EFFECTS O F C Y C L I C L A T E R A L L O A D S

ON PILES IN SAND

By J. H. Long, t Member, ASCE, and Geert Vanneste z

ABSTRACT: The effect of repetitive lateral loads on deflections of two drilled piers in Tampa Bay were significantly greater than predicted by a p-y procedure com- monly used in practice. Reasons for the discrepancy between predicted and mea- sured deflections are discussed. Two methods for predicting the effect of repetitive lateral loads are developed using results of 34 cyclic lateral load tests to quantify model parameters important to the behavior of piles subjected to repetitive lateral loading. The two methods model cyclic lateral load behavior of a pile by degrading soil resistance as a function of number of cycles of load, method of pile installation, soil density, and character of cyclic load. The two methods differ in the compu- tational effort required to make the prediction. The first method is most suitable for hand calculation and rule-of-thumb estimation and is based upon a beam-on- an-elastic foundation model with a soil reaction modulus, Kh, increasing propor- tionally with depth. The second method modifies nonlinear static p-y curves to derive a cyclic p-y curve. The two methods provide a simple means for estimating effects of cyclic lateral load.

INTRODUCTION

The effects of cyclic la teral loads on piles in sand are impor tant to quantify due to the occurrence of cyclic la teral loads in nature. Wind, waves, ear th pressures, and water pressures, may subject cyclic lateral loads to pile sup- ported structures. Methods commonly used for predict ing the response of piles to cyclic lateral loads were evaluated for two piers in Tampa Bay, Florida, and found to predict poor ly the behavior due to cyclic loading. Using information from these tests and addit ional case histories, parameters that influence the behavior of piles subjected to cyclic la teral loads are identified, and two methods for predict ing load deflection behavior are proposed.

On September 12, 1982, static and repet i t ive la teral load tests were con- ducted on two offshore piers in Tampa Bay adjacent to the Sunshine Skyway Bridge. Predictions of the behavior of the piers were made using a method proposed by Reese and his coworkers (Reese et al. 1974). This method was selected because it is based upon results of full-scale la teral load tests on piles in sand and the method provides reasonable agreement with results from other uninst rumented load tests (Meyer and Reese 1979).

The two piers at Tampa Bay exper ienced deflections due to cyclic loading greater than predic ted using a p-y method out l ined by Reese , et al. (1974). Illustrated in Figs. 1 (a) and l (b ) are measured and predic ted load-def lect ion (H-g) relationships for the first cycle of loading and for 50 cycles of loading. Several possible explanat ions for differences between predic ted and mea- sured deflection were investigated. However , differences in construction, soil propert ies, and loading characterist ics for the tests conducted at Tampa

1Assoc. Prof. of Civ. Engrg., Newmark Scholar, Univ. of Illinois, Urbana, IL 61801.

2Engr., lngelmunster, Belgium. Note. Discussion open until June 1, 1994. To extend the closing date one month,

a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on March 5, 1990. This paper is part of the Journal of Geotechnical Engineering, Vol. 120, No. 1, January, 1994. �9 ISSN 0733-9410/94/0001-0225/$1.00 + $.15 per page. Paper No. 27047.

225

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Z

to o

..J

to k - i D

. 4 . -

0 ._1

0 5 0 0

400

300

200

100

0 -

500

400

300

200

100

0

Lateral Deflect ion of

50 100

East Shaft I . f "

�9 M e a s u r e d ~ / _ qN~

n I J J I a n n n I I I I

Shaft, mm

150 200 u I i i i i

o e O e �9 00

Note: Delta ploffed for 1, 2 . 5. 10, 20 , a •d 4 0 c y c l H

, I

West Shaf t / , , ~ � 9 - - ~ , , . d ) I / /

[ NOte: Dola plofled for ~ P I 1. z. s, lo. =o,

[ o.d ,0 oyo,.. ,,,

0 50 1 O0 150 200

Lateral Deflect ion of Shaft, mm

FIG. 1. Comparison of Measured and Predicted Response for Two Laterally Loaded Piers at Tampa Bay, Fla.

Bay and Mustang Island (Reese et aL 1974) are too numerous to be quan- tified with results from only these two sites; therefore, results of 34 repetitive lateral load tests in sand were investigated. Two simple methods are pro- posed herein to allow prediction of effects of cyclic lateral load on piles. The two methods include effects due to the characteristics of cyclic load, the number of cycles, the installation method, and soil density. The two methods provide a means to estimate effects of cyclic lateral loads on piles in sand.

BEHAVIOR OF PILES L O A D E D R E P E T I T I V E L Y

Qualitative Discussion of Cyclic Behavior The behavior of a vertical pile subjected to repetitive lateral loads depends

upon characteristics of the lateral load, geometrical and structural properties of the pile, the properties of the soil in which the pile is embedded, and the change in soil properties as the pile is loaded repetitively.

A simplified soil-pile model is used to illustrate the behavior of a soil and

226

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

pile to the application of a cyclic, lateral load at the head of a pile, In this model, the pile is assumed to be elastic, infinitely long, vertical, and embed- ded in a cohesionless soil. A two-way lateral load applied at the head of the pile varies sinusoidally with time at a frequency low enough that only effects of repeated load are important (the effects of inertia are minimal) and any excess porewater pressures generated in the soil are dissipated quickly. Furthermore, the cohesionless soil is assumed to exhibit no signif- icant cohesion or creep. The behavior of the pile is described for four phases during one cycle of load. The effect of each quarter-cycle of load is described and the influence of further cycles is mentioned.

During the first quarter-cycle, the magnitude of lateral load varies from a value of zero to a maximum horizontal load Hmax in a direction to the right. The head of the pile rotates and translates to the right in response to the applied load. Resistance to pile deflection is provided by the soil along the right side of the pile while the soil along the left side of the pile maintains contact by flowing with the pile. The soil surrounding the pile may change in volume depending on its initial density and state of stress (Chang and Whitman 1988).

During the second quarter-cycle, the lateral load decreases from a value of Hmax to zero, and the head of the pile deflects toward its original position. As the pile translates to the left, the soil resistance along the left side of the pile increases while the soil resistance on the right side decreases. If the soil pressure along the right side decreases to an active state, the cohesionless soil will flow and prevent a gap, thus ensuring contact with the pile surface. As with the first quarter-cycle of load, the cohesionless soil may change volume depending on its density and change in state of stress.

The direction of the lateral load, Hmax, and the corresponding deflection of the pile head are reversed for the third quarter-cycle. The magnitude of horizontal load changes from zero to -H~ax causing the pile to deflect to the left. The pile may resist significant lateral loads before reaching the original location of the pile head because of the presence of cohesionless sand that flowed with the back of the pile during the first quarter-cycle of load. As the load approaches - H m a • the pile deflects to the left while the soil maintains contact along the right side of the pile preventing any gap between the pile and soil.

The response of pile and soil during the fourth quarter-cycle is similar, but opposite in direction, to the response described during the second quarter- cycle. Depending on the density of the soil and the stress state in the soil, volume changes in the soil may occur.

Effect of further cycles on the maximum horizontal deflection of the pile and on bending moments within the pile depend upon changes in mechanical properties (strength, modulus) and the accumulation of permanent strains in the soil.

Characteristics of the load can influence significantly the behavior of piles subjected to cyclic lateral loads. If cyclic pile displacement is primarily in one direction, then effects of cumulative deformations are more pro- nounced. For example, one-way cyclic loading (load varies from 0 to Hma x to 0 with no reversal of load direction) will induce more permanent strains and greater cumulative deformations than piles subjected to two-way cyclic loads (load varies from/-/max to - H m a x to Hma x to -Hmax) .

Structural details of the pile may also play a role in the behavior of a pile when subjected to cyclic lateral loads. As the pile is loaded, moments gen- erated within the pile cause the pile to bend and mobilize tension and

227

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

compression within the pile cross section. Steel cross sections usually remain elastic for magnitudes of maximum bending moment anticipated in design; therefore, the flexural stiffness of the steel cross section remains unchanged for all magnitudes and cycles of load. However, the flexural stiffness of reinforced concrete sections decrease with increasing moment and load cycles due to progressive cracking of the cross section (Little and Briaud 1988). Changes in flexural stiffness are most pronounced for reinforced pile cross sections that are neither post- nor pretensioned because tensile stresses are greatest and crack formation is more prevalent. Since the deflection of a pile is influenced by changes in flexural stiffness, the influence of these changes on pile performance should be a design consideration. Often, effects of degradation in flexural stiffness are insignificant because only a small portion of the pile experiences large bending moments. Therefore, only a small portion of the pile experiences significant degradation in flexural stiff- ness (Long and Reese 1982; Kramer and Heavey 1988), and the deflection of the pile at working loads is affected minimally.

History for Predicting Effects of Cyclic Lateral Loads Attempts by others have been made to quantify the effect of cyclic lateral

loads on pile behavior by modeling the soil-pile system with a beam-on-an- elastic-foundation (BOEF) analysis. A summary of previous attempts pro- vides a perspective on parameters considered to be important and methods employed for modeling effects of cyclic loading.

Reese and Matloek (1956) and Vesic (1977) suggest that solutions using a linear, elastic soil response with a soil reaction modulus, Kh, increasing proportionally with depth provides a reasonable model for determining the lateral behavior of piles in sands. The coefficient of soil reaction, nh, is used to identify the increase in soil reaction modulus, Kh, with depth as shown here:

Kh = nh'Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where z = depth below the ground surface. Effects of cyclic loads are modeled by reducing the static value of n h.

Summarizing results from Prakash (1961), Davisson and Salley (1970), and Alizadeh and Davisson (1970), and Davisson (1970) suggests reducing nh to 30% of the static value if the load is cycled 50 times or more.

Broms (1964) suggests that deterioration of n h depends on density of the cohesionless soil and recommends that for 40 cycles of load, the value of nh should be reduced to one-fourth and one-half the original value of r/h for low and high relative densities, respectively. Broms cautions that these recommendations are based upon limited data.

Reese et al. (1974) used results of static and cyclic load tests on instru- mented, full-scale piles to develop a semi-empirical, nonlinear p-y (soil resistance-pile deflection) approach. Procedures developed to predict cyclic p-y relationships are based upon degraded staticp-y curves, with degradation factors determined empirically from results of the instrumented load tests. The cyclic p-y curves proposed by Reese et al. (1974) were developed to represent the resistance provided by the soil at a large number of cycles of load. Therefore, recommendations for cyclic p-y curves are independent of the number of cycles.

O'Neill and Murchison (1983) used a number of case histories of static and some cyclic load tests to evaluate current procedures and develop im- proved procedures for generating p-y curves. Although the main emphasis

228

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

was for static lateral loading, cyclic p - y curves are generated by reducing the static soil resistance, p, for a given deflection, y. Like the method proposed by Reese et al. (1974), the cyclic p - y curves are independent of the number of cycles.

Little and Briaud (1988) model the deterioration of the soil reaction modulus, Kh, due to cyclic loading as

KhN = K m " N -~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

where KhN = Kh at the Nth cycle of load, Khl = the value of the soil reaction modulus for the first cycle of load, and a = a degradation param- eter.

Little and Briaud use results from static pressuremeter tests to obtain static, nonlinear p - y relationships. Cyclic p - y curves are constructed by reducing the static soil resistance according to (3)

PN = p l " N - a �9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

where PN ~" the cyclic soil resistance for N cycles of load, pl -- the value ofp for the first cycle of load, and a = a degradation parameter determined from the results of cyclic pressurerneter tests. Little and Briaud found rea- sonable agreement between values of a from full-scale tests on piles sub- jected to one-way loading and from cyclic pressuremeter tests. Two advan- tages of Little and Briaud's method are the ability to model the effect of number of cycles, and the ability to determine parameters from in situ test results.

Theoretical studies using a more sophisticated approach for modeling soil behavior have been conducted by Swane and Poulos (1982), and Matlock et al. (1978). These authors model each p - y curve for the complete load history for every load cycle and solve for the response using a discrete element model for the BOEF problem. While the two approaches are fun- damental, the parameters required for analysis are usually unavailable for typical soil exploration and site characterization studies.

Turner et al. (1987) collected results of 23 case histories on piles and drilled shafts subjected to cyclic lateral loads. They suggest the cyclic be- havior of piles is influenced by the tendency of the soil to dilate or contract during cyclic loading.

The uncertainty associated with the aforementioned methods for pre- dicting effects of cyclic lateral load remains unquantified as do the major factors that affect cyclic behavior. Results of several full-scale load tests were investigated to determine the effect of cyclic lateral loads on piles in sand, and to assess uncertainties associated with the prediction method proposed.

CASE HISTORIES ON CYCLICALLY, LATERALLY LOADED PILES

Results from 34 full-scale, cyclic lateral load tests in sand are used to illustrate and quantify the influence of important parameters on pile be- havior. Details of the cyclic lateral load tests are presented in Table 1. The collection includes a wide range of soil density, pile type and material, construction technique, and cyclic load characteristics. Load tests were con- ducted by applying a specific load repetitively to the pile head, and reporting the increase in deflection of the pile with number of cycles of load. Only the load test by Morrison (1986) was conducted by controlling displacements and recording the degradation of lateral load with cycles.

229

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

TAB

LE 1

. S

umm

ary

of C

yclic

Lat

eral

Loa

d Te

sts

O

Test

(1

) 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

Pile

ty

pe

(2)

Tim

ber

pile

T

imbe

r pi

le

/-/-

pile

Con

cret

e pi

le

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Dri

lled

sha

ft

Spec

iall

y fa

bric

ated

w

ide

flan

ge b

eam

Sp

ecia

lly

fabr

icat

ed

wid

e fl

ange

bea

m I

Spec

iall

y fa

bric

ated

I

wid

e fl

ange

bea

m I

Dri

lled

sha

ft

I P

ipe

pile

I

Con

cret

e pi

le

I D

rill

ed s

haft

D

rill

ed s

haft

Wid

th

diam

eter

(r

am)

(3)

305

310

145

510

610

915

915

1,22

0 1,

220

1,43

0 1,

220

1,43

0 40

5

405

405

915

610

510

1,06

5 1,

065

Met

hod

of

inst

alla

tion

(5)

Dri

ven

Dri

ven

Dri

ven

Son

ic V

ib

Dri

lled

D

rill

ed

Dri

lled

D

rill

ed

Bac

kfil

led

Bac

kfil

led

Dri

lled

D

rill

ed

Bac

kfiU

ed a

nd c

om-

pact

ed

Bac

kfil

led

and

com

- pa

cted

B

ackf

ille

d an

d co

m-

pact

ed

Dri

lled

D

rive

n D

rive

n D

rill

ed

Dri

lled

Max

imum

nu

mbe

r of

cy

cles

(7

) 24

24

10

0

100 10

10

, 15

15

10

0 80

100 80

50

0

500

500 21

21

21

21

21

Cyc

lic lo

ad

ratio

(n

min

/nm

ax)

(8)

0 0 0 0 0 15

0 0 0 0 0 0 0 0 0 0 0,

0.5

0

,0.5

0,

0.5

0,

0.5

0,

0.5

Ref

eren

ce

(9)

Ali

zade

h (1

968)

1A

A

liza

deh

(196

8) 1

B

Ali

zade

h an

d D

avis

son

(197

0)

6 A

liza

deh

and

Dav

isso

n (1

970)

I1

A

Bhu

shan

et

al.

(198

1) 4

B

hush

an e

t al

. (1

981)

5

Bhu

shan

et

ai.

(198

1) 6

B

hush

an e

t al

. (1

981)

7

Dav

isso

n an

d Sa

lley

(196

8) I

N

Dav

isso

n an

d Sa

lley

(19

68)

2N

Dav

isso

n an

d Sa

lley

(19

68)

IS

Dav

isso

n an

d S

alle

y 19

68)

2S

Hel

ler

(196

4)

Hel

ler

(196

4)

Hel

ler

(196

4)

Lit

tle

and

Bri

aud

(198

8) 1

L

ittl

e an

d B

riau

d (1

988)

2

Lit

tle

and

Bri

aud

(198

8) 3

L

ittl

e an

d B

riau

d (1

988)

4

Lit

tle

and

Bri

aud

(198

8) 5

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

21

22

23

24

25

26

27

28

29

30

31

32

33

Dri

lled

sha

ft

Dri

lled

sha

ft w

ith

casi

ng

Dri

lled

sha

ft w

ith

casi

ng

H-p

ile

/-/-

pile

Pip

e pi

le

/-/-

pile

Pip

e pi

le

Tim

ber

pile

T

imbe

r pi

le

Tim

ber

pile

T

imbe

r pi

le

/-/-

pile

H

-pil

e

1,06

5 1,

220

1,22

0

355

355

275

355

610

290

305

305

330

355

355

39.0

15

.5

15.5

17.1

17.1

13.4

15.9

21.0

11

.3

15.2

5.

2 10

.7

20.4

20

.4

Dri

lled

V

ibra

ted

Vib

rate

d

Dri

ven

Dri

ven

Bac

kfil

led

and

com

- pa

cted

D

rive

n

Dri

ven

Dri

ven

Dri

ven

Dri

ven

Dri

ven

Dri

ven

Dri

ven

Loo

se

Den

se

Den

se

Den

se

Den

se

Med

iu

Den

se

Den

se

Loo

se

Den

se

Loo

se

Den

se

Med

iuJ

Med

iu__..

~

21

40,

125

40,

125

25

25

100 23

tOO

5 5 5 23

25

25

0, 0

.5

0 0 0 0

-1.0

- 1.

0

- 0.

25

0 0 0 0.1

0 0

Lit

tle

and

Bri

aud

(198

8) 6

L

ong

and

Ree

se (

1984

) E

ast

Lon

g an

d R

eese

(19

84)

Wes

t

Mey

er a

nd R

eese

(19

79)

Bai

lley

1

Mey

er a

nd R

eese

(19

79)

Bai

lley

2

Mor

riso

n (1

986)

O'N

eill

and

Mur

chis

on (1

983)

, T

3 R

eese

et

at.

(197

4)

Rob

inso

n (1

979)

6

Rob

inso

n (1

979)

8

Rob

inso

n (1

979)

9

Ste

vens

et

al.

(197

9)

Tuc

ker

and

Bri

aud

(198

8) 1

T

ucke

r an

d B

riau

d (1

988)

2

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

The response of a pile to cyclic lateral load depends on the change in stiffness of the soil and pile with applied cycles of load. Changes in soil and pile stiffness are influenced by the magnitude of load, the character of load (one- versus two-way loading), the initial stiffness of the pile and soil, and the change in stiffness of the pile and soil with number of cycles. The soil is assumed to be insensitive to creep, and the pile material is assumed to remain elastic.

Parameter for Quantifying Effect of Cyclic Lateral Load Davisson (1970), Broms (1964), and Vesic (1977) have suggested that the

lateral response of a pile could be modeled simply as a BOEF with a linearly increasing soil reaction modulus, nh. Furthermore, they suggested the effect of cyclic loading could be modeled by reducing the static value of nh. The model suggested by Davisson, Broms, and Vesic is simple and used often for preliminary assessment of lateral load behavior. Therefore, the effect of cyclic lateral loads for all 34 load tests was investigated using a BOEF approach and a soil reaction nh. Parameters for this soil-structure interaction model are the flexural stiffness of the pile (El) , the length of the pile, L, the coefficient of soil reaction (nh), and the magnitude of load (or moment). The pile properties and the magnitude of maximum lateral load are assumed to remain unchanged during cyclic loading; therefore, the increase in pile deflection is affected only by a change in coefficient of soil reaction, nh.

The effects of cyclic lateral loads are studied by back-calculating values of nh from measured load-deflection data, and comparing nh for the first cycle of load with nh for subsequent cycles in terms of the ratio, Rn (Rn = HhN/nhl ). The parameter R. is selected because most cyclic lateral load tests present only load-deflection data, deflection data are usually more reliable than moment data for load tests conducted in which both moment and deflection are measured, values of n h are more sensitive to changes in de- flection than moment, and results of both instrumented and uninstrumented pile tests can be compared with a common parameter (nh).

Effect of Number of Cycles of Load Cyclic lateral loads applied to the head of a pile result in deformations

that may increase with every cycle. The increase in pile-head deformation with continued cyclic loading may be modeled by reducing the coefficient of soil reaction, nh. The effect of cyclic loading on the reduction of nh is shown in Fig. 2 by plotting Rn versus the number of cycles, N, on a log-log scale. A straight line relationship is expressed as

R n - n h N _ N - ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4) ~hl

where - t = the slope of the straight line. The magnitude of t represents a relative effect of cyclic loading on the deterioration of nh.

Results from full-scale tests have shown that one-way cyclic loading may continue to influence peak deflections up to 500 cycles (HeUer 1964); how- ever, the quantity of available data is limited. Most of the load-test data summarized are for 50 cycles or less (Table 1). The effect of cyclic loading is greatest for the first cycle of loading, with the effect of subsequent cycles diminishing as cycling continues.

232

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

2 , i

c

d 0

e~

"-I m

-I0 0

0

(3

(.3

1

0 . 5

0 . 2

0.1

L r ~ A t = 0.02 -

Legend �9 D a ~ * y t = 0.33 1

V Long and Reese (1984) �9 Little and griaud (1988) 1 r ] Reese, et, al. (1974) �9 klorrison (1986) A O'Neill and Mui'chlson (1983)

i ~ i i i i i J j . . . . . I

2 5 10 20 50 100 200

R H = -1

R H = - 0 . 2 5

R H = 0.5

R H = 0.0

N u m b e r of Cycles, N

FIG. 2. Effect of Number of Cycles on Cyclic Modulus Ratio

Effect of Character of Cyclic Load A cyclic load ratio, R~/, is used to quantify the character of cyclic load

and is defined as

•/min ,% - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 5 )

//max

where Hmi n = the magnitude of minimum lateral load, and Hm,x = the magnitude of maximum lateral load. A pile cycled from 0 (Hmi,) to Hma, (one-way loading) is calculated to have a cyclic load ratio, Rn = 0. A pile cycled with equal load magnitude in both directions (two-way loading) has a ratio, Ru = - 1 , and a pile loaded statically would have a value of R , = 1. Most cyclic lateral load tests reported in the literature and con- ducted in practice use RH = 0 (one-way cyclic loading); however, some notable lateral load tests have also been conducted using R/~ -- - 1 [two- way cyclic loading (Morrison 1986)], R, = -0 .25 (Reese et al. 1974) and Ru = 0.5 (Little and BriaNd 1988). The soil modulus ratio, R,,, versus number of cycles is shown in Fig. 2 for different magnitudes of the cyclic load ratio, RH. The corresponding degradation parameter, t, represents the slope of a straight line fit and can be calculated as:

log(R,u) t = log(N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

where Rnu = the value of R, at N cycles of load. Larger values of t cor- respond to a greater effect of cyclic loading. Values of t shown in Fig. 2 are 0.03, 0.08, 0.27, and 0.13 for RH of - 1 , -0 .25, 0, and 0.5, respectively. Results of these full-scale tests show that one-way cyclic loading results in greater degradation than two-way loading, and that intermediate cyclic load ratios result in degradations between one- and two-way loading. Although no comprehensive full-scale field tests have been conducted to confirm or quantify the effect of RH specifically, results of model-scale pile tests suggest

233

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

one-way cyclic loading results in larger deflections than two-way cyclic load- ing (Parry and Sanglamer 1977; Barton 1982). Thus, the degradation pa- rameter, t, is assumed to be greater for one-way loading and less for two- way loading. Finally, the degradation parameter, t, is 0 for R, = 1 since this loading condition corresponds to a static load.

Effect of Magnitude of Deflection and Precycling Results from the 34 case histories were used to investigate effects of

magnitude of deflection on the deterioration of soil modulus with number of cycles, t. In Fig. 3 are shown values of t back-calculated from results of each cyclic load test versus normalized deflection, ~/D (pile head deflection/ pile head diameter) for piles which had no previous significant cyclic loads (virgin cycling). The effect of cyclic lateral loads on t appears to be relatively unaffected by the magnitude of normalized deflection. Fig. 4 shows t values for piles subjected previously to cyclic loads, at a lower magnitude of load. The values of t exhibit considerable scatter. The value of t for virgin cycling

C

a) E P o

O. C .o

"o E o l

r-I

0.600

0.400

0.200

0.000 0.0002

:, I

' , , j : p .......... . . . . ....... i , ,...i,i,,',, " , ~ ' ........ ; . . . . . . . . ...... ~ ' o ; " " .i .................

0.001 0.01 0.1 0,2 Normalized Deflection, 8/D

FIG. 3. Cycling

l Nizodeh and Dc~luon (:1970) 46 Nizod.ah and .Dgvfaeon (1970) 811A ~izaoeh (1958) 1A Allzodeh (1968) 1B . Bhuehon, at el. (1981) #4 Bhu=hon, et ale (1981) J5 Bhushon, et al. (1981) J6 Bhuehan, at ol. (1981} J7 DovLelon and Solley (1"96B) #IN uavisson and Salley (1968) #2N uavlsson and Salley (1968) #1S uavia=on and Salley (1968) #25

i Heller (1964-) #I Heller (1964-) #2 Hailer {1964-~ 43 Little and Bnoud (19B8) #1 Little and Bdoud (1988) #2 Uttle end Bdoud (1988) #3 Uttle end Brloud (1988) #4. Little end Brloud (1988) r Little and Bdoud .(1988) #6 Long and Reeee (1984.~ -Eost Long and Reese (1984) -West

Zl Meyer ond Roen (1979) #I �9 Meyer and Rees.e (1979) #2 �9 Nob'leon (1988) 0 O'Nenl and Murchiegn

Rpaee. at 91. (1974). =,1[evens, ~ ~I. (1979)

.~- luckar one urlaud (1988) #I Tucker and Brlo~d (1988) #2

<> Robinson (1979) #6 �9 Robinson (1979) #8 ~> Robinson (1979) 49

Effect of Normalized Deflection on Degradation Parameter, t, for Virgin

234

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

, 4 - /

I L

E P 0

Q. r 0 ~4-,- 0

"10 P 01

r t

0.600

0.400

0.200

O.O00 0.0002

�9 . . i , t i

..................................... P R E - C Y C L E D I

........ ............ i - - ~ . i - . i . . i �9 ................. ......... ~ . . . . . . �9 . . . . . . . . . . . . . . . . . . . . - - - . . . - . i . ! . . . . . . . . . . .

! i ! ! i � 9 i o i ~ ........

......... ........ j . . : ! ! : .............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.001 0.01 0.1 0.2

Normalized Deflection, 4/D

l Alizadeh and Dov~eeon (1970) 86 Allzodeh end Day[seen (1970) 811A Nizadeh (1968) 1A Alizndeh (1968) 1B Bhulhan, et el. (1981) 84 Bhushan, et eL (1981) 85 Bhushan, et el. (1981) 86 Bhushon~ et el. (1981) 87 Davisian and Solley (1968) 81N

~r Davis=on and Solley (1968) 82N &L Dovisson and Solley (1988) 81S

Davieeon end Salley (1968) 42S ~ Hener (1964) 81

Hailer (19w 82 Heller (196~) 83 Little and Bnoud (19B8) 01 Little and Brloud (1988) 02

~ Little end Briaud (1988) 83 Little and Briaud (1988) Q4 Little and Brioud (1988) #5 Little end Brloud [1988) # 6 Long and Reel= (1984~ -East Long and Reese (1984) -West

A Meyer and Reeel (1979) 41 �9 Meyer and Reeee (lg79) 82 �9 Mondeon (1986) O O'Neill end Murchilan "<P Reeee, et ol. ( lg74) .

Stwens, etal. (197.9) Tur and Briaud (1988) 81 Tucker and Briaud (1988) 82

~> Robineon (1979) #6 �9 Robinson (1979) 88 ~> Robinson (1979) 89

FIG. 4. Effect of Norma l i zed De f lec t i on on D e g r a d a t i o n Parameter , t , for Precycled Piles

ranges between 0.52 and 0.00 with an average near 0.22. The values of t for precycled piles are smaller with a range between 0.0 and 0.35 and an average of 0.18.

D E V E L O P M E N T O F M O D E L S F O R C Y C L I C L O A D I N G E F F E C T S

Both methods developed in this paper employ results of 34 cyclic lateral load tests and use the same parameters for determining the effect of cyclic loading. The two methods differ in the computational effort required to solve the soil-structure interaction problem to obtain deflection. The first method is based upon a closed-form solution for a BOEF with a linearly increasing soil reaction modulus (LISM) that varies proportionally with depth. The LISM method is simple to apply and uses parameters obtained directly from the results of the cyclic lateral load tests.

The second method is based upon the degradation of static p-y (DSPY)

235

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

curves. A p-y curve for static loading is modified to a cyclic p-y curve by reducing the static soil resistance, p, while increasing the static displacement, y. The DSPY method can accommodate nonlinear p-y curves and different procedures for generating static p-y curves; however, the solution for the soil-structure interaction equations requires the use of a computer.

Linearly Increasing Soil Modulus (LISM) The LISM method employs a BOEF analysis. The soil reaction modulus

is assumed to increase linearly with depth according to (1). Hetenyi (1946) developed solutions for deflection of the pile head in the form of infinite series, but the solution can be simplified by calculating separately the con- tribution to deflection by lateral load, H, and bending moment, M, as

A .H B . M ON - - i t ? 1 0 . 4 . ~ 0 . 6 "~- l t 2 / 0 . 6 . . 0 . 4

JL~t S ~ h N ~t~Jt r ~ h N

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

where gN = the lateral deflection at the Nth cycle of load, E1 = the flexural rigidity (product of pile modulus and the moment of inertia), nhN = the coefficient of soil reaction at N cycles of load. A and B = constants deter- mined from the length of the pile, L, and the relative stiffness ([EI/nhn] ~ according to beam-on-elastic-foundation theory (Hetenyi 1946). All the var- iables are taken as known except the coefficient of subgrade reaction for cyclic loading, nhN, which is calculated as

nhS = nhl"N-' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

where nhl = the coefficient of subgrade reaction for the first cycle of load. All 34 load tests were evaluated to determine appropriate values of t.

Figs. 5 and 6 illustrate the effect of load, installation, and soil density for piles subjected to cyclic loads for the first time (virgin cycling), and for piles previously subjected to cyclic loads at a lower level of load, respectively. Frequency histograms are superimposed on the figure when necessary. The effect of load ratio is shown in Figs. 5(a) and 6(a). Figs. 5(b) and 6(b) illustrate the effect of pile installation for virgin cycling and for precycled piles. Figs. 5(c) and 6(c) show effects of soil density. Figs. 5(b), 5(c), 6(a), and 6(c) use only results from tests conducted with a cyclic load ratio greater than zero. Based upon trends in Figs. 5(a)-5(c), and 6(a)-6(c), the follow- ing observations are made.

Virgin Cycling (Fig. 5) Piles installed by driving or by vibration exhibit the least effect of cyclic

loading (smallest values of t), while drilled shafts and shafts backfilled with- out compaction exhibit the greatest effect of cyclic loading and the greatest variation in t. Installation methods listed in order of increasing average t values are as follows: vibrated, backfilled and compacted, driven, sonic vibrated, drilled, and backfilled. Foundations in dense soil exhibit less effect of cyclic loading than foundations in loose soil.

Tests that Have Been Cycled Previously The average value of t is smaller than values of t for virgin cyclic loading,

and t values are much less sensitive to differences in soil density and in- stallation procedure.

236

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

I I

CtfcIlc Load l �9 fects ~"25

L .

)

g ~ f .~ 0.2 ,~ 0.1 ~ 0 0

f - - .

If' * t ~ 1 7 6 I I I

- 1 .0 - 0 . 5 0.0 0.5 Cyclic Load Ratio, R H

0025

=

0.6 , , , , ~E I Ib) Installation

0 . s j " 0"2, E,,.ots

e 0, i - - . - -

�9 ~ o . o - - , , , , ; ;

�9 "=- - - . - o

g o ~

i T T - - - - - - ~ c ) So|I De nsity'l

~ - - o ~ s -" [ Effects I

- ~ ~

L .

�9 0 . 6 - - E 0.5

no 0.4

0.3 .T. 0.2

0.1

0.0

1.0

FIG. 5. Value of Degradation Parameter, t, for Virgin Cycling as Affected by: (a) Cyclic Load Ratio; (b) Installation; and (c) Soil Density

For Both Precycled and Virgin Cycfic Loading The cyclic load ratio appears to affect the cyclic behavior most signifi-

cantly. The least effect of cyclic loading is seen for RH = --1 (two-way loading) while the greatest effect of cyclic loading is seen when R , = 0 (one-way loading).

Method for Determining Degradation Parameter, t A specific value of t for a cyclically laterally loaded pile depends on

characteristics of the cyclic load ratio, RH, the installation method, the soil density, and if the pile has been precycled. The value of the degradation parameter, t, that includes effects of load direction, installation procedure, and soil density can be calculated as

237

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

~a

i E o

o .

o

o "o o o~ o

0

@

E

c o

=o "o P o~ @

o

C o

o

o.

c o

"o P

0.6 0 .5

0 .4

0 .3

0 .2

0.1

0 .0

a) Cyclic L o a d ] ' ' Effects J- o~0 o~o o~o

J i

- 1 . 0 - 0 . 5 0 . 0 0 . 5

Cyclic Load Ratio, R H 1.0

0 . 6 ,

0.5

0.4

0.3

0 .2

0.1

0.0

' ' ' ]b) Installation J Effects 1

0 ",0 o ", ,0

o "~o J~

=o

0.6 1 1 1-[c) Soll Denslt 0.5 . . . . . . ~ .. . . . . . . . . . . . . . . . . . . . . . . . - t ~ Effects

o 3o o 3o 0.4 . . . . . . . . . . . :~ . . . . . . . . . . . . . . - ~ - . . . . . . . . . . . . . . . . i

0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.1~ _T 2- 0.0

._~

FIG. 6. Value of Degradat ion Parameter , t, for Precycled Piles as Af fected by: (a) Cyclic Load Ratio; (b) Instal lat ion; and (c) Soil Densi ty

t = 0 .17 .FL.Fz 'Fo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

where FL, F~, and Fo, are factors based upon details of the cyclic load ratio, pile installation, and soil density, respectively. Suggested values for FL, Fz, and Fo, based on results of the 34 load tests, are given in Tables 2-4. Values for FL in Table 2 reflect the effect of cyclic load with the greatest value for R , = 0 and 0.5, decreasing nonlinearly to 0.2 for R , = - 1 , and to 0.0 for Rn = 1 (static load). Linear interpolation can be used to determine FL at load ratios between specified points. The effect of cyclic load ratio appears to be the most important factor.

A value of 0.24 for t can be calculated using (9) for a drilled shaft (F~ = 1.3) subjected to one-way cyclic loading (FL = 1.0) in loose soil (Fo = 1.1). For comparison, recommendations by Davisson (1970) suggest t equals

2 3 8

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

TABLE 2. Effect of Cyclic Load Ratio on Parameter Fr

Load ratio RH FL (1) (2)

- 1.0 (two-way loading) - 0.25

0.0 (one-way loading) 0.5 1.0 (static loading)

0.2 0.4 1.0 1.0 0.0

TABLE 3. Effect of Installation on Parameter F1

Method of installation FI (1) (2)

Driven Vibrated Backfilled Backfilled and compacted Drilled Precycled (regardless of installation)

1.0 0.9 1.4 1.0 1.3 1.0

TABLE 4. Effect of Soil Density on Parameter FD

Soil density (1)

Loose (contractive) Medium Dense Precycled (regardless of density)

F,~ (2)

1.1 1.0 0.8 1.0

0.31, while Broms recommends 0.38 and 0.19 for loose and dense soils, respectively.

The uncertainty for estimating t was determined by comparing the values of t measured from the 34 lateral load tests with values of t predicted using (9). Fifty percent of the measured values of t exceeded values of t predicted using (9). If the predicted value of t is multiplied by 1.4, only 16% of the measured values exceed those predicted. Similarly, if the predicted value of t is multiplied by 2, a mere 3% of the measured t values exceed the predicted value.

The LISM method provides a simple procedure for predicting the effect of cyclic lateral loading; however, the method is restricted to analyses that employ a linearly increasing soil reaction modulus. Additionally, the LISM method cannot explicitly account for effects of nonlinear soil response, layered soil, and many fundamental parameters (soil unit weight, soil strength, and so forth) that affect lateral load response. Because p-y methods can include effects of nonlinearity, soil layering, and other soil properties, rec- ommendations for using results from the 34 load tests with nonlinear p-y curve analyses are provided next.

Deterioration of Static p-y Curve (DSPY) The use of nonlinear p-y curves to represent the static soil resistance

provided by piles is a common approach for analyzing the response of

239

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

laterally loaded piles. Recommendations for developing p - y curves for both static and cyclic loading have been given by (Reese et al. 1974; Briaud 1988; O'Neill and Murchison 1983). The DSPY method presented herein modifies a static p - y curve to a p - y curve for cyclic loading.

The DSPY approach is similar to the LISM approach; namely, the static soil reaction modulus is reduced to account for effects of cyclic loading according to (10)

KhN = K h , ' N - ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 0 )

The degradation parameter, t, is determined using (9). Since staticp-y curves are nonlinear, additional recommendations for the reduction in soil resis- tance, p, must be provided, otherwise, any combination of decrease in p and increase in y could be used to satisfy (10).

Little and Briaud (1988) suggest constructing the nonlinear cyclic p - y curve by maintaining deflection, y , constant for both static and cyclic p - y curves while reducing the soil resistance, Per = Pl" N-t . Thus, the reduction in soil reaction modulus prescribed in (10) is satisfied. Values of t were back-calculated for the 34 case histories using nonlinear, p - y curves modified by reducing soil resistance. Values of t for the Little and Briaud method were significantly lower in magnitude than values of t backcalculated using the LISM method.

Requirements for reducing the cyclic soil reaction modulus according to (10) can also be satisfied by modifying the soil deflection according to the relationship, YN = Yl" N ~. This approach gives the cyclic p - y curve a larger deflection, y, while maintaining the same soil resistance, p, for both static and cyclic load. Values of t back-calculated for the 34 load tests using this method were much greater than t values back-calculated using the LISM method.

The aforementioned methods for modifying nonlinear p - y curves should yield t values different from those obtained with the LISM method, because the load is held constant during a cyclic lateral load test while the pile head progressively increases in deformation. Thus, the decrease in soil reaction modulus is caused by both a reduction in the soil resistance, p, and an increase in pile deflection, y.

The DSPY method specifies a change in both soil resistance and deflection by including a term, et, into (10) as shown here:

PN = Pl "N(~'-I)' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

YN = Yl "N~'t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (12)

where PN = the soil resistance for N cycles of load and p~ = the soil resistance for the first cycle of load.

The factor, o~, controls the relative contribution of soil resistance and deflection to decrease the soil reaction modulus. The value of eL varies from 0 (to produce a change in p only) to 1 (to produce a change in y only). For et values between 0 and 1, both p and y are changed. A value of 0.6 for can be derived by using the same BOEF analysis used for the LISM method, where 5 = the groundline deflection of a pile subjected to a lateral load, H, at the ground surface. From (7), the ratio of groundline deflection of a pile for the first cycle of load, 5~, and the deflection at N cycles of load, 8N, is shown here

2 4 0

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

A ' H

/ "(nhN~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (13a) E I O . a . n O i 6 -

~N A " H \ n h x / EiO.4..0.6

t ~ h N

continuing ( o6 ~N = 81" g/hi = ~ l ' ( N t ) 0"6 = ~ I ' N ~ . . . . . . . . . . . . . . . . . . . . . ( 1 3 b )

\ n h u /

and since near the ground surface, y is approximately 8

nhl ~ y l ' ( N t ) ~ = y l ' N ~ . . . . . . . . . . . . . . . . . . . . . (13c) YN = YI" \ n h N /

Good agreement between t values back-calculated with the DSPY method and t values back-calculated with the LISM method is observed when a = 0.6. Theoretically, the value of a varies with depth, however, numerical investigations using e~ varying with depth provided no better agreement with the LISM method than with a constant value of 0.6. The DSPY method can be applied to nonlinear p - y curves to account for effects of cyclic lateral loading by modifying the soil resistance, p, and soil deflection, y, according to

PN = P l " N - O ' 4 t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)

Y N = Y l " N O ' 6 t �9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (15)

Values of parameter, t, can be determined using values listed in Tables 2 - 4 and the formula provided in (9).

LIMITATIONS

The method proposed is an empirical approach intended to provide the designer with a simple and expedient means to estimate effects of cyclic lateral load on piles in sand. Because the methods are empirical, efforts should continue to include more results to verify or modify the recommen- dations herein. Approaches based on more fundamental soil properties are needed.

The proposed method may overpredict the effect of cyclic load for piles subjected to cyclic load when the load ratio is less than 0. While the deg- radation using (9) is predicted to be minimal, the stiffness at the pile head may actually increase due to soil densification in the proximity of the pile.

Results of this study are believed to be valid for long piles in sand sub- jected to 50-100 cycles of nondynamic lateral loads. Although one test showed continued effects of cyclic load at 500 cycles, the majority of load tests were for 50 cycles or less. Caution should be exercised when predicting effects of cyclic loading beyond 50 cycles of load. Finally, the flexural rigidity of the pile is assumed to remain constant.

CONCLUSIONS

Two simple methods for determining the effect of cyclic lateral loads on piles in sand are presented. The two methods use parameters derived from

241

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

the results of 34 full-scale, cyclic, lateral load tests to determine the effects of cyclic loading. The LISM method employs a closed-form solution using a BOEF analysis with a linearly increasing soil reaction modulus degraded from a static modulus. The DSPY method deteriorates the resistance pro- vided by a given static p-y curve to account for the effects of cyclic lateral load. The DSPY procedure can be applied to nonlinear static p-y curves; therefore, current procedures for predicting the static p-y curves can still be employed, while the DSPY method can be applied to est imate the effect of cyclic loads.

The most important pa ramete r found to govern the behavior of piles during cyclic loading are the characteristics of the cyclic load. Other factors include the method of installation and the soil density.

ACKNOWLEDGMENTS

This study was supported by a research initiation grant from the University of Illinois and by a fellowship from Shell Oil Company Foundation. Their financial support is gratefully acknowledged.

APPENDIX I. REFERENCES

Alizadeh, M. (1969). "Lateral load tests on instrumented timber piles." Performance of deep foundations, ASTM STP 444, American Society for Testing and Materials, 379-394.

Alizadeh, M., and Davisson, M. T. (1970). "Lateral load test on piles--Arkansas River project." J. Soil Mech. and Found. Engrg. Div., 96(5), 1583-1604.

Barton, Y. O. (1982). "Laterally loaded model piles in sand, centrifuge tests and finite element analyses," PhD thesis, University of Cambridge.

Bhushan, K., Lee, L. J., and Grime, D. B. (1981). "Lateral load tests on drilled piers in sands." Drilled piers and caissons, Proc. Geotech. Engrg. Div. at ASCE Nat. Convention, St. Louis, Mo., Oct. 28.

Broms, B. (1964). "Lateral resistance of piles in cohesionless soils." J. Soil Mech. and Found. Engrg., ASCE, 90(3), 123-156.

Chang, C. S., and Whitman, R. V. (1988). "Drained permanent deformation of sand due to cyclic loading." J. Geotech. Engrg. Div., ASCE, 114(10), 1164-1180.

Davisson, M. T. (1970). "Lateral load capacity of piles." Highway Res. Record, 333, 104-112.

Davisson, M. T., and Salley, J. R. (1968). "Lateral load tests on drilled piers." ASTM Symp. on Deep Foundations, San Francisco, June 24.

Davisson, M. T., and Salley, J. R. (1970). "Model study of laterally loaded piles." J. Soil Mech. and Found. Engrg., ASCE, 96(5), 1605-1627.

HeUer, L. W. (1965). "Lateral thrust on piles." Technical Report R283, U.S. Civ. Engrg. Lab., Port Hueneme, Calif., June 15.

Hetenyi, M. (1946). Beams on elastic foundations. University of Michigan Press, Ann Arbor, Mich.

Kramer, S. L., and Heavey, E. J. (1988). "Lateral load analysis of nonlinear piles." J. Geotech. Engrg., ASCE, 114(9), 1045-1049.

Little, R. L., and Briaud, J-L. (1988). "Full scale cyclic lateral load tests on six single piles in sand." Miscellaneous Paper GL-88-27, Geoteehnical Div., Texas A&M Univ., College Station, Tex.

Lock and dam No. 4, Arkansas River and tributaries, Arkansas and Oklahoma. (1964). U.S. Army Engineer District, Little Rock, Corps of Engineers.

Long, J. H., and Reese, L. C. (1982). "Prediction of lateral load behavior for reinforced concrete pile." letter report to L. Johnson, WES, Mar.

Long, J. H., and Reese, L. C. (1984). "Testing and analysis of two offshore piles subjected to lateral loads." Laterally loaded deep foundations: analysis and per- formance, ASTM STP 835, J. A. Langer, E. Mosely, and C. Thompson, eds., American Society for Testing Materials, Philadelphia, Pa., 214-228.

242

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Matlock, H. (1974). "Correlations for design of laterally loaded piles in soft clay." Second Annual Offshore Technology Conf., Paper No. 1204, Houston, Texas, May, 577-594.

Matlock, H., Foo, S. H. C., and Bryant, L. M. (1978). "Simulation of lateral pile behavior under earthquake motion." Proc. ASCE Specialty Conf. on Earthquake Engrg. and Soil Dynamics, June, 600-619.

Meyer, B., and Reese, L. C. (1979). "Analysis of single piles under lateral loading." Research Report 244-1, Ctr. for Transp. Res., Dec.

Morrison, C. S. (1986). "A lateral load test of a full-scale pile group in sand," PhD thesis, University of Texas, Austin, Tex.

O'Neill, M. W., and Murchison, J. M. (1983). "An evaluation of p-y relationships in sands." Research Report No. GT-DF02-83, University of Houston, Houston, Tex., May.

Parry, R. H. G., and Sanglamer, A. (1977). "Lateral load tests on single model piles with radiographic observations." Cambridge University Interim Report, CUED~C, Soils TR 36.

Poulos, H. G. (1982). "Single pile response to cyclic lateral load." J. Geotech. Engrg., ASCE, 108(3), 355-375.

Prakash, S. (1962). "Behavior of pile groups subjected to lateral loads," thesis, University of Illinois, Urbana, II1.

Reese, L. C. (1984). "Handbook on design of piles and drilled shafts under lateral load." FHWA-1P-84-11, U.S. Dept. of Transp., Federal Highway Administration, July.

Reese, L. C., Cox, W. R., and Koop, F. D. (1974). "Analysis of laterally loaded piles in sand." Paper No. 2080, Sixth Annual Offshore Tech. Conf., Vol. 2, Hous- ton, Texas, May.

Reese, L. C., and Matlock, H. (1956). "Non-dimensional solutions for laterally loaded piles with soil modulus assumed proportional to depth." 8th Texas Conf. on Soil Mech. and Foundation Engrg., Sep. 14.

Robinson, K. E. (1979). "Horizontal subgrade reaction estimated from lateral load tests on timber piles." Behavior of deep foundations, ASTM STP 670, Raymond Lungren, ed., American Society for Testing Materials, Philadelphia, Pa., 520- 536.

Sanglamer, A. (1979). "Model study of laterally loaded single piles." Proc. Seventh European Conf. on Soil Mech. and Foundation Engrg., Brighton, England, Sep., Vol. 2, 115-120.

Stevens, J. B., Holloway, M. D., Moriwaki, Y,, and Demsky, E. C. (1979). "Pile group response to axial and lateral loading." Proc. Symp. Sponsored by Geotech. Engrg. Div., ASCE, Oct. 25.

Swane, I. C., and Poulos, H. G. (1982). "A theoretical study of the cyclic shakedown of laterally loaded piles." Research Report No. R415, School of Civ. and Mining Engrg., Univ. of Sydney, July.

Tucker, L. M., and Briaud, J. L. (1988). Analysis of the pile load test program at the lock and dam 26 replacement project. U.S. Army Engineer District, St. Louis, Mo., June.

Turner, J. P., Kulhawy, F. H., and Charlie, W. A. (1987). "Review of load tests on deep foundations subjected to repeated loading." Report EL-5375, Electrical Power Res. Inst., Palo Alto, Calif., Aug.

Vesic, A. (1977). "Design of pile foundations." National cooperative highway re- search program synthesis of highway practice, Report No. 42, Transportation Re- search Board, Washington, D,C.

APPENDIX II. NOTATION

The following symbols are used in this paper:

A = deflection constant for B O E F analysis; a = degradation parameter for method by Little and Briaud;

243

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

n D =

E / = H =

/ / m i n = / m a x z

K,= KhN = Kha =

L = M = N =

n h =

n h N

n h l = p =

P~v =

P l = R14 =

R n =

RnN =

R n l = t =

y =

Y l =

YN =

Ot = =

~3 N =

deflection constant for BOEF analysis; diameter of pile (L); bending stiffness of pile, modulus times moment of inertia (FL2); lateral load applied to top of pile (F); minimum horizontal load during cyclic loading (F); maximum horizontal load during cyclic loading (F); soil reaction modulus ( F / L 2 ) ;

soil reaction modulus at N cycles of load ( F / L 2 ) ;

soil reaction modulus for first cycle of load ( F / L 2 ) ;

length of pile (L); bending moment in pile (FL); number of cycles of load; coefficient of soil reaction (F/L3); coefficient of soil reaction at N cycles of load (F/L3); coefficient of soil reaction for first cycle of load (F/L3); resistance provided by soil ( F / L ) ;

soil resistance N cycles of load ( F / L ) ;

soil resistance for first cycle of load ( F / L ) ;

cyclic load ratio, ratio of minimum to maximum horizontal load ( = n m i n l H m a x ) ; cyclic modulus ratio, ratio of cyclic to static nh;

value of Rn at N cycles; value of Rn on first cycle of load; degradation parameter for elastic soil modulus, nh; pile deflection corresponding to specific soil resistance at specific depth (L); pile deflection corresponding to specific soil resistance at specific depth for first cycle of load (L); pile deflection corresponding to specific soil resistance at specific depth for N cycles of load (L); degradation parameter for soil resistance, p; lateral deflection at top of the pile (L); and

on Nth cycle of load (L).

244

J. Geotech. Engrg. 1994.120:225-244.

Dow

nloa

ded

from

asc

elib

rary

.org

by

EL

YA

CH

AR

CE

NT

RA

L L

IBR

AR

Y o

n 05

/08/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.