NSF/CEE-81081 SEISMIC SOIL-PILE-STRUCTURE INTERACTION PILE GROUPS Report to NATIONAL SCIENCE FOUNDATION INFORMATION RESOURCES NATIONAL SCIENCE FOUNDATION
NSF/CEE-81081
SEISMIC SOIL-PILE-STRUCTURE INTERACTION PILE GROUPS
Report to NATIONAL SCIENCE FOUNDATION
INFORMATION RESOURCES NATIONAL SCIENCE FOUNDATION
50272-101 REPORT~DOC~~U~M~E~N~T~A~T~IO~N~Ir.l~.~R~EPO~R~T~N~O~.-------------------r.I~~------------1.3~.~R~ec7iP7ie-n~t.s-A~"-e-S~Si-on-N~0-.------~
___ PA.:;::;G:;;:E:--__ .-l...-__ N_SF_I_CE_E_-B_1_0B_1 ___ ---'L-____ +::-i:.illl PYl~L-1---,1~7 ...:::.R:...:4~is..._ -i.1=---I :- Title and Subtitle 5. Report pate
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.
II I I !
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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
1
;1
1
II I'
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!I I * * * Ii Ii II
I' I' II :1 Ii il
'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 ,(
-,
I I !
:,1
Page II I
V I II
1 II 1 II 2 II , 3 iI
lJ iI :j
3 i
·r ,j
3 i/ :1
4 II j
5
5 I 7
8 ! I
11 'I
12 II 13 Ii 14 I
i I
14 I 16 d
'I 16 II 16
II 18 18 II 20 20
I
i 21
22 I! II
23 I
23
24 H :' I
24 I 25 II 26 II
27 II 28
II
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 .........•..........
,I
I I'
-1 i
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
2 U I'
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
I:
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
'I
il 'I Ii
:1
II II 'I
II
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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