­

sonably accurate soil-pile stress pattern.

To generate exact pile-soil-pile interaction, we discretized

a pile into several strip segments as shown on Plate 5. Uniform

stress acts over the width of each segment, but its magnitude is

determined using the condition that all segments within a pile

move together. Six to eight strip segments usually are required

to approximate the correct stress variation over the width of a

pile. Although the method may be attractive from an academic

view point, the method is prohibitively expensive for a large

number of piles. Therefore, the pile-soil-pile interaction was

I

I I' ,I Jj

II )1

I

obtained using simple soil-pile stress patterns, and the results

were evaluated in the light of solutions from this rigorous

t================ 1v1cCL[;:LLM~D !!:NGI[~EC:RS ===========~

15

method.· The simple stress distribution patterns used in this

study included the uniform and Boussinesq types as described by

Eqs. 22 and 25. :' II 'I Plate 6 shows the lateral pile-head spr ing and damping con- II

stants of a pile for both uniform and Boussinesg type sOil-pile II stress patterns. Also shown on Plate 6 are the mathematical

solutions for a pile with a circular cross section by Kagawa and ,I

Kraft (1981). For the uniform and Boussinesq type stress pat-

terns, the soil displacements at the center of a loaded area were

considered to be representative of the soil motion due to the

soil-pile stresses. The soil displacements caused by these soil­

pile stresses, however, vary from the center to the edge of the

loaded area, and the soil near the center moves more than that at

Ii I'

i

I , ! 1

II

Ii pile stiffnesses and dampings from I

I Therefore, the edge. the

these stress patterns are less than the theoretical solutions. I i

The Boussinesq type stress pattern, however, provided good I I

approximation to the theoretical solutions at low frequency I ratios, although it resulted in pile stiffnesses similar to that !

11

of the uniform stress pattern at high frequencies. Pile re- I

sponses with the uniform stress distribution can be improved by I

II

II

pile groups will be evaluated below.

Plate 8 shows the effects of the difference in assumed soil- I pile stress patterns on 2-pile responses. The two piles are II located in-line with loading, with the directional angle e being 1

equal to zero. Pile responses were obtained using the three

l!:=============== McClELlJI\ND ENGIl\J[E~S ================1

16 ! ,

different soil-pile stress patterns: (1) uniform stress pattern I ;1

with a factor of 0.85, (2) Boussinesq type stress pattern, and !

(3) var iable

strip segments

uniform stress

stress pattern that simulates exact solutions (six

were used). Plate 8 shows clearly that the

pattern approximates closely the exact solutions

and that the Boussinesq type stress pattern results in erroneous

pile-group effects for closely-spaced piles. Thus, the uniform

stress pattern with a factor of 0.85 was used in the remaining

study to evaluate pile-group effects.

the

type

The vertical vibration mode is secondary to the objective of

present study. Therefore, the validity of the "cross-blade"

distribution was confirmed by comparing the single pile

!I

responses obtained from this distribution and the theoretical I solution derived by the author previously. The two solutions I compared favorably. II

!I !I Comparison with Other Solution. The lateral pile-group ill

effects from our method were compared with those by Poulos (1979)

for static pile-head loading conditions, Plate 9. Our results

are based on the piles fully embedded into the soil layer,

whereas Poulos' results are for a floating pile group. The group

deflection factor here is defined, according to Poulos (1979), as

the ratio of the pile-group displacement to the displacement of a

free-head

results

pile carrying average load per pile in the group. Our

are in general agreement with those by Poulos (1979),

although the present solutions are rather insensitive to the

variation of KR for the fixed-head condition.

Pile-Group Effects

Major -Factors Affecting Pile-Group Effects. Pile-soil-pile

interaction is due to the soil motion generated by the vibration

of piles. Typical soil motion attenuations around a pile for the

lateral vibration mode are shown on Plate 10 for frequency ratios

of 10 and 30. The soil motion generated by the pile vibration

depends strongly on frequency and involves phase changes along

the distance from the pile. Thus, the soil motion at the second

pile generated by the first pile is not in phase with the motion

Ii Ii Ii Ii

I I

II I' !

t================ McCL~LLAN!) ENGI0!EErlS ==============='

17

of the second pile, and effective stiffness and damping of the

second pile are altered due to the vibration of the first pile.

The spacing ratio and the excitation frequency, therefore, have

large effects on pile-group responses.

The effects of spacing ratio and frequency on two pile

interaction are shown on Plate 11. Since the soil motion gen­

erated by the pile vibration vanishes at a large distance from

the pile, both spring and damping constants of a pile in a group

approach those of a single pile for large pile spacing. Under the

static condition, this distance is about 30 pile diameters for

the lateral mode and about 20 pile diameters for the vertical

mode. As the frequency increases, the ratios of dynamic to

static

the

spring and damping constants exhibit wavy variations with II

spacing ratio. These ratios, however, are nearly unity at

spacing ratios of about 50.

The influence of the pile slenderness ratio H/2ro on the

shown on Plate 12. The pile lateral pile-group effects are'

slenderness ratio, H/2ro ' has a similar influence on the vertical

pile-group effects. The influence of H/2ro on lateral as well as

vertical pile-group effects, however, can be masked if we adopt a

nondimensional frequency wro/vs as the frequency scale instead of

the frequency ratio f/f , Plates 13 and 14. In these figures, r '

the pile radius was varied while the pile length, H, was kept

constant. With the effects of the pile slenderness ratio, H/2r o '

masked, we can redefine the relative stiffnesses between the soil

and pile as in Eg. 27 that were kept constant in these results.

(local pile flexibility) (27)

(local pile compressibility)

II :1

II II if :1

II II

II

I I i

II

I'

II The results on Plates 13 and 14 indicate that the pile-group !I effects depend primarily on the spacing ratio and the

nondimensional frequency for given soil-pile relative stiffness. I pile flexibility and compressibility factors

KR and Kc in Eq. 27 have relatively minor effects on the

The local

,i

l':::::::============== McCLC:LlAND G1GIN[Ef'iS ================'111

18

pile-soil-pile interaction for the range of flexible and com­

pressible piles examined in this study, Plates 15 and 16. The

spacing ratio and the nondimensional frequency have larger impact - -

on dynamic pile-group effects than RR and Rc'

Directionality. 2-pile interaction is affected by the direc- I tional angle as well as absolute distance between the piles. The I

directional angle 6 is defined on Plate 17 where the angle is ji

measured from the x axis counter clockwise. On Plate 17, the two

piles have the same directional angle 6. Our study showed that

the 2-pile interaction is about the same when the first pile is

at the origin of the local coordinates (x,y) and the second pile

is located on an ellipse

x2 +'(2y)2 = (constant)2 (28)

II

II

II I

This observation was examined for two piles with directional

angles of 0 and 90 degrees. Plate 18 demonstrates the 2-pile II interaction results for the cases with the constant in Eq. 28 ::

11 being equal to 4 and 16 pile diameters. This observation is Ii

II II

nearly exact under static loadi~g conditions and only approximate

at high frequencies.

Spring and Damping Constants of Pile Group. Spring and

damping constants of a pile group can be evaluated using 2-pile

interaction results. Our analytic model is linearly elastic. I I i

I i Therefore, 2-pile interaction results can be superposed to obtain i

the pile-group effects for any number of piles. A superposition I procedure to obtain the spring and damping constants of a pile I group is summarized below.

When d~, is the lateral complex pile-head displacement of the 1J

i-th pile due to the unit lateral pile-head forces on the i-th

and j-th piles, the complex lateral displacement of the i-th pile

is given as

H H H H H H H Pl(d·l-d .. )+ ... +P. led. 'l-d .. )+P.d .. +P·+l(d, '+l-d .. )+ ... 1 11 1- l,l- 11 1 II 1 1,1 11

H H H +PN(diN-dii) = d i

(29)

where P. = lateral complex pile-head force on the i-th pile.

d~j equ~ls d~i due to reciprocity. When we set d~ to unity, the

I

I II

II iI

I

l!:=============== McCL:ct~LMJD ENG![~[ERS ==-=-=--::=-_=~==========~

19

pile-head forces Pl"",PN represent the complex pile stiffnesses II,'

that include the pile-group effects. The sum of these forces

gives the complex stiffness of the pile group. Eg. 29 can be

simplified and represented also as

H H H PI (ll . 1-1) + ... + P. 1 (ll. . 1-1) + P . + P . + 1 ( 6. . 1-1) + ... 1 1- 1,1- 1 1 1,1+

I II il h

I H H H '

H +PN(Ai:-l) H~ d i / : ii H .••••• (30) II

where 6 ij = dij/d ii = kii/kij . k ij is the complex lateral I! I[

stiffness of the i-th pile when the i-th and j-th piles carry the I

I same

piles

with

pile-head

in the

vertical

loads. Spring and damping values for a group of

rocking vibration mode can be evaluated similarly

2-pile interaction results. With a complex pile

stiffness k computed, equivalent spring and damping coefficients

1

i I L 1I of the pile are obtained as II

k = K + iwC • • • • • • ( 31) 'i ,I

Dynamic stiffness and damping of pile groups are shown on l.ii,1

Plates 19 and 20 for 2x2 and 3x3 groups. Dynamic stiffness of a .

pile group is strongly frequency-dependent. The dynamic stiffness II

of a pile group can be larger than the stiffness estimated from

the satic stiffness without the pile-group effects. For clus- i!1

tered pile groups, the dynamic stiffness can be negative. Also,

'I the damping for a pile group shows a wavy Variation with fre- i

quency. The damping has several peaks. The large peaks tend to I

I occur at higher frequencies for piles with closer spacings.

The major difference between the damping characteristics of a IJ

surface footing and a pile foundation was stUdied. Plate 21 com-

pares the damping of pile groups with that of surface footings.

The damping is essentially due to radiation damping except below

frequency ratio of 1.0 where material damping is dominant. Three

foundation sizes are considered with the plan dimensions of the

surface footings equal to the outer dimensions of the pile

groups. Plate 21 shows that the damping of a pile group can be

larger than that of an equivalent surface footing at low fre­

II I[ 11

quencies when the piles are closely spaced. The damping of a I

i pile group at high frequencies, however, does not increase lin- iI

II l!::=============== McCt~LLtH\!D ~NGjI\JEERS ==============='1.

------,1 20 ! - ~

early with frequency, and can be considerably lower than that of

an equivalent surface footing for widely spaced piles. For most

seismic response analyses of pile foundations that involve low

frequency responses, damping may be approximated by that of a

surface footing. For high frequency machine foundation problems,

it appears appropriate not to account for radiation damping.

Shear and Moment Distributions. Pile-head shear and moment

distributions among piles can be affected considerably by the

pile-group effects. Distribution patterns of the pile-head shear

and moment vary with frequency. The pile-head shear and moment

distribution patterns computed for static loading conditions may

be invalid for dynamic loading conditions. Plate 22 shows the

distributions of shear forces for a 3x3 group with spacing ratios

of 2, 4, and 8. For the case with a spacing ratio of 2, the

center pile carries the least load under the static condition and

the maximum load at a frequency ratio of 60. Thus, the effective

stiffness of the center pile increased by a factor of about 3 due

to the pile-group effects as the frequency ratio increased from 0

to 60. On the other hand, the corner pile became less stiff as

the frequency increased. For pile groups with large spacings,

the variations become less pronounced. Similar phenomena are

observed for the pile-head moment distribution patterns on Plate

23.

Seismic Pile-Group Effects. Effective stiffness of a pile is

the pile is loaded either at the different

pile hea~

deformation

theoretically when

or seismically. The difference is due to the pile

due to the free-field excitation. To study the

effect of the difference in loading condition on the pile-group

response, we computed the effective stiffnesses of pile groups by

applying sinusoidal lateral excitation at the rigid base. Our

study indicated that the pile-group effects are essentially inde­

pendent of loading conditions for flexible piles. Thus, the

effective stiffness and damping of a pile group for a seismic

response analysis can be determined using single-pile responses

under the seismic loading condition and the pile group effects

obtained for the pile-head loading condition.

~============== McCL'CLlAND ENGINZEClS =-=--=-=-=-=-=============='-

21

Soil-Pile Springs and Damping. Equivalent soil-pile springs

provide useful information to the determination of the soil-pile

springs for a beam-on-Winkler foundation analysis of piles.

Equivalent soil-pile springs were evaluated for the present ana­

lytic model following the method by Kagawa and Kraft (1980a,

1980b, 1981) for single piles. The lateral load-displacement

relation (p-y) was defined 'as

P E:toH 5 Y (32)

I p = lateral soil reaction on a unit pile length, E: = Iii!

complex Young's modulus of soil (=2(1+v) G:t). oH = lateral

where

H . H 5 I soil-pile spring coefficient (= 0 1 + 102 ), and y = pile I

I displacement relative to the free field. All quantities in Eq.

32 are complex numbers. The real part of oH, o~, is the "true" il soil-pile spring coefficient, and the imaginary part represents 11

il

the mater ial as well as the radiation damping associated with the it

soil-pile interaction. The SOil-pile spring coefficient oH ill 'II

var ies with de'pth even for homogeneous soil conditions. H II

Equivalent average of 0 with depth, however, can be defined as II (Kagawa and Kraft, 1980b). ,I

II

II

NH H H 2 H 2 o = f 0 y dz/ J y dz (33)

o 0

which may be used with a beam-on-Winkler foundation model for

layered soil conditions (Kagawa and Kraft, 1980b).

The axial load-displacement relation (f-z) can be defined in

a similar manner as

f = E* ovz s (34)

v where f = axial soil reaction on a unit pile length, 0 = soil-

pile spring coefficient (= or + iO;), and z ~ axial pile dis­

placement. Equivalent average of Ov with depth can be defined

I I

II 'I I:

I:

i I

similar to Eq. 33. ,

The average soil-pile spring efficients are related uniquely I

to pile-head spring constants. When we consider a pile loaded

with a unit lateral force at the pile head, we can equate the !I

work done at the pile head to the work done along the embedded 11.::.il

l

portion of the pile as

--- McClE~Ltt:f\!D ;;:NGII\lE:::~S

22

H

= f o

py dz (35) I, II

(1) d

where d = pile-head lateral displacement. With Eqs. 32 and 33,

Eq. 35 can be reduced to

d E* -H H y2 dz = o J s

0

Thus, the pile-head spring constant is given as

kH = lid = 1.0/{E;OH! y2 dz}

o

(36)

(37)

!I

11

II Ii II

II II II

Eq. 37 shows that the average soil-pile spring coefficient is

related to the pile-head spring constant through the integration II of y2. A similar relation holds for the _~ertic~~ vibration mode. II Our study showed that the behavior of 0 and 0 for pile groups II

I·

is very similar to that of pile-head spr ing and damping con- :1

stants. Typical behavior of the average lateral soil-pile spring II coefficient for 2 piles is illustrated on Plate 24.

Summary

Pile-group effects were studied parametrically for an ideal-

ized analytic model of a pile group. Major findings are

summarized below.

(1) Correct pile-soil-pile interaction can be assessed using

uniform soil-pile stress patterns over the width of a

pile for a wide frequency range, although this assump-

tion fails for a single pile at high frequencies.

(2) Pile-group effects are affected primarily by the non-

dimensional frequency wro/vs and the spacing ratio s/2ro II for flexible and compressible piles. Other factors have i

~ I

for the vertical vibration mode. . I I il

11-'=1 ============== i'vlctLILlt\:m ENGINEERS ==============='.111

(3 )

only minor influence on the pile-group effects.

2-pile interaction is pronounced at the spacing ratio

less than 30 for the lateral vibration mode and about 20

23

(4) Stiffness of a pile group varies strongly with fre­

quency.

can be

tion of

Damping

:::a:i:!u:::r:~p~!el:::::'t::: !r:~~p::l:~:::: II static single pile stiffnesses.

( 5 ) of a pile group also is frequency-dependent.

(6)

Damping of a pile group can be approximated by that of I· an equivalent surface footing at low frequencies, where II the seismic soil-pile interaction is important. I Distribution patterns of shear and moment among piles I depend largely on frequency. center piles, for example, I

can be stiffer and carry a greater load than corner II'

piles under dynamic loading conditions than they do II

under static conditions. l

(7) Pile-group effects are strongly

Pile-group efficiency from a static

sarily appropriate for designing

pile foundation.

frequency-dependent.

theory is not neces­

a dynamically loaded

SIMPLIFIED METHOD FOR PILE GROUPS

Introduction

Pile-group effects were studied in the last section for a

homogeneous, elastic soil. To study the pile-soil-pile inter-

action in layered soil conditions that are found in practice, we

extended the results in the last section to include soil layering

effects and an approximate, but efficient method was developed

using the beam-on-Winkler foundation. Discrete soil-pile springs

and dashpots were used to represent the continuous nature of

lateral as well as axial soil resistance. These discrete para­

meters were determined from the equivalent dynamic soil-pile

springs for single piles presented by Kagawa and Kraft (1980b)

and the pile-group effects described in the last section.

Description of the analytic model for the method and the pro­

cedures to determine the discrete soil-pile springs and dashpots

for a pile group will be discussed below. The approximate method

I I

ii========--==--->-'===~:=:>C'''''=CO-'''=~------------=======:j111

24

will be

response

piles.

evaluated by comparing computed and observed seismic

data of an apartment building supported by a group of

Analytic Model

The method is based on a beam-on-Winkler foundation model of

a soil-pile system, Plate 25. The superstructure is modeled in

the same manner as on Plate 1. The rigid foundation block is

connected to the free-field surface with a sliding spring and a

rotational spring to simulate the interaction between the soil

and pile-cap. The foundation also can have a translational mass

and a rotational mass. The soil deposit is layered with hyster­

etic soil damping. All vertical piles are identical. Piles are

discretized following the layering of soils, and their properties

can vary with depth from one element to another. Although the

bottom soil layer rests on a rigid base in this analytic model

and pile elements extend down to this base, floating pile groups

can be analyzed in an approximate manner by assigning appropriate

soil moduli to "pile elements" below pile tips. Each pile ele­

ment has bending as well as axial stiffnesses, but the contri­

bution of shear deformation to the pile stiffness is neglected.

Each pile element is connected to the free-field soil through the

soil-pile springs described below.

Excitation to the model can be applied either to the pile-cap

or seismically. The pile-cap excitation is limited to sinusoidal

steady-state shear force in the x direction and moment around the

y axis. A free-field control motion can be specified at any

layer boundary. The seismic excitation also is limited to the x

direction.

Soil-Pile Spring for a Single Pile

Dynamic characteristics of equivalent soil-pile springs were

studied in detail by Kagawa and Kraft (1980b, 1981) for a pile in

a homogeneous, elastic soil layer. The study showed that the

lateral. soil reaction, p, at some depth on a unit pile length can

be approximated by

--'==_=' __ ="-=-====-===7 --~---=~~~-ll

25 I

p = E 5

(38)

i I I

Ii where Es = Young' 5 modulus of soil, 6~1 = average soil-pile :",', spring coefficient that is invariant with depth, p = mass density -

of soil, and B = equivalent width of a pile. The soil-pile ele-

;; ment in Eq. 38 is shown on Plate 26. The soil-pile spr ing II I; coeff ic ient 5~1 for homogeneous, elastic soil conditions can be II II related to ~~he "local pile flexibility factor," K

R, as shown on II

I Plate 27. 011 for layered, elastic soil conditions may be II i approximated by those for homogeneous, elastic soil prof iles II I ,I 1 if a weighted soil modulus determined by Eq. 39 is used to repre- I

" Ii sent the so il (Kagawa and Kraft, 1980b) .

. r

Ii !I 11

il ,i II 'I II II J!

Ii Ii

i! II II 11 11

II II

il Ii I: "

- H 2 H 2 Es = J EsY dzl f y dz (39)

o 0

Similarly, the vertical soil reaction f for a homogeneous

soil condition at some depth on a unit pile length can be approx-

imated by

f = E s (40)

~v

where 0Il = average soil-pile spring coefficient. The soil-pile

spring coefficient

bility factor," Kc'

condition and the

to the p-y relation.

~v

°Il is related to the "local pile compressi­~v

as shown on Plate 28. 0Il. for a layered soil

average soil modulus Es are defined similar

Soil-Pile Springs for a Pile Group

I' The soil-pile spr ings for piles

I, the pile-group effects. The p-y and f-z relations for a single

in a group are affected by

Ii :~~:ox:::~:t 5 ::Pl:se:et:~:ec~~~ed in on a th:i~::~~::P o;n~~~:~:~eo:: 1; ii soil conditions is presented below to determine the soil-pile if springs for a pile group. In this approximate method, we con-

I sidered that the pile-group effects for layered soil conditions

II could be ~l with the if Ii pile-group, I' ,i

approximated by those of homogeneous soil conditions

weighted moduli in Eq. 39. For this equivalent

we can relate easily the discrete soil-pile springs

I I I, 'I Ii I;

II I'

Ii II I! 'I

II ,J

I! II ,I H i! II I I II I' JI

'/ II

,,====-c:--===_=========_= " I

26 i ,

\' II I:

to pile-head stiffness and damping, and the pile-Ii and \' group

dashpots

effects

Ii at pile heads.

can be determined from the equilibrium conditions il

I! i l: ,

Correction Factors for Pile-Group Effects. For the lateral

vibration mode, the complex lateral pile-head displacement of the

Ii i-th pile can be written as Eg. 30. We set the ratio between II ' !i the i-th pile-head displacement in the group, and the pile-head II

II displacement for a single pile condition, d~/d~i r to be unity and II

!,

i,1 solve for pile-head forces Pi (i=1,2, ... ,N). These pile-head !I quantities can be related to the lateral soil reaction on the il

I! !I lj i-th pile, Pl" and the pile displacement relative to the free I Ii

Iii field, y i' by equating the work done at the pile head and along

the pile depth. I,

I, 'I

ji "i

;1

i I ! ~H !I where 5

l, =

Ii average soil-pile spring

the pile-group effects.

( 41)

coefficient for the i-th

,\ i

'I i

Ii iI il ;\

Our study showed that the i Ii pile with il integral in Eq. 41 can be approximated with good accuracy by I

II I' II II It II " ;1

o

N - H N ~ H 2 [E p, (y .. /d .. ) - E P. (y .. /d .. )]

j J lJ II j~i J II 11 (42)

il II

II I I i

"i

l: where the second summation excludes the i-th term. The root mean '

H Ii ;Ii' square integral of the pile displacement y ij and d ii are given as ii

H II II Yij = [f y~j dz]O.S 1/

Ii",,: 0 (43) :: • • • • • • Ii

Ii Ii " I! Ii 'I \ i

,I

i, where Yij is the pile displacement of a 2-pile group with unit 1

lateral loads on both piles. II I,

II ~~th Egs. 41 through 43, we can express the ratio between 6~ II II and 511 as \1

II "ct ;c."::L,',~!::; E:'S:~IC:::::, ~

N N = p. 1 [2: p. (y .. IY . . ) - 2: p.] 2

2711 - i

l (44) iI

H

1 j J 1J 11 j¢i J

which represents the correction factor for the i-th pile on the

p-y relation in Eg. 38 to include the pile-group effects.

replaced

il by

For the rocking mode, d~j in the a~ove procedure is

that of the vertical mode and d. is represented as 1

i , x .

xi is the x coordinate of the i-th pile when the origin of the x '1 iI

II coordinate is located at the center :1 Ii , is the rotation of the pile-cap.

of gravity of the pile group.

The correction factor for the

II i-th i'

pile on the f-z relation in Eg. 40 is obtained as q

-v -v xi/[ N

6i/6l1 = p, 2: p, (y, ,/y, ,) 1

j J 1J 11 (45)

! where Yij is defined for the pile displacement for the vertical

Ii vibration mode.

II The correction factors on the p-y and f-z relations are I, II determined using Egs. 44 and 45 and 2-pile interaction results.

Ii Lateral 2-pile interaction, however, is influenced by the Ii II 't' Ii POSl lons of the piles relative to the load direction and the l'

Ii pile spacing. Thus, an extensive amount of data on the lateral

i

lll 2-pile interaction is required to obtain the correction factors

), for any arrangement of piles. To simplify the procedure, we 11 :; adopted an assumption that the 2-pile interaction is about the

:1 same when the second pile is located on an ellipse represented by II Ii Eg. 28. This assumption is nearly exact under static loading I,

III conditions, and it provides a reasonable assumption at low fre-

,! quencies where the seismic soil-pile interaction is important. Ii 1: With this assumption, we determine the 2-pile interaction at any

relative position using the results at a specific directional

angle.

Evaluation of Correction Factors. Using the approximate

:1 procedure, we predicted the correction factors on the p-y and f-z

Ii relations for homogeneous soil conditions. The results were

Ii compared with those from the theoretical solutions in the last I' ,I section. An example of this comparison for the lateral vibration

i

II I, tj Ii I! Ii

Ii ,I !I Ii Ii t' 'j

II II II II !! il I' II

II II II

\1 .[

=====,'1

28

mode is show on Plate 29 for the corner piles of 2x2 and 3x3

ii groups. !j

Ii

The approximate procedure is shown to be very good at

Ii !" L

low frequencies. Even at high frequencies, the procedure

vides reasonable estimates of soil-pile spring coefficients.

pro- :1 II II

11 Numer ical Procedure Ii Ii il q

II

'I

!I !I '\ 11 ii il 'I II

I

The procedure was automated into a computer program "PILES"

to perform dynamic response analyses of pile groups loaded either

The major steps of computation are

i'

II II II at pile caps or seismically.

illustrated on Plate 30. ,I Analysis is done in the frequency domain using the complex il

il , response method. Seismic loading is represented as a super-

position of sinusoidal waves using the Fast Fourier Transform

technique, and responses of the soil-pile-structure system are :1

computed at discrete frequencies. The computed responses are :1 :\ :1 summed using the inverse Fast Fourier Transform to generate time :1

II histor ies of responses of the system. il if Responses of the structure and the piles are solved inde- \! !i 'I I pendently with unknown pile-cap movements and loads. Complete il I responses of the structure and the piles are determined by eli- I

I II

II Ii II d II 1\ il i-

II ,I

minating the unknown pile-cap quantities using pertinent boundary

conditions at the pile cap. I

Introduction II II II I!

of the pile-group method "PILES" presented Ii

CASE STUDY

General validity II

11,,1' in

seismic response of a pile-supported apartment building. Com-

Ii was evaluated with a case study of the II the last section

! Ii puted results, were compared with field observational data to

II evaluate if stiffness as well as damping character istics of a

II pile group can be represented correctly by the program PILES.

Ii Observed data were of low seismic intenSity. Therefore, the

Ii Ii

II

I I

limi ted to the linear range, although the 11 il

predictions were

be modified to incorporate soil nonlinearity II equivalent-linear parameter concept (Seed and :1

iI II

I' program PILES may I I effects using the I

'I Idriss, 1969) . II

:, i'

ii 29

Ii Earthquake Response Observation ,I !l 11

II Ii Ii ;:

The field observational data that we used in our study were

obtained by the Building Research Institute of Japan. Details of

the

by

observational data and analyses were published, for example,

Sugimura (1975), the Building Research Institu~e (1976), and 1\ i! ! ~ I'

i' the Japan Residence Corporation (1979). Major points are ex­

!i tracted from these publications and are descr ibed below.

for a 14-story reinforced concrete, apartment building located at

Toshima 5-Chome, Kita-ku, Tokyo. Plate 31 shows the plan views

II II Earthquake response measurements have been made since 1972

II II

I

I,

j

i !

of the building and the foundation pile layout. The building iSI ,;

i supported by 44, 4-pile groups (prestressed concrete piles,j

I length=25 m, diarneter=O. 6-0.7 mt wall thickness=O. 09-0 .10 m). :1

II Typical spac ing ratio within a 4-pile group is 2.3. The soil 1\

/1 conditions at the site and the points of acceleration measurement II il Ii II at which seismic response data were available for this study are :\

II shown on Plate 32. The piles are dr iven through the soft layers :\

II and are supported by the under lying stiff sandy gravel layer with ,[

Ii SPT values exceeding 50. Seismic response data recorded were I !i mostly of low intens ity. The seismic events used in this study I !I had maximum acceleration amplitudes at the pile tip on the order I II 1\ ·1 " II of 0.002 to O. 003g. Thus, the responses of the soil-pile- II II structure system were essentially within the linear range. il II i1 Ii Analysis Procedure 11

The apartment building was modeled by five lumped masses

II connected by beams. The mass and spr ing data for the building

II were published in the report by the Japan Residence Corporation

Ii (1979), Plate 33. These data were used in our analysis with the " I' I: analytic

for all

model on Plate 25. Modal damping was assumed 4 percent

modes. The mass of the soil enclosed by the embedded

Ii Ii I' Ii H I' Ii

II il !: II !I p ;\

frame was computed and treated as a !I II

II ii

II

portion of the foundation

base mass

embedded

subgrade

in our analysis. The lateral soil resistance to the

portion of the foundation frame was estimated using a

reaction theory and was modeled by a base spring. The

II

:1 ~ f

II I,

l)

h~~~;"-~~~Lr;\3;:l :;:XGL'J[E:?S =~--=::-:============~ii

30

values of the base mass and the base spring used in our analysis

are shown also on Plate 33.

The foundation soil above -25.5 m was discretized into ten

layers and the variation of soil properties was included in the

analysis. Free-field soil motion was computed for this soil

column of 25.5-m thickness by specifying observed seismic records

at -25.5-m depth. Only vertically propagating shear waves were

included in the free-field analysis. Material damping of the

soil layers was assumed 3 percent.

The piles also were discretized into ten segments. '/

The pile d ;1 i[ foundation has more than 170 piles. To simplify our analysis, we ii 1! replaced each group of four piles by an equivalent pile. Bending Ii

as well as axial stiffnesses of the four piles were assigned for

this equivalent pile. But, the diameter of the equivalent pile

was assumed 100 cm, from our experience, that equals 75 percent

of the center-to-center distance of the 4-pile group. The

flexural and axial rigidities of the equivalent pile were 7.6 x il !\

1010kgf-cm2 and 3.0 x 109 kgf. Unit weight of the equivalent :1

pile was 1. 7 gf/cm3 • No damping was cons idered for the piles. Ii '!

Although the building is supported by 44, 4-pile groups, these ::

pil~s were replaced by regularly spaced 42 equivalent piles.

The observational data used here were for seismic events near ;

Tokyo

(1974)

with

and

epicenters at the south coast of the Izu Peninsula 11 ii I! II

the southwest of the Ibaraki Prefecture (1975). The

epicentral distances, from the observational pOint, were about

. 155 krn for the Izu event and 55 km for the Ibaraki event. Thus,

it the observ;d data for

11

Ii Ii

:j

" :1 jl

j1 j;

Ii ,I \' \1 II 'I

it II 'I Ii II Ii ii Ii

frequency

histories

Plate 34.

components

for these

the Izu event had considerably more low

than the Ibaraki event. Acceleration time

events at the pile tip level are shown on

Although the observed records included about 30-second

shaking, major shaking was within the first 15 seconds. Thus, we

used only the first l6-second data for our analysis. The maximum

frequency used in our analysis was 4 HZ, since major dynamic

amplification of the system occurs below this frequency.

II l'==============- ;;'JcC'L~:'~/dJJ ~:\!G;f,.5;:::2f:;S ~

!; L il lj Ii II Ii ii il " I II II 'I II

!I Ii 11 Ii Ii Ii

31

Analysis Results

Comparison for the 1974 Izu Event. Plate 35 compares the

observed and predicted acceleration time histories at the 14th

floor and the base of the apartment building. Slight difference

in the predicted and observed motions may be due to the following

reasons. The observed motions do not include the very beginning

of the responses. The observed motions include the frequency

components up to 12.5 Hz, whereas the predicted motions include

frequency components up to 4.0 Hz. Estimated damping values for

the structure and the soil layers can be slightly different from

those of the field condition. The predicted motions, however,

il are in reasonable agreement with the observed motions. i To evaluate the predicted motions in more detail. we computed

Ii acceleration response spectra of the predicted and observed Ii II motions. The results are shown on Plate 36. The predicted and

]! observed results are in good agreement. This indicates that the I' Ii Ii predicted motions have essentially the same frequency andampli-

tude characteristics as those of the observed motions. The ac­

II celeration spectra of the motions at the top of the building have

:1 a pronounced peak at 1. 45 Hz that corresponds to the fundamental

11 natural frequency of the building itself, and do not possess

!I peaks at around 1. 7 Hz that is the fundamental natural frequency

! of the soil layer. The building base moved essentially with the i

; free field and a strong peak occurs at the fundamental natural ! ~ ': frequency of the soil layer. A slight input power loss is ob-ii

served at the building base level: the predicted response spec-ii il trum of the building base is slightly lower than that of the

II free-field surface. The effects, however, are not pronounced. A

:1 similar phenomenon was observed for the pile motions at 16 m

Ii below the ground level. H If Ii Comparison for the 1975 Ibaraki Event. Similar comparisons !l I' were made for the seismic records of the Ibaraki Event. Response 'I Ii ,I

II :1 11 il

!I

spectra computed

on Plate

for the predicted and observed motions are

compared

reproduced

building

by

base

the

level

37. The motion at the 14th floor is well

program PILES. The predicted motions at the

and of the pile, however, appear somewhat

32

different in nature from the observed motions. The response

spectra of the observed motion at the building base at fre­

quencies less than 1.0 Hz are about four times larger than those

of the motion within the pile. On the other hand, we see only a

slight difference, at this freuency range, in the response

spectra of the computed motions at these two points. Therefore,

the differences between the predicted and the observed responses

at the building base and of the pile are due to the difference in

the predicted and observed free-field behavior. The observed

ground surface motion involves more low frequency components than

the predicted motion, and it does not show clearly the peak

corresponding to the fundamental natural frequency of the soil

layer at 1.7 Hz. The assumption of the vertically propagating

shear wav~s in our analysis appears inappropriate to evaluate the

free-field behavior for this event. The large dynamic amplifi­

cation near the ground surface indicates that, surface waves,

such as Rayleigh and Love waves, might be dominating the site

response. In spite of the difference of the motions due to the

;: difference in the free-field behavior, the predicted motions did

II explain the general response character istics of the soil-pile­ii Ii structure system. \: II Summary

II Performance of the pile-group method "PILES" was evaluated in i! II the light of seismic response observational data. The study

Ii showed that the program PILES reproduced satisfactorily the Ii Ii seismic response character istics of the 14-story building sup-i II ported on piles. This indicates that the dynamic stiffness and

II damping character istics of the pile group were evaluated cor­

II rectly using the procedure. Thus, the method may be effective

!I ~ ! 1i

Ii :1

for practical problems to evaluate the seismic response charac­

teristics of pile-supported structures.

Through the analysis of the Ibaraki event, we encountered a

II diff iculty of reproducing correctly the free-f ield behavior.

i/ Since most piles move together with soil except probably near the it Ii ground surface, a correct assessment of the free-f ield motion is

Ii a key to the seismic response evaluation of pile-supported

, ~.1t:CL::'::LL;:'~i~D :::;\~Gn\lE:~~~S

r

l

33

structure. The difference between the predicted and observed

free-field behavior for the Ibaraki event might be due to the

effects of surface waves. The proposed method can be modified to

incorporate any type of

become available.

seismic environments when such data

CONCLUDING COMMENTS

I I

:1

i The present study illustrated that pile-group effects are

I strongly frequency~dependent. Pile-group stiffness can be larger

I than the direct summation of single pile stiffnesses, and it also

i

'I

can be negative. Damping of a pile group is generally smaller i,:'1

than that of an equivalent surface footing whose dimensions are Ii

equivalent to the outer dimensions of the pile group. These ii

il II II results cannot be der ived from static theories that have been I

11

Ii Ii often used to predict the dynamic pile-group effects. I'

Use of the i

Ii pile-group effects from a static theory can lead to a serious

assessing the dynamic pile-group effects. A rational

is required to assess correctly the dynamic pile-group

'I :, I, ii error in I : li ,I

:1 II procedure Ii II effects. II [I

:1 Ii

proposed by other Ii Several procedures have been II Ii Ii investigators

empirical

and used to perform design analyses of pile Ii I foundations under

procedure

(Parmelee,

is based

Penzien,

dynamic loading. The most commonly used Ii I'

on the concept of the effective soil mass Ii !:

Scheffey, Seed, and Thiers, 1964) that is I assumed to vibrate with piles. The effective mass accounts for I

i the inertia force generated in soil due to pile vibration, and it

represents the dynamic nature of pile-group effects. No pro- i

cedure, however, is present to account for the radiation damping

associated with soil-pile interaction. Based on this concept,

many investigators studied seismic response problems of pile

groups. Seismic responses of pile-supported structures obtained

from this concept were in general agreement with observed re­

sponses (e.g. Japan Residence Corporation, 1979, and Ohta, Niwa,

and Ueno, 1978). These studies suggested that the stiffness of a

pile

the

group is about the same as static pile-group stiffness and

radiation damping may be neglected for most seismic response

~~~~==~========================================== '=r1 !I

34 :1

analyses. From this point of view, the case study presented in

this report may not fully justify the value of the study. The

value of the study is in the findings of potential significance

of dynamic pile-group effects and in the development of the

rational procedure that can be used to quantify the dynamic

pile-group effects. The method can be used to evaluate or

confirm the results obtained from rather simple empirical

approaches.

Although the present study clarified the fundamental aspects

:1 p Ii I:

:1 of

II the pile-group effects and provided a method to analyze com-

L II Ii

II. il II II Ii

Ii 'I II

plex soil-pile-structure interaction, several important topics

remain unsolved. The theories in the present study are limited

to the linear range. Also, the pile-group effects are strongly

frequency-dependent. Thus, the results cannot be extended

directly to the time-domain analyses of pile groups that involve

several forms of nonlinearity. Development of a procedure to

determine soil-pile springs for nonlinear beam-on-Winkler models

li of pile groups may be an important subject of future research. :\

, ii 1) ;[ Most piles are known to follow the deformation of free-f ield

Ii r II if I: jI

"' 1: il

:1 !I ;1 I' 11 11

soils. Correct assessment of free-field soil response is a key Ii "

factor to the successful prediction of seismic sOil-pile- :1

structure interaction. q

Future effort should be directed to'

develop numerical procedures that can incorporate any form of

seismic environment including surface waves.

Finally an extensive effort, of course, is required to

collect and generate field observational data that can be used to d ,I calibrate numer ical methods currently available. I

:!

Ii I' Ii

"

Ii

i; ii

"

Ii i:

II ii "

;1 !!

'I Lqt:ct~~~~i~f\!:J ~:\J3i;\Jr.::~f?S ========~~~--=======----===---.---.:----=:::::=::::::=:-== ~I

ILL U S T RAT ION S

;1 II 1.'1 ~ I'

I

I !

!

I I II

I II I I

l!::============= McCc.E!"L:lND f;:NGINEERS =-=_-=============:!!II

FLEXURAL RIGIDITY, Ell

RIGID FOUNDATION

H

EI2

y x

G s = SHEAR MODULUS OF SOil P = MASS DENSITY OF SOil V = POISSON'S RATIO OF SOil D = DAMPING RATIO OF SOil EI = flEXURAL RIGIDITY OF PilE ra = RADIUS OF PilE H = HEIGHT OF SOIL LAYER

mp = MASS OF UNIT PilE LENGTH

RIGID BASE

ANALYTIC MODEL OF A PILE-SUPPORTED STRUCTURE

McCLELLAND ENGINEERS

36

PLATE 1

McCLELLAND ENGIIIIEERS

RANGE OF VALUES

PILE SLENDERNESS RATIO (H12rol 33-133

SPACING RATIO (S12rol 2-100

FREQUENCY RATIO (fffr) 0-80

PILE FLEXIBILITY FACTOR (EIIEsH4) 10-6-10-3

PILE COMPRESSIBILITY FACTOR (EA/EsH2) 10-2-1

POISSON'S RATIO OF SOil (V) 0.30-0.45

RANGES OF NONDIMENSIONAL PARAMETERS FOR PARAMETER STUDY

PLATE 2

McCLELLAND ENGINEERS

z •

Y

yl

z

i-th PILE

Fi(z) = SUM OF fi AT z

\ SOIL-PILE STRESS fl(x.y.z.)

Xl x

SOIL-PILE STRESS

fi(x.y.z.)

SOIL-PILE INTERFACE STRESS

PLATE 3

y i-th PILE

yl

Xl Z ., ..... ___ ---'r..-.._ .......... X

(a) UNIFORM SOIL-PILE STRESS PATTERN

y i-th PILE

yl

Xl

z~·~--------------~~x

z

(b) BOUSSINESQ SOIL-PILE STRESS PATTERN 9

SOIL-PILE INTERFACE STRESSES FOR ANALYSIS

McCLELLAND ENGINEERS PLATE 4

McCLELLAND ENGINEERS

j Y i-th PilE

T yl ~~ PilE 1--8 WID TH

1 z . Xl

-'" x

REPRESENTATION OF A PILE SECTION BY DISCRETE ELEMENTS

PLATE 5

e ........ :2

c:c Q -'.:Ii

e ........ :2

r--

McCLELLAND ENG I NEE R 5

Q -U 3

6

5

4

3

2

1

0

120

100

80

60

40

20

0

4 KAGAWA AND -- - - --...;--- KRAFT (1981) -... .........

......... 3

BOUSSINESQ DISTRIBUTION

2

FIXED-HEAD PILE KR = 10-6

H/Zfo c 67 UNIFORM 1 II = 0.45 DISTRIBUTION {3 = 005 WI FACTOR = 0.85

0 0 20 40 60 80 100

FREOUENCY RATIO, flf r

8 FIXED-HEAD PILE KAGAWA AND

KR = 10-6 KRAFT (1981) ~/ H/2fo = 67

./ II = 0.45 6 (3 : 0.05 ./

./ BDUSSINESO ./ DISTRIBUTION /'

4

DISTRIBUTION

2 DISTRIBUTION

0 0 20 40 60 80 100

FREOUENCY RATIO, f/fr

SINGLE-PILE STIFFNESS AND DAMPING FROM SEVERAL METHODS

if/

l-"'-........ CI)

= ...I

r--Q -'.:Ii

I-"'-........ CI) = ...I

,...., C -t.:)

3

PLATE 6'

McCLELLAND ENGINEERS

4

FIXED-HEAD PILE - KR = 10-6

?"O 3 H/2ro = 67

l"Ci v = 0.45 ~ = 0.05

KAGAWA AND ~ .f. KRAFT (1981) 0 2 BOUSSINESQ

DISTRIBUTION l-e:: --- ..... -c:r CI..

..... 1 \ U'If"M c:r DISTRIBUTION w WI FACTOR = 0.85 c:

_ UNIFORM DISTRIBUTION

0 0 20 40 60 80 100

FREOUENCY RATIO, f/fr

4

l~ FIXED·HEAD PilE KR = 10.6 KAGAWA AND /

('<i H/2ro = 67 KRAFT (1981) ~ 3 v = 0.45

/ (t = 0.05 u.. / 0

I- BOUSSINESO / c: 2 DISTRIBUTION c:r CI..

>-\.. UNIfO •• c: DISTRIBUTION c:r

2 1 W I FACTOR = 0.85

c,:) UNIFORM <C

:! DISTRIBUTION

0 0 20 40 60 80 100

FREQUENCY RATIO, f/fr

SINGLE-PILE SOIL-PILE SPRING COEFFICIENTS FROM SEVERAL METHODS

. .PLATE 7

McCLELLAND ENGINEERS

en 1.5 --~-..-~-----.-.,.......,..-~--.----..-~ w ..J

cs:: u.. o

c..o ~z

g; x t.:Iw

..J -c:cc.. o u..w

..J

::c: ~ 0.5 -en c:c o u..

2 PilES (e = 0°)

) Sl2ro

---0- =16

--- __ . l2 ------- UNIFORM DISTRIBUTION

- - - BOUSSINESQ DISTRIBUTION _.- SIMULATING EXACT SOlUTION

O~L-~~~~~~~~~~~~

en w ..J -CI..

u.. o

c.. 0 1.0 ~:2

~ x t.:Iw

..J -c:cc.. o u..w

(.) cE 0.5 :2 en c:c o u..

o 20 40 60

FREOUENCY RATIO. f/fr

S12ro = 2

~~~~-:~ 2 PilES (() = 0°)

- UNIFORM DISTRIBUTION

- - - BOUSSINESQ DISTRIBUTION _.- SIMUlATING EXACT SOLUTION

O~~~~~~~~~~~~~~~

o 20 40 60 FREOUENCY RATIO. tlfr

2-PILE INTERACTION FOR DIFFERENT SOIL-PILE STRESS PATTERNS

PLATE 8

c: ~ 2.0 r----r-----,----r---,------,----, u <t u..

a::: Q ~ u <t u..

iii!: Q

~ u w ..... I.&. w Q

Q. ::;, Q a::: t.:I

1.0 ~~~9U7~~S

~-->----....... r r-----..,

PRESENT 22 GROUP STUDY S!2ro = 2

H12ro = 67 flfr = 0

o~--~-~-~-------~--~--~

10-7 10-5 10-3 10-1

FLEXIBILITY FACTOR, KR

3.0

2.0 ~~~~

-::Or ~lOS (1979)

1.0 22 GROUP

S!2ro = 2 H!2ro = 67

tlfr = 16

0

10-7 10-5 10-3 10-1

FLEXIBILITY FACTOR, KR

COMPARISON WITH POULOS' GROUP DEFLECTION FACTORS

McCLELLAND ENGINEERS PLATE 9

l-Z w :E w Co.:)

<C .... Q.. CI) -Q

.... Q CI)

McCLELLAND ENGINEERS

I-Z w :E w Co.:) <C .... Q. CI) -Q

w .... s::

1.0

GROUND SURFACE SOIL DISPLACEMENT

0.5

0

-0. 5 '--'--'-......... ~~--.I.....I....."'--'--L.....L-.-I--.I......J-~ ........... ...I-.I.-.L.....I-...IL....I

o 10 20 30 40 50

DlSTANCE/2ro

SOIL MOTIONS DUE TO PILE VIBRATION

PLATE 10

'" IoU -' c: ..... 2.0 Q 2 PILES

~ 0 • FIXED HEAD ~ z L:,. 0 x • e = Dc c:: • t!I IoU

-' 1.0 0 c:: c: 0 CI ..... IoU

-' ::.:: t!I I LATERAL I 2

V;

c:: 0 0 ..... ::.:: 1 5 10 50 100

SPACING RATIO, S/2ro en IoU -' c: 2.0 ..... 0

~ 0 I LATERAL I ~ z 0 x c:: t!I IoU ....

1.0 c:: ~ Q ..... IoU flfr -' Co.) t!I

Z L:,. 0.001 0 20 V;

10 CI 40 • c:: 0 0 ..... Co.)

1 5 10 50 100

SPACING RATIO, S12ro en IoU -' c: 2.0 ..... 0

~ 0 2 PILES

~ z Q

x c::

~.~ t!I IoU 1.0 -'

c:: c: L:,. 0 ..... ... • .... ::.:: t!I I VERTICAL I z

iii c:: 0 0 ..... 1 5 10 50 100 ::.::

SPACING RATIO, S12ro en ... -' c: 2.0 ..... Q

~ 0

~ ~ z 0 x c:: t!I IoU

c:: ;: 1.0 6 0 .... ... .... Co.) t!I

Z V;

c:: 0 .... 5 10 50 100 Co.)

SPACING RATIO, S12ro

EFFECTS OF S/2ro AND FREQUENCY ON 2-PILE INTERACTION

McCLELLAND eNGINEERS

'16

PLATE 11

McCLELLAND EIIIGIIIIEERS

en 1.5 w ..J

I KR = 10-61 - 2 PILES Q..

u.. ( e :: 0°) 0

Q.. 0 1.0 ~ :2 0 x ca::: c,:, W

..J -ca::: Q.. =0=-0 azCih ~} 2 u.. W

..I :::.=:: c,:,

:2 0.5 H/2ro

en I LATERAL I 0--0 33 ca::: • • 67 0 u.. o--a 133 :::.=:: 0

0 20 40 60 FREQUENCY RATIO, flfr

en 1.5 w ..J -Q..

u.. 0

Q.. 0 1.0 ~ :2 0 x ca::: c,:, w I KR = 10-6 \

..J -ca::: CI. 0 u.. w

2 PilES ..J 0.5 ~ c,:, ( e :: 0°) H/2ro :2 -en 0--0 33 c:c I LATERAL I • • 67 0 u.. o--a 133 ~ 0

0 20 40 60 FREQUENCY RATIO, fffr

EFFECTS OF H/2ro ON 2-PILE INTERACTION FOR LATERAL MODE

1f7

PLATE 12

Cf) 1.5 .---.....----.----.---,---r---,--,----,~__r-__, U.J -' c..

a: o ~

2 PILES (6= 0°)

--b- -0- --0- _ ~ ____ L S12rO = 2

---~

:1.5 IRR=366\ 0 H/2ro

33 I LATERAL I 61

o~~-~-~--~--~--~--~----~--~ o 0.5 1.0

NON DIMENSIONAL FREQUENCY, wro/Vs

Cf) 1. 5 ,----,---,.----,..--,---,---...,---.,..---r----,---, U.J -' Q: LI­o

c..O ::;:)2

~ X c,:,w

-' a:Q: o ~ w

-' c.,)c,:,

McCLELLAND ENG I NEE R S

2 Cf)

a: o ~

0.5 H12ro

IRR = 366\ 0 33

• 67 • I LATERAL I 0 133

o~~--~--~--~--~-~-~----~--~ o 0.5

NONDIMENSIONAL FREQUENCY, wro/Vs

EFFECTS OF H/2ro ON 2-PILE INTERACTION FOR LATERAL MODE

1.0

PLATE 13

McCLELLAND ENG I NEE R S

Q.. ~ c ce c,:,

ce C u..

::.:::

CI) W ...I

Q..

u.. c

C 2: x w ...I -Q.. w ...I c,:, 2: -CI)

ce C u..

::.:::

u.. C

Q..c ~2

~ x c,:,w

...I -ceQ.. C u..w

...I

2.0 I I I -1 l I I I I

I VERTICAL I = 2 PILES r

-1.5 f- -

-I-

-e/Sl2ro = 8 --

.... "c'" -1.0 r- 9" " ~_ ,;:re ........ -

j ~ .. / -I r--6--(5-, -

H/2ro -S/2ro = 2 -

0.5 - 0 33 -

IKe:; 243 1 • 67 - -0 133

0 I I I I I I I I I

0 0.5 1.0 NONDIMENSIONAl FREQUENCY, wro/Vs

2.0 -rr T

I- 2 PilES r r

------

----(..) c,:, _ o

• o

33

67

133

-2: C;; 0.5- -ce c u..

~ r-,--Kc-:;-2-4-3'""1 -

-O~I---~I-~I-~I-~I_~I_~I~--~I_~I~-o 0.5 1.0 NONDIMENSIONAl FREQUENCY, wro/Vs

EFFECTS OF H/2ro ON 2-PILE INTERACTION FOR VERTICAL MODE

PLATE 14

McCLELLAND ENGINEERS

c.. :l 0 c: c,:)

c: 0 1.1-

~

c.. :l 0 c: c,:)

CC 0 1.1-

c.J

CI) w ...J -c.. 1.1-0

0 Z x W ...J -c.. W ...J c,:) z CI)

c: 0 1.1-

~

CI) w ...J -c.. 1.1-0

0 Z x w ...J -c.. W ~ c,:)

Z CI)

cc 0 1.1-

c.J

1.5

2 PILES ( e = 0°)

Sl2ro =8

0.5 -.

Sl2ro = 2 KR

I LATERAL I ...... 3.7 x 102

0--0 3.7 x 10 5

0 0 0.5

NONDIMENSIONAL FREOUENCY, wro/Vs

1.5

2 PILES ( e = 0°)

S12ro = 2

0.5 -. KR

I LATERAL I ...... 3.7 x 102

0-03.7 x 105

0 0 0.5

NONDI MENSIONAl FREOUENCY, wrO/VS

EFFECTS OF KR ON 2-PILE INTERACTION FOR LATERAL MODE

So

1.0

1.0

PLATE 15

0

McCLELLAND ENGINEERS

c.. :::l 0 a: t:)

a: 0 ~

:::.=::

c.. :::l Q a: t:)

a: Q ~

~

51

CI) 2.0

IoU ...I 2 PILES -c.. ~

0 1.5 0 Z x IoU ...I -c.. -IoU Kc ...I t:) z • 243 CI) 0.5 a: I VERTICAL I 0 1012 0 ~ 0 2024 :::.=:: 0

0 0.5 1.0 NONDIMENSIONAl FREOUENCY, wro/Vs

CI) 2.0 &.U

2 ...I PILES -c.. ~

Q 1.5 c:::i Z x

IoU ...I 1.0 -c.. &.U -...I Kc t:) z CI) 0.5 • 243

a: I VERTICAL I 0 1012 Q ~ 0 2024 ~

0 0 0.5 1.0

NONDIMESIONAl FREOUENCY, wro/Vs

....... EFFECTS OF KC ON 2-PILE INTERACTION

FOR VERTICAL MODE

PLATE 16

McCLELLAND ENG I NEE "R S

y

y

(0, CON~TANT)

__ 1--- --- PllE2

~~, ~ '~(CONSTANT' 0)

PilE 1 1/ \ x ( DIRECTIONAL J

ANGLE, (J /1 ... _ x

DIRECTIONAL ANGLE FOR 2-PILES

PLATE 17

McCLELLAND ENGINEERS

2.0

2 PILES en LATERAL I..a -' Q: 1.5 ~ Q

Q. c:i := z Q x a:: c.::J U.I

-' a:: Q: Q ~ U.I

-' ::.::: c.::J ~ POSITION OF en

CONSTANT 2nd PILE a:: 0.5 IN En. 28 X V Q ----~ ----..

4 4 0

::.::: ... - ... 0

0----0 16

16 0 0---<> 0

0 0 20 40 60

FREQUENCY RATIO, flfr

2.0

2 PILES --en LATERAL ..... .... Q: 1.5 ~ Q

Q. c:i := z Q x a:: c.::J U.I \ .... a:: ii: \ Q ~ UoI \ I .... (.) c.::J

~-P z (i) POSITION OF

0.5 CONSTANT 2nd PILE a:: IN EO. 28 X V Q ---... ~ 4 0 .. - .... 4

0 2 (.)

0---<> 16 16 0

0---0 0 8

0 0 20 40 60

FREQUENCY RATIO, f/fr

DIRECTIONALITY OF 2-PILE INTERACTION

53

PLATE 18

McCLELLAND ENG I NEE R S

~ :;I 0 c:

'"' c: 0 ~

::.::

~ :;I 0 c: c..:l

c: 0 ~

U

51 CI) 1.5 UJ -' 2 x 2 GROUP s/2ro ~

~ LATERAL L:::. 2 0

FIXED HEAD • 4 0 1.0 0 8 2

CJ 16 x UJ -' ~

UJ -'

'"' 0.5 2 CI)

c: 0 ~

::.:: 0 0 20 40 60

FREQUENCY RATIO, tlfr

2.0

2 x 2 GROUP CI) LATERAL

S12ro UJ -' FIXED HEAD c..

~

0

0 2 X

UJ -' ~

UJ -' c..:l 2 CI)

c: 0 ~

U

0 0 20 40 60

FREQUENCY RATIO, tlfr

PILE-GROUP EFFECTS FOR 2 X 2 GROUP

PLATE 19

McCLELLAND ENGINEERS

Q,. ~ 0 c:: ~

c:: 0 u..

::z:::

c.. ~ 0 c:: ~

c:: 0 ..... ~

55

Cf) 2.0 w ...l 3 x 3 GROUP -c..

LATERAL u.. FIXED HEAD 0

0 1.0 :2

x W ...l -c..

W ...l ~ 0 :2 -Cf)

c:: 0 • • 4 u..

0 0 8 ::z:::

-1.0 0 20 40 60

FREQUENCY RATIO, flfr

4.0

~ x 3 GROUP Cf)

LATERAL w S/2ro ...l - FIXED HEAD c.. 6 2 ... 3.0 • • 4 0

0 0 0 8 :2 x

W ...l -c..

W ...l ~ ;:: -Cf)

c:: 0 ... ~

O~~~~~~~---~~~~~-J

o 20 40 60

FREQUENCY RATIO, flfr

PILE-GROUP EFFECTS FOR 3 x 3 GROUP

PLATE 20

McCLELLAND ENG I NEE R S

B.O

s-6.0

l- 2 x 2 GROUP c:t (S121 0 = 4)

~ '- 4.0 u 3

2.0

00 20 40 60

FREOUENCY RATIO, flfr

6.0

= SURFACE

4.0 FOOTING '> ~

,/' ",

~ '- 2.0 u 3

(SI2,o = 8)

0 0 20 40 60

FREOUENCY RATIO, flf r

6.0

= 4.0 3 x 3 GROUP

l-(S/2,o = 8) c:t

:. '-u 3

FREOUENCY RATIO, flfr

COMPARISON OF DAMPING FOR PILE GROUPS AND SURFACE FOOTINGS

56

PLATE 21

McCLELLAND ENGINEERS

cc cz: .... :z: en

Q cz: .... :z: ...:. ...J g:

cc cz: .... :z: en

Q cz: IoU

~ .... ...J g:

ct: cz: .... :z: en Q cz: .... :z: ...:. ~

a:

57

2.0

3 x 3 GROUP (S/2r 0 = 2, FIXED HEAD)

CC (4) cz: 1.5

"" :z: en

Q (3)

cz: .... :z: ...:. 1.0 ~ (2) g: .... It..

(1) ~ cz:

(2) cc (1) IoU 0.5 0 :> cz:

FREQUENCY RATIO. f/fr

cc cz: IoU :z: en

Q 1.0 cz: .... :z: ...:. ~

g: .... 0.5 (4) C!I cz: cc w :>

3 x 3 GROUP (SI2, 0 = 4, FIXED HEAD) cz:

0 0 20 40 60 80

FREQUENCY RATIO. Ufr

1.5

ct: (4) cz: u.s :z: en

Q 1.0 cz: .... ~ .... ...J

a: u.s 0.5 ~

'" cc .... :> :I x 3 GROUP (Sl2r 0 = 8, FIXED HEAD)

'" 0

0 20 40 60 80

FREQUENCY RATIO. flfr

DISTRIBUTION OF PILE-HEAD SHEAR

PLATE 22

McCLELLAND ENG I NEE A 5

2.0

3 '3 GROUP (SI2, 0 = 2. FIXED HEAD)

... z .... 1.5 :iE ... c z :iE "'" (1) :iE c Q

:iE c:t

"'" Q =:: 1.0 (3)

"'" c:t -' ...... is: ::: (2) uJ ...... -' t:l is: c:t (\)

c:;

0 ...... 0.5 (4) :> c:t

(3)

~

0 0 20 40 60 80

FREQUENCY RATIO, f/ft

1.5 ... z ......

... :iE c z :is ...... 1.0 :is

c Q

:is c:t ...... :::

Q uJ c:t -' (4) .... is: :: uJ .... 0.5 -' t:l is: c:t c:;

"'" 3 x 3 GROUP (SI2,o = 4. FIXED HEAD) :> c:t

0 0 20 40 60 80

FREOUENCY RATIO, flf t

1.5 ... z ....

... :is (4) c z :is U..I

:is Q 1.0 c

:iE < • U..I ::

c uJ < -' ...... is: :: uJ ...... 0.5 -' t:l is: < c:;

...... :> < 3 x 3 GROUP (SI2,o = 8. FIXED HEAD)

0 0 20 40 60 80

FREOUENCY RATIO, flf r

DISTRIBUTION OF PILE-HEAD MOMENT

S$

PLATE 23

2.0

"'" ...I f Ifr 2 PILES

Q. Q,. • 0.001

:;:) FIXED HEAD 0 0 11)

a: "'" 0 20 e = 90° ...I t:I t:I A 41)

a: iii!!: 1.0 -0 V)

u.. a:: ::e _ 0

lc.o u.. ::e_ 1'0

0 1 5 10 50 100

SPACING RATIO, S/2ro

2.0

"'" Q,. .....

:;:) Ei: FIXED HEAD

0 a: w t:I ....I

t:I tlfr :2 1.0 a:: • 0.001 0 V)

u.. 0 10 a: 0 20 ::eN 0

A 40 1'0 u..

::eN lc.o

0 1 5 10 50 100

SPACING RATIO, S/2ro

PilE-GROUP EFFECTS ON SOil-PilE SPRING COEFFICIENTS

McCLELLAND ENG I NEE R S PLATE 24

McCLELLAND ENG I NEE R S

FLEXURAL RIGIDITY, Ell

EI2

RIGID FOUNDATION ~ Eln hn

'.<1' .' :.' p'.' " .. '?: : .. : .. -". '. co· •.

(llAYERI/{~:=111 ~ EI'1 ::i:ii iiJ ___ _

LAVER 2 :!{ EI' 2 -----.~--!

• iiii· •

-lA-V-~R-J. --L'ol i@ ..

y x

ANALYTIC MODEL OF A PILE-SUPPORTED STRUCTURE

60

PLATE 25

McCLELLAND ENGINEERS

I III I I I

~/ ABSOLUTE REFERENCE AXIS

CONNECTED TO FREE-FIELD SOIL DISPLACEMENT

SOIL-PILE SPRING AND DASH POT

PLATE 26

:::--

McCLELLAND ENGINEERS

I'¢

..,: Z w -(,,) -... ... W 0 (,,)

(,:,

z -a: a-U)

3~--~---r--~--~----r---~--~--~

1

0 1

+25%, ~ HOMOGENEOUS

" " SOIL CONDITION ~ ........

--.... ---• •

CLAV SITE

102 104 106 108 ...... 4

LOCAL PILE FLEXIBIL TV, KR = EI/(Esro )

AVERAGE SOIL-PILE SPRING COEFFICIENT FOR LATERAL MODE

PLATE 27

>--

McCLELLAND ENGINEERS

il¢

~ 2 w -(..) -..... ..... w 0 (..)

c,:, 2 -a:: a.. CI)

3~------~------~--------~------~

2

HOMOGENEOUS SOIL CONDITION

1

0 1 10 102 103

LOCAL PILE COMPRESSIBllTY, -- 2 Kc = EA/(Esro )

AVERAGE SOIL-PILE SPRING COEFFICIENT FOR VERTICAL MODE

104

PLATE 28

McCLELLAND ENG I NEE R S

2.0

/ ' / / .>:, - ,r:f ?"O ./ ,/ 'e-_ ... / "

l~ 1.0 /P /,/ 7 • THEORETICAL

u.. RESULTS Q

I- 0 SIMPLIFIED CC PROCEDURE ~ Q..

.... ~ w CC

- - - 22 GROUP (S/2ro :: 8) 32 GROUP (S1210 = 2)

-1.0 0 20 40 60

FREOUENCY RATIO, f/tr

3.0

- - - 22 GROUP (S/210 = 8)

l~ 32 GROUP (S/21 0 = 2)

l~ 2.0 • THEORETICAL

u.. RESULTS Q

0 SIMPLIFIED I- PROCEDURE cc ~ Q..

> 1.0 cc ~ 2 ~ ~ :2

0 0 20 40 60

fRE~UENCY RATIO, t/fr

PERFORMANCE OF APPROXIMATE METHOD

PLATE 29

McCLELLAND ENG I NEE R 5

NO

READ INPUT DATA

YES READ STRUCTURAL PROPERTIES

NO

DETERMINE SOIL-PILE SPRINGS AND DASHPOTS

COMPUTE PILE RESPONSE TO UNIT LOAD

SOLVE FOR PilE-CAP RESPONSE

READ E.n. MOTION

COMPUTE FREE-FielD RESPONSE

COMPUTE MODAL STRUCTURAL RESPONSE

NUMERICAL SCHEMES FOR PROGRAM PILES

65

PLATE 30

McCLELLAND ENGINEERS

r-

I-I-l-~

.-""-.... -,.... ----~ U U U

I~

I-

... --, r--""1 /,ACCElEROMETER

~ 1 r-- l-~

I-I-I-I- T .. I-. I-

8.85 m 3 I-I-I-I-I-

or U H U U I2tUUU~

78.5 m -/ SECTION

78.5 m ·1

PILE LAYOUT

14-STORY BUILDING FOR CASE STUDY

66

r"T"" n J!I -.

i I I

J J!

I J

I I

I I .- I I

I J •

1;.2 ~I

PLATE 31

GROUND """ Vs(m/s)

•

14-STORY APARTMENT BUILDING

67

t

38.85 m

LEVEL ~ 0 600 • ~~~----__ ~~ __ ~ ____ ~~~K-__ ~ ____ -+ __ _ 11/.£/11 I I r-LL 0

FILL ~ 'd 11 SAND ~~~ ~:~ 16.0 m

SILT c CD -SILTY

SAND SILT c

c CLAY

N

'- ACCELEROMETER

SAND c CD

GRAVEL Ln

SOIL CONDITIONS AND SEISMIC OBSERVATIONAL POINTS

McCLELLAND ENG I NEE R S PLATE 32

McCLELLAND ENGINEERS

MASS SPRING STORY (kgf .s2/cm) (106 kgf / em)

1 1967 0.66

2 2691 0.61

3 2450 2.54

4 2502 6.13

5 3812 12.48

BASE MASS = 2903 kgf. s2/em

BASE SPRING = 8.2 x 106 kgf /em

HEIGHT (em)

1055

785

805

810

430

STRUCTURAL PROPERTIES FOR CASE STUDY

PLATE 33

IZU EVENT (1974)

-4~~~~~~~~~~~~~~~~L-~~

2 C i= 0 < c::: IoU ...I IoU ~

~ -2

o 5 10 15 20 TIME, SECONDS

IBARAKI EVENT (1975)

-4~~~~~~~~~~~~~~~~~~~

McCLELLAND ENGINEERS

o 5 10 15

TIME, SECONDS

EARTHQUAKE MOTIONS AT PILE-TIP LEVEL FOR CASE STUDY

20

PLATE 34

McCLELLAND ENG I NEE A 5

40

... 20 c:r Co:)

Z Q

~ 0 J

c: I.lol .... u.I

'" :i ·20

·40

5

114th flOOR I

10 15 20 TIME. SECONDS

I BUILDING BASE I

- OBSERVED

---- PREDICTED

-400L....J..-.J.---'.-J-

5J.--l.--'--"--'-1.l...0 -.I.-...1...-..;1...-I...-::

1"='"5 -.I.--'--L...-.I--720

TIME. SECONDS

COMPUTED AND OBSERVED ACCELERATION TIME HISTORIES FOR IZU EVENT

PLATE 35

== Z Q

;::: <C a: ...., 0.5 -' ...., ~ ~ <C

vi co <C

TOP OF STRUCTURE

OBSERVED 0--0 COMPUTED

DAMPING'" 5%

Z Q ;::: <C a: ...., uj 0.05 ~ ~ <C

en CXI <C

-- OBSERVED 0--0 COMPUTED

FREE FIElD

....... COMPUTED

DAMPING" 5%

71

O~~JJ~~--~~~~~~-~~ O~Lw~--~~~~--~ 0.3

0.2

== Z Q ;::: <C a: ...., -' ...., Co) Co)

<C

vi CO <C

0 0.3

McCLELLAND ENGINEERS

1.0 5.0 10 lO O.l 1.0 5.0 10 30

FREQUENCY. Hz FREQUENCY. Hz

0.10 = STRUCTURAL BASE Z

--- OBSERVED Q

0--0 COMPUTED ;::: <C

FREf FIELD Q: ...., -'

..-. COMPUTED ...., ~ ~ <C

vi CO <C

1.0 5.0 10 30 1.0 5.0

FREQUENCY. Hz FREQUENCY. Hz

COMPUTED AND OBSERVED RESPONSE SPECTRA FOR IZU EVENT

10 30

PLATE 36

=n

Z Q

i= <C a:: .... 0.5 .... ..... Co.) Co.)

<C

cri CO <C

1.0

=-2 Q

i= <C c: ..... .... ..... Co.) Co.) <C

en CO <C

1.0

McCLELLAND ENGINEERS

, I

,

TOP OF STRUCTURE

OBSERVED 0--0 COMPUTED

DAMPING = 5%

5.0 to 50

FREQUENCY. Hz

-- OBSERVED

c:--o COMPUTED

FREE·FIElD SURFACE

~ COMPUTED

5.0 to 50

FREQUENCY, Hz

O. to =n

Z Q

i= <C a:: ..... 0.05 .... ..... '-" '-" <C

cri CO <C

O.tO =-2 Q

i= <C a:: ..... 0.05 .... ..... Co.) Co.)

<C

cri CO <C

1.0

1.0

5.0

WITHIN PilE

- OBSERVED

0--0 COMPUTED

FREE FIELD

_____ COMPUTED

10

FREQUENCY, Hz

OBSERVED MOTION AT PilE TIP

5.0 10

FREQUENCY, Hz

COMPUTED AND OBSERVED RESPONSE SPECTRA FOR IBARAKI EVENT

50

50

PLATE 37

Ii II I!

I' d II :I '[

i!

'i

I I

,j

:1

"

II .1 I

A P PEN D I X A

'I I,

.Ii

A-I

APPENDIX A: REFERENCES

Blaney, G. W., Kausel, E., and Roesset, J .M. (1976), "Dynamic Stiffness of Piles," Numerical Methods in Geomechanics, edited by C.S. Desai, Vol. II, pp. 1001-1012.

Building Research Institute (1976), Digitized Earthquake: Accel­erograms in a Soil-Structure System, Kenchiku Kenkyu shiryo, Vol. 12, Ministry of Contruction, Japan (in Japanese).

Fukuoka, M. (1966), "Damage to Civil Engineering Structure,"Soils and Foundations, Vol. 6, No.2, pp. 45-52.

Japan Residence Corporation (1979), Research on Seismic-Resistant Characteristics of High-Rise Apartment Buildings Based on Obser­vational Data, Report No. 79-064.

Housner, G.W. and Castellani, A. (1969), Discussion of "Compar­ison of Footing Vibration Tests with Theory'" by F.E. Richart, Jr. and R.V. Whitman, Journal, Soil Mechanics and Foundations Divi­sion, ASCE, Vol. 95, No. SM1, pp. 360-364.

Kachadoorian, R. (1968), "Effects of the Earthquake of March 27th, 1964 on the Alaska Highway System,"Geological Survey Pro- , fessional Paper 545-C, U.S. Department of Interior, Washington, ,I

:~:~wa. T. and Kraft, L.M., Jr. (1980a), ·Seismic p-y Responses :i of Flexible Piles", Journal, Geotechnical Engineering Division, j! ASCE, Vol. 106, No. GT8, pp. 899-918. !!

Kagawa, T. and Kraft, L.M., Jr. (1980b), "Lateral Load-Deflection Relationships of Piles Subjected to Dynamic Loadings," Soils and II

Ii Foundations, Vol. 20, No.4, pp. 19-36. !I

Kagawa, T. and Kraft, L.M., Jr. (1981), "Dynamic Characteristics "of Lateral Load-Def lection Relationships of Flexible Piles," I Journal, Earthquake Engineering and Structural Dynamics, Vol.

9, No. 1, pp. 53-68.

:1 :j Ii " !1 II H Ii

Ii Kobor i, T., Minai, R., and Baba, K. (1977), "Dynamic II a Later ally Loaded Pile," Proceedings, the Spec ialty II. 9th International Conference on Soil Mechanics and

J Engineering, TOkYo, pp. 175-180.

ii Behavior of il

Session 10, Foundation

II Kuh1emeyer, R. (1979) , "Static and Dynamic Laterally Loaded 'I Floating Piles," Journal, Geotechnical Engineering Division, i; ASeE, Vol. 105, No. GT2, pp. 289-304. Ii Ii Ii Liou, D.D. and Penzien, J. (1977), Seismic Analysis of an Off-!:';,I, shore Structure Supported on Pile Foundations, EERC Report 77-25,

Earthquake Engineering Research Center, University of California, , Berkeley. 'I

II ;'

ii

:1

II I ;

r Ii

A-2

r Nogami, T. and Novak, M. (1977), "Resistance of :i zontally Vibrating Pile," Journal, Earthquake II structural Dynamics, Vol. 5, No.3, pp. 249-26l.

Soil to a Hori­Engineering and

Ii Ogata, N. and Kotsubo, S. (1966), "Seismic Force Effect on Pile i, Foundation," Proceedings, Japan Earthquake Eng ineer ing Sympos ium, I Tokyo, Japan (in Japanese).

Ohta, T., Niwa, M., and Ueno, K. (1978), "Seismic Response Char­ii acteristics of Structure with Pile Foundation on Soft Subsoil !!

1: Layer," Proceedings, Japan Earthquake Engineering Symposium (in :1 Japanese).

,Parmalee, R.A., Penzien, J., Scheffey, C.F., Seed, H.B., and ii Thiers, G.R. (1964), Seismic Effects on Structures Supported on ji Piles Extending Through Deep Sensitive Clays, Report submitted to ~:".,',II the California State Division of Highways, SESM 64-2, University

of California, Berkeley.

11 !i Poulos, H. G. (1971) , "The Behavior of Laterally Loaded Piles: il I r -P ile Groups, 11 Journal, Soil Mechanics and Foundations Di vi­ii sion, ASCE, Vol. 97, No. SM5, pp. 733-751.

Poulos, H.G. (1979), "Group Factors for Pile-Deflection Esti­mation," Journal, Geotechnical Engineering Division, ASCE, Vol. 105, No. GT12, pp. 1489-1509.

:1 :: Prakash, S. and Chandrasekaran, V. (1973), IIp ile Foundations " \i under Dynamic Loads," Symposium on Behavior of Earth and Earth 'j Structures Subj ected to Earthquakes and other Dynamic Loads,

Roorkee, India, March, Vol.·l, pp. 165-173.

;! 1; Roesset, J .M. and Angelides, D. (1979), "Dynamic Stiffness of 'i Piles," Proceedings, Numerical Methods in Offshore Piling, In­j

ii stitute of Civil Engineers, London, May, pp. 57-63.

II :1 "

Seed, H.B. and Idriss, I.M. (1969), "Influence of Soil Conditions on Ground Motions during Earthquakes," Journal, Soil Mechanics and Foundations Division, ASCE, Vol. 95, No. SMl, pp. 99-137.

I"j' Sugimura, Y. (1975), "Earthquake Observation and Dynamic Analysis :1 of Pile-Supported Building," Proceedings, Japan Earthquake En­

gineering Symposium. I Ii Ii Tajimi, H. (1969), "Dynamic Analysis of a Structure Embedded in II an Elastic Stratum," Proceedings, 4th World Conference on Earth-

quake Engineering, Santiago, Chile, Vol. 3, pp. 54-69. Ii

'I:'\! Wolf, J . P. and von Arx, G. A. (1978), "Impedence Function of a Group of Vertical Piles," Proceedings, Conference on Soil Dynamics and Earthquake Engineering, ASCE, Pasadena, CA., Vol. 2,

:\ pp. 1024-1041. , !I II II

I I

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A-3

Yoshida, I. and Yoshinaka, R. (1972), "A Method to Estimate Modu­lus of Horizontal Subgrade Reaction for Pile," Soils and Founda­tions, Vol. 12, No.3, pp. 1-17.

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