Table Of Content3325 March, 1964 SM 2
Journal of the
SOIL MECHANICS AND FOUNDATIONS DIVISION
Proceedings of. the American Society of Civil Engineers
LATERAL RESISTANCE OF PILES INCOHESIVE SOILS
By Bengt B. BromsJ M. ASCE
SYNOPSIS
Methods are presented for the calculation of the ultimate lateralresist¬
ance and lateral deflections at working loads of single piles and pile groups
driven into saturated cohesive soils. Both free and fixed headedpiles have
been considered. The ultimate lateralresistancehasbeencalculated assuming
that failure takes place either when one ortwo plastic hinges form along each
individual pile or when the lateral resistance of the supporting soil is ex¬
ceeded along the total lengthof the laterally loadedpile. Lateraldeflections
at working loads have beencalculatedusingthe concept of subgrade reaction
taking into account edge effects both at the ground surface and at the bottom
of each individualpile.
The results from the proposed design methods have been compared with
available test data. Satisfactory agreement has beenfound betweenmeasured
and calculated ultimate lateralresistance andbetween calculated and meas¬
ureddeflections at working loads. Fordesignpurposes,the proposedanalyses
shouldbe used with caution due to the limitedamounts of test data.
; Note.—Discussionopen until August 1, 1964. To extend the closing date one month,
ÿ awritten request must be filedwith the Executive Secretary, ASCE. This paper la part
[ of the copyrighted Journal of the Soil Mechanlos and Foundation* Division,Proceedings
'r
of the American Society of Civil Engineers, Vol. 90, No. SM2, March, 1964.
'l 1Assoc. Prof,of Civ. Engrg., Cornell Univ., Ithaca, N. Y.
t
27
I
i
i
l
28 March, 1964 SM 2
INTRODUCTION
Single pileB and pile groups are frequently subjectedto highlateral forces.
These forces may be caused by earthquakes, by wave or wind forces or by
lateral earth pressures. For aiample, structures constructed off-shore, in
the Gulf of Mexico, the Atlantic or PacificOceans, are subjected to the lateral
forces caused by waves and wind.2 The safety of these structures depends on
the ability of the supporting piles to resist the resultinglateralforces.
Structures built in such areas as the states of California, Oregon, and
Washington, or in Japan, may be subjected to high lateral accelerations
caused by earthquakes and the supporting piles are called upon to resist the
resultinglateral forces. For example, the buildingcodesgoverning the design
of structures in these areas specify frequently that the piles supporting such
structures should have the ability to resist a lateral force equal to 10% of the
applied axial load.3,4
Pile supported retaining walls, abutments or lock structures frequently
resist high lateral forces. These lateral forces may be caused by lateral
earth pressures acting on retaining walls or rigid frame bridges, by differ¬
ential fluid pressures acting on lock structures or by horizontal thruBt loads
acting on abutments of fixed or hinged archbridges.
The lateral bearing capacity of vertical piles driven into cohesive and
coheslonless soils will be investigated in two papers. This paper is the first
in that series and is concerned with the lateral resistance of piles driven
into cohesive soils. Methods will be presented for the calculation of lateral
deflections, ultimate lateral resistances and maximum bending moments in
that order.
In the analyses developedherein,thefollowingpreceptshave been assumed:
(a) the deflections at working loads of a laterally loaded pile should not be so
excessive aa to impair the proper function of the member and that (b) its
ultimate strength Bhould be sufficiently high as to guard against complete
collapse even under the moBt unfortunate combination of factors. Therefore,
emphasis has been placed on behavior at working loads and at failure
(collapse).
The behavior at working loads has been analyzed by elastic theory assum¬
ing that the laterally loaded pilebehaves as an ideal elastic member and that
the supporting soilbehaves as an ideal elastic material. The validity of these
assumptions can only be established by a comparison with teBt data. The
behavior at failure (collapse) has been analyzed assuming that the ultimate
strength of the pile section or the ultimate strength of the supporting soil has
been exceeded.
It should be noted that the methods developed inthis paper to predict
behavior at working loads are not applicable when localyieldingof the soil
or of the pile material takes place (when the applied load exceeds about half
the ultimate strength of the loaded member).
2 Wiegel, R. L., Beebe, K. E., and Moon. J., "Ocean-Wave Forces on Circular Cy¬
lindrical Piles,"Transactions, ASCE, Vol. 124, 1959, pp. 89-113.
3 "Recommended Lateral Force Requirements," Seismology Committee, Structural
EngrB. Assoc., San Francisco, Calif., July, 1959.
4 "Uniform BuildingCode," Pacific Coast Bldg. Officials Conf.,Los Angeles, CalLf.,
1960.
gM 2 PILE RESISTANCE 29
BEHAVIOR OF LATERALLY LOADED PILES
A large number of lateralload testa have been carried crut on piles driven
into cohesive soils.5-27
5 Bergfelt, A., "The Axial and Lateral Load BearingCapacity,and Failure by Buck¬
lingof Piles in Soft Clay," Proceedings, FourthInternatl.Coof. on Soil Mechanics and
Foundation Engrg., Vol. II, London, England 1957, pp. 8-13.
® Browne, W.H., "Testa of NorthCarolina Poles for Electrical Distribution Lines,"
North Carolina State College of Agriculture and Engineering Experiment Station Bul¬
letin. No. 3, Raleigh,NorthCarolina August, 1929.
' Evans, L.T., "Bearing PUeB Subjected to Horizontal Loads," Symposium on Lat¬
eral Load Tests on Piles,ASTM Special Technical Publication,No.154, 1853,pp.30-35.
8 Usui, R. D., "Model Study of a Dynamically Laterally Loaded Pile,* Jpurmi of the
Soil Mechanics and Foundations Division, ASCE, Vol. 84, No. SMI, Proc. Paper 1536,
February, 1958.
9 Krynlne, D.P., "Land Slides and PileAction," EngineeringNews Record,Vol.107,
November, 1931, p. 860.
10 Lazard, A., "Moment limits de renversement de fondatlons cyllndriques et
parallel6-plpediques Isoldes," AnnaleB de llnstltute Technique du Bailment et das
Travaux Publics, January, Paris, France 1955,pp. 82-110.
11 Lazard, A., "Discussion," Annales de l'lnstltute Technique du Bailment et dea
Travaux PubllcB, July-August, Paris, Franoe 1955, pp.786-788.
12 Lazard, A., and Gallerand, G., "Shallow Foundations," Proceedings, Fifth Inter¬
natl. Conf. on Soil Mechanics and Foundation Engrg.,Vol. HI, Paris, France 1961,pp.
228-232.
10 Lorenz, H., "Zur Tragfflhlgkelt starrer Spundwfinde und Maatgrflndungen,"
Bautechnlk-Archly, Heft 8, Berlin, Germany 1952,pp. 79-82.
1* Matlock, H., and Rlpperger, E.A., "Procedures and Instrumentation for Testa
on a Laterally Loaded Pile," Proceedings, Eighth Texas Conf. on Soil Mechanics and
Foundation Engrg. Research, Univ. of Texas, Austin, Tex., 1950.
15Matlock, H.,and Rlpperger, E.A., "Measurement of Soil Pressureon a Laterally
Loaded Pile," Proceedings, Amer. Soc. of Testing Materials, Vol. 58, 1958, pp. 1245-
1259.
16 McCammon, G. A., and Ascherman, J. C., "Resistance of Long Hollow Plies to
Applied Lateral Loads," Symposium on Lateral Load Tests on Piles, ASTM Special
Tectolcal Publication, No. 154, 1953, pp. 3-9.
17 McNulty, J. F., "Thrust Loadings on Piles," Journal of the Soil Mechanics and
Foundations Division, ASCE, Vol. 82, No. SM2, Proc. Paper 940, April, 1958.
18 Osterberg, J. O., "Lateral Stability of Poles Embedded Ina Clay Soli," North¬
western University Project 208, Bell Telephone Labs., Evanston, 111., December, 1958.
19 Parrack,A.L.,"An Investigationof Lateral Loads on a Test Pile," Texas AIM
Research Foundation, Research Foundation Project No. 31, College Station, Texas
August, 1952.
20 peck, R. B., and Ireland, H. O., "Full-Scale Literal Load Test of a Retaining
Wall Foundation," Fifth Internatl, Conf, on Soil Mechanics and Foundation Engrg.,
Paris, France, Vol. ET, 1961, pp. 453-458.
21 Peck, R. B., and Davisaon, M.T., discussion of "Design and Stability Consider¬
ations for Unique Pier," by James Mlchalos and David P.BLllington, Transactions,
ASCE, Vol. 127, Part IV, 1962,pp.413-424.
22 Sandeman, J.W., "Experiments on the Resistance to Horizontal Stress of Timber
Piling,"von Nostrand's Engineering Magazine, Vol. XXHI, 1880,pp. 493-497.
23 Seller, J.E., "Effect of Depthof Embedment on Pole Stability," Wood Preserving
News. Vol. 10, No. 11, 1932, pp. 152-161, 167-168.
24 Shllts, W. L.,Graves, L.D.,and Driscoll, C. G.,"A Report of! Fieldand Labora¬
tory Tests on the Stability of Posts Against Lateral Loads,"Proceedings,Second Inter¬
natl.Conf. on Soli Mechanics and Foundation Engrg.,Rotterdam,Holland Vol. V, 1948
p. 107.
25 Terzaghl, K., "Theoretical Soil Mechanics,"John Wiley & Sons, Inc., New York,
N. Y., 1943.
'(cid:127)0 March, 1964 SM 2
In many cz#em the available data are difficult to interpret. Frequently,
load tests have been carried out for the purpose of provingto the satisfaction
of the owner or the design engineer that the load carrying capacity of a pile
or a pile group is sufficiently Large to resist a prescribed lateral design load
Under a specific condition. In general, sufficient data are not available con¬
cerning the strength and deformation properties, the average relative density
and the angle of internal friction of cohesionless soils or the average ubcon-
fined compressive strength of the cohesive soil. It is hoped that this paper
will stimulate the collectionof additional test data.
The load-deflection relationships of laterally loaded piles drivgri into
Dohesive soila is similar to the BtreBs-strainrelationships as obtained from
consolidated-undr&ined tests.28 At loads less than one-half to one-third the
Ultimate lateral resistance of the pile, the deflectionsincrease approximately
linearly
with the applied load. At higher load levels, the load-deflection re-
iatlonshdps become non-linear and the maximum resistance is in general
Reached when the deflection at the ground surface Is approximately equal to
ÿLQ% of the diameter or side of the pile.
The ultimate lateral resistance of a pile is governed by either the yield
3-trength of the pile section or by the ultimate lateral resistance of the sup¬
porting soil. It will be assumed that failure takes place by transforming the
'pile into a mechanism through the formation of plastic hinges. Thus the same
principles will be used for the analysis of a laterally loadedpile as for a
Citatically indeterminate member or structure and it will be assumed that the
-moment at a plastic hinge remains constant once a hinge forms. (A plastic
hLnge can be compared to an ordinary hinge with a constant friction.)
The possible modes of failure of laterally loadedpiles are illustrated in
Figs, 1 and 2 for free headed and restrained piles, respectively. An unre¬
strained pile, which is free to rotate around Its top end, Is defined herein as
Onfree-headed pile.
Failure of a free-headed pili (Fig. 1) takes place whso (a) the maximum
bending moment In the pile exceeds the moment causingyielding or failure
of the pile section, or (b) the resulting lateral earth pressures exceed the
lateralresistance of the supporting soilalong the full length of the pile and it
"rotates as a unit, around a point located at some distance below the ground '
Surface [Fig. 1(b)). Consequently, the mode of failure depends on the pile |
Langth, on the stiffness of the pilesection, and on the load-deformation char¬
acteristics of the soil. Failure causedby the formation of a plastic hinge at
the section of maximumbending moment [Fig. 1(a)] takes place when the pile
penetration is relatively large. Failure caused by exceeding the bearing
Capacity of the surrounding supporting soil [Fig. 1(b)] takes place when the
Length of the pile and Its penetrationdepth are small.
The failure modes of restrained piles are illustrated in Fig. 2. Fixed-
keaded piles may be restrained by a pile cap or by a bracingsystem, as is
frequently the case for bridgepiers or for off-shore structures. Inthe case
26 Wagner, A.A., "Lateral Load Teats on Piles for DesignInformation,"Symposium
n Lateral Load Tests on Piles,ABTM Special Publication, Ho. 154, 1953, pp. 59-72.
27 Walsenko, A., "Overturning Properties of Short Piles," thesis presented to the
fniverslty of Utah,at Salt Lake, Utah,In 1958, Inpartial fulfilment of the requirements
or the degree 0# Master of Scleooe,
2-8 McClelland, B., and Fooht, J.A., Jr., "Soil Modulus for Laterally Loaded Piles,"
ransactions, A8CE, Vol. 123, 1958, pp. 1049-1063.
SM2 PILE RESISTANCE 31
when the length of the piles and the penetration depths are large, failure may
take place when two plastic hinges form at the locations of the maximum
positive and maximum negative bending moments. The maximum positive
moment is located at some depth below the ground surface, while the maxi¬
mum negative moment is located at the levelof the restraint (at the bottom
of a pile cap or at the levelof the lower bracingsystem for pile bends).
For truly fixed-headed conditions, the maximumnegativemomentIs larger
than ths maximum positive moment and hence, the yield strength of the pile
section is generally exceeded first at the top of the pile. However, the pile
is still able to resist additional lateral loads after formation of the first
plastic hinge and failure does nottakeplaceuntil a second plastic hiiige romm
at the point of maximum positive moment. The second hinge forms when the
magnitude of this moment is equal to the moment causing yielding of the pile
section IFig. 2(a)]
Failure may also take place after the formation of the first plastic hinge
at the top end of the pile if the lateralsoil reactions exceed the bearing ca¬
pacity of the soil along the full length of the pile as shown in Fig. 2(b), and
the pile rotates around a point located at Bome depthbelow the ground sur¬
face. The mode of failure, shown in Fig. 2(b), takes place at intermediate
pile lengths and intermediate penetration depths. When the lengths of the
piles and the penetration depths are small, failure takes place when the ap¬
plied lateral loadexceedB the resistance of the supporting soils, as shown in
Fig. 2(c). Inthis case, the action ofa pile can be compared to that of a dowel.
Methods of computing the distribution of bending moments, deflections and
soils reactions at working loads (at one-half to one-third the ultimate lateral
resistance) are reviewed inthe following section and a method for the calcu¬
lation of the ultimate lateral resistance of free and restrained piles is pre¬
sented In a succeeding section.
—
Notation. The symbols adopted for use In this paper are defined where
they first appear and are arranged alphabetically InAppendix I.
BEHAVIOR AT WORKING LOADS
At working loads, the deflections of a single pile or of a pile group can be
considered to increase approximately linearly with the applied load. Part of
the lateral deflection is caused by the shear deformation of the soil at the
time of loading and part by consolidation and creep subsequent to loading.
(Creep is defined as the part of theshear deformations which take place after
loading.) The deformation caused by consolidation and creep increases with
time.
It will be assumed in the following analysis, that the lateraldeflections
and the distribution of bending moments and shear forces can be calculated
at working loads by means of the theory of subfrade reaction. Thus, Itwill
be assumed that the unit soli reaction p (In pounds per square inchor tons
per square foot) acting on a Laterally loadedpile Increases Inproportionto
the lateraldeflectiony.(ln inches or feet) expressed by the equation
v&ctisfi) p ÿ k y U)
[ where the coefficient k (in pounds per cubic inchor tons per cubic foot) is
l defined as the coefficient of subgrade reaction. The numericalvalue of the
I
}
i
........
..
c~<
to
-ft ÿo M n
u 1 : n 1<7- n, 1.* r~>-V
JVkW // Wf V-. ÿ» M '(cid:127) (cid:127) v
'/ waÿwss TOSWeiF
// //
I I //
i i
/
/ L lJ
/
/
/ O
( 0) (b) rr
CD
ty <M 2
ILU
(a) (b) (C )
FIG. 1.-FAILURE MODES FOB; FREE- FIG. 2.-FAILURE MODES FOR RESTRAINED PILES
HEADED PILES
en
............ .. 2
.
(O
-— —
MltW|BWrarr~nTr-Tri»rnfa 1 r~i ;mii in mi "iihiiiih,»u nil
SM 2 PILE RESISTANCE 33
coefficient of subgrade reaction varies with the width of the loaded area and
£1*9loaddistribution,as wellas withthedistance fromthegroundsur£ace.29-33
The corresponding soil reaction per unit lengthQ (In pounds per inch or
tons per foot) can be evaluated from
Q « k D y (2)
in which D is the diameter or width of the laterally loadedpile. Ifk D is de¬
notedK (inpounds per square inchor tons per square foot), then
Q « K y , (3)
Methods for the evaluation of the coefficient K for pileB driven into cohesive
soils have been discussed by Terzaghlÿl and will be summarized subse¬
quently. However, the numerical value of this coefficient is affectedby con¬
solidation and creep.
Inthe following analysis, Itwillbeassumedthat the coefficient of subgrado
reaction is constant within the significant depth. (The significant depth is
defined as the depth wherein a change of the subgrade reactionwill not affect
the lateral deflection at the ground surface or the maximumbending moment
by more than 10%.)
However, the coefficient of subgrade reaction is seldom a constant but
varies frequently as a function of depth. Itwillbe shown that the coefficient
of subgrade reaction for cohesive soils is approximately proportional to the
unconflned compressive strengthof the soil.34 Astheunconflned compressive
strength of normally consolidated calys and silts Increases approximately
linear with depth, the coefficient of subgrade reaction canbe expected to
Increase in a similar manner as Indicated by field data obtained by A. L.
ParracklO andby RalphB. Peck, F.ASCE and M. T. Davisson.21The uncon¬
flned compressive strength of overconsolldated clayB may be approximately
constant with depth if,for example, the overconsolldation of the soil has been
causedby glaclationwhile the unconflnedcompressive Btrengthmay decrease
with depth if the overconsolldation hasbeencausedby desiccation. Thus, the
coefficient of subgrade reaction may, for an overconsolldated clay, be either
approximately constant or decrease as a function of depth.
Bo't, A. M., "Bending of an Infinite Beamon an Elastic Foundation," Journal of
Applied Mecbanlca. Vol. 4, No. 1,A1-A7, 1937.
39 DeBeer, E. E., "Computation of Beams Resting on Soil," Proceedings, Second
Internatl.Gonf.on Soil Mechstnioa and Foundation Engrg.,Vol.1,1948, Rotterdam, Hol¬
land,pp. 119-121.
31Terzaghi, K., "Evaluation of Coefficients of Subgrade Reaction,* Geotechnique,
London, England, Vol. V, 1955,pp. 297-326.
32 Veslc, A. B., "Bendingof Beams Restingon Isotropic Elastic Solid," Journal of
the EngineeringMechanics Division,ASCE,Vol. 87,No. EM2, Proc. Paper 2800, April,
1981, pp. 35-51
33 Vealo, A. B.t "Beams on Elastic Subgrade and the Winkler's Hypothesis," Pro¬
ceedings, Fifth Internstl.Conf. on 8oll Mechanics and Foundation Engrg., Vol. I,1961,
Paris, France pp. 845-850.
34 SJcempton, A. W., "TheBearingCapacityof Clays," BuildingResearchCongress,
London, England 1951,pp. 180-189.
March, 1964 SM 2
The limitations imposed on the proposed analysis by the assumption of a
constant coefficient o( subgrade reaction can be overcome. It canbe shown
+tat the lateral deflections can be predicted at the ground surface when the
Coefficient of subgrade reaction increases with depth If this coefficient is as-
CMjmed to be constant and If its numericalvalue is taken as the average within
depth equal to 0.8 /J L.
Lateral Deflections.—For the case when the coefficient of subgrade reac-
f}r\r\ la p/>natont wlfli /IavUK tKjn dIÿ V>iii-4/%ri o/ jv/1"ftIfin" woiidiriÿ
f oments and soil reactions can be calculated numerically,35,36,37 axialytl-
LAlly,30.3® or by means of models.40 Solutions are also available for the case
iJhen a laterally loaded pile has been driven into a layered system consisting
;r an upper stiff crust and a lower layer of soft clays.41
The deflections, bending moments and soil reactions depend primarily on
ÿkD/4EpIp.ÿ
the dlmensionlesslength BL,Lnwhÿch B Ls equal to 5-3® Inthis
expression,Eplp Is the stiffness of thepile section,k the coefficientof a sub-
sT'ade reaction, and D the diameter or width of the laterally loaded pile. A.B.
X/eslc,32 M. ASCE has shown that the coefficient of subgrade reaction can be
'Valuated assuming that the pilelength is large when the dimenslonlesslength
Is larger than 2.25. In the case when the dimenslonless length of the pile
&L Is less than 2,25, the coefficient of subgrade reaction depends primarily
i?n.the diameter of the test plleÿand on the penetration depth.29,30,31,32,33
It can be shown that lateral deflection yQ at the ground surface canbe ex-
L/BÿThls
ffessed as a function of the dimensloidesB quantity yD k D quantity
};, plotted in Fig. 3 as a function of the dimenslonless pile length ÿ L, The
'c-teral deflections as shown in Fig. 3 have been calculated for the two cases
'>hen the pile is fully free or fully fixedat the ground surface. Frequently,the
laterally loaded pllels only partly restrainedand thelateral deflections at the
jvound surface will attain values between those corresponding to fully fixed
rdfully free conditions.
The lateraldeflections at the ground surface can be calculatedfor a free-
f\Jaaded pile as canbe seen from Fig. 3 assuming that the pile is infinitely
jfcLff when the dimenslonless length BL is less than 1.5. For this case, the
(literal deflection ls equal to:
(1*1.5£)
_4F
y « (4a)
k D L
35 Qleser.S.M.,"Lateral Load Testa onVertlcal Fixed-Headand Free-HeadPiles,"
STM Special Publication, no, 154, 1S53, pp. 75-93.
30 Howe, ft. J., "A Numerical Method for Predicting the Behavior of Laterally
(cid:127)*ided Piling,"Shell Oil Co., TS Memorandum 9, Houston, Tex., May, 1955.
37 Ne-wmark, N. M., "Numerical Procedure for Computing Deflections, Moments,
ui Buckling Loads," Transactions, ASCE, Vol. 108, 1943, pp. 1161-1188.
38 Chang,Y. L.,discussionof 'Lateral Pile-LoadingTests,"by Lawrence B.Feagin,
ransactlons,ASCE, Vol. 102, 1937, pp. 272-27-8.
Hetenyl,M.,"Beams on Elastic Foundation," Unlv.of Michigan PreaB,Ann Arbor,
ich., 1946.
40 Thorns. R.L.,"A ModelAnalysis of a Laterally Loaded Pile,"thesis presented to
e University of Texas, at Auatin, Tex., in 1957, inpartial fulfilment of the requlre-
onts for the degree of Master of Science.
41 Davlsson, M. T., and QUI, H. L., "Laterally Loaded Piles Ina Layered System,"
-ureal of the Soil Mechanios and Foundations Division.ASCE, Vol. 89, No. 8M3, Proc
-.per 3509, May, 1&S3, pp. *3-94.
&M 2 PILE RESISTANCE 35
A retrained pile with a dimexuaionleaa length pL less than 0.5 behaves a*
an Infinitely atit? pile (Fig. 3) and the lateraldeflection at the ground surface
can be calculated directly from the equation
(4b)
k DL
It should be r.cted that ar. increase of ihe pilelength decreases appreciably
the lateral deflection at the ground surface for short piles (ft L less than 1.5
and 0.5 for free-headedandrestrained piles,respectively). However,a change
of the pile stiffness has only a small effect on the lateral deflection for such
plies. The lateral deflections at the ground surface of short fixed piles are
theoretically one-fourth or less of those for the corresponding free-headed
piles (Eqs. 4a and 4b).
Thus, the provision of end restraint Is an effective means of decreasing
the lateral deflections at the grourdjLurfÿtrff~or_aTRinglÿtÿai-ly_ÿoaded pile.
This has been shown clearlyÿbyÿfhe tests reported by G. A. MbQammon,
F. ASCE, and J.C. Aschepadan, M. ASCE.l® These tests Indicate that the lat¬
eral deflection of a free pile driven Into a soft clay deflected at the same
lateral load onthe-ayeragq 2.6 times as much as the corresponding partially
restrained/pile.
The lateral deflection* at the ground surface of a free-headed pile can be
calculated assuming that the pile La infinitely long (Fig. 3) vrban the dlmen-.
atonies* length p L exceeds S.5. For this case (pL larger than 2.5) the lab
eral deflection can be computed directly from
-
2 P Me + l)
k D
inwhich koo Is thhÿaeffRient of —subgrade-reactlofueOrrespondlng to an Infi¬
nitely longpile. ~~ ~--
A restrained pilebehaves as an Infinitely longpile when the dimension!ess
length pL exceeds 1.5 as can be seenfrom Fig. 3. The corresponding lateral
deflection {p L larger than 1.5) can be calculated from
P P
(5b)
o k D
(cid:127)O
The lateral deflections at the ground surface depends on the value of the
coefficient of subgrade reaction within the criticaldepth. This depth can be
determined from the following considerations. It can be seen from Fig. 3 that
the lateral deflections at the ground surface are approximately 10% larger
than those calculatedassuming that the pile is infinitely longwhen the dlmen-
sionleBB pile length or embedment length p L la equal to 2.0 and 1.0 for re¬
strained and free-headed plies, respectively. Thus the properties of the piles
or of the soil beyond these dlmensionless depths have only a small effect on
the lateral deflections at the ground Burface. The dlmensionlesB depths p L
of 2.0 and 1.0 are thereforethe critical depths for restrainedand free-headed
piles, respectively.
CO
c»
1
ÿacrÿ
-t>
(a) AXIAL AND LATERAL LOADS
s
o
=r
M CO
, £
Eq (4o)
Eq(4b)
ÿEq(5b)
DIMENS80NLESS LENGTH, £L (b) OVERTURNING MOMENT
CO
— 3!
FIG. 3.-COHESIVE SOILS—LATERAL DEFLECTIONSAT FIG. 4. DISTRIBUTIONOF SOIL REACTIONS
GROUND SURFACE to
niÿiiniiunitwipui
MP
