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11629 OCTOBER 1975 GT10

JOURNAL OF THEGEOTECHNICAL

ENG INEERING DIV IS IONTORSIONAL RESPONSE OF PILES

By Harry G. Poulos;' M. ASCE

INTRODUCTION

Although piles may be subjected to torsional loading by virtue of eccentriclateral loading of a pile group, there appears to be very little work availableto enable the response of piles to torsion to be obtained. Kaldjian (4) has carriedout finite element analyses of short rigid piers while Broms and Silberman(I) carried out model tests on steel piles in sand. Stoll (10) suggested that,for friction piles in clay" it may be easier and cheaper to determine the ultimateaxial load capacity of a pile from a torsion loading test rather than a conventionalaxial load tests. Stoll developed an apparatus whereby torsional tests couldbe performed, and a number of full-scale load tests were carried out; however,no comparative axial load tests were carred out.In this paper, an analysis is described for the determination of the responseof a single cylindrical pile subjected to torsion. Parametric solutions for therotation of the pile head are presented, for both a uniform soil and a soilin which shear modulus and pile-soil adhesion increase linearly with depth.The results of a series of model pile tests in clay are then described in whichthe axial and torsional responses of the piles are investigated. The pile-soiladhesion from each type of test is compared and the shear modulus of thesoil deduced from axial load tests is used to predict the rotation. of thetorsionally-loaded piles. The results indicate that Stoll's proposals regardingthe utility of torsional pile load tests are worthy of further investigation.ANALYSIS

The problem considered is shown in Fig. l(a). The pile is circular, of lengthL, having a constant shaft diameter, d, a base diameter, d", and the shearmodulus of the pile material is G p o The pile is subjected to a torque, T, atNote.i--Discussion open until March 1, 1976. To extend the closing date one month,a written request must be filed with the Editor of Technical Publications, ASCE. Thispaper is part of the copyrighted Journal of the Geotechnical Engineering Division,Proceedings of the American Society of Civil Engineers, Vol. 101, No. GTlO, October,1975. Manuscript was submitted for review for possible publication on March 6, 1975 .1Reader in Civ. Engrg., Univ. of Sydney, Sydney. Australia.

1019

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1020 O CTO BE R 1 975 GT10the ground surface and is situated in a semi-infinite elastic soil mass havingshear modulus G sand Poisson's v 5' The pile shaft-is divided into n equal cylindricalelements while the base comprises m annular elements, each element beingacted upon by an unknown uniform interaction stress (or traction) [Fig. l(b)].

TABLE 1.-Effect of Number of Elem.,nts on Pile Rotation SolutioniNumber Number Ground-Line Rotation Factor, 140of of baseshaft eiernents KT=elements (m) 390,625 3,906.3 390.6 18.1C 1 ) ( 2 ) . (3) (4) ( 5 ) (6)

5 3 0.01241 0.01448 0.02939 0.0683810 3 (}.0l238 0.01444 0.02891 0.0643215 3 0.01236 0.01442 0.02878 0.0632410 1 0.01242 0.01447 0.02892 0.06432to $ 0.01237 0.01443 0.02891 0.06432

Note: rotation < l> = (T/Gsd3 ) 14>;Lid = 25; \Is =0.5.

5011

TSur1aca

cc' --+-f+ff&!ItI-++ot- Plan otBO!>

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GT10 TORSIONAL 1021at the pile-soil interface remain elastic, the expressions for soil and pile rotationscan be equated and solved, together with the equilibrium equation, to obtainthe interaction stresses and thus the pile rotations. The analysis may readilybe extended to allow for pile-soil slip at the interface.Soil Rotations.-Considering a small elemental area at the pile-soil interface[F ig . lee)], the tangential load on this-area is dP =05rj . dBO . 8z~ in whichT i = interaction stress; 88 = included angle of area; 8z = length of elementalarea. This load will cause a deflection, dp 4 > ' tangential to the pile surface atany point in the soil mass, which can be expressed asd P 4 > = dpxx cos e + dpxx sin e (1)in which dp xx = component of deflection parallel to direction of load dP; dp xx= component of deflection normal to d P; e = angle defined in Fig: lfc): anddp xx and dp xx may be evaluated from the equations of Mindlin (6) for a horizontalsubsurface point load. By integration of Eq, 1 oyer a cylindrical or annularelement, the tangential deflection, and thus rotation, at any point, i, may beobtained. This double integration may be carried out partly analytically andpartly numerically. For an elements on the pile, the son rotations may be expressedas{ < I > , } ~ [ ~ ' , ] {T} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)in which [lsi 0 s J = (m + n) by (m + n) matrix of soil rotation influencefactors obtained from integration of Mindlin's equation; {q, s } = soil rotationvector; and {T} = interaction stress vector ..Eq. 2 applies strictly only for uniformsoil with constant Os; however, it may be applied approximately to nonuniformsoil by using the appropriate value of G si at an element, i, in the soil rotationfactor matrix. This procedure in effect assumes that the stress distribution inthe soil is the same as for the uniform soil, but that the strain at a pointis governed by the value of G 5 at that point.Pile Rotations.-By application of the torsion equation for a circular cylinder,the following expression may be obtained for the pile rotation at the midpointsof the elements:

LdJ{ q > p} = G J [AD][FEQ] {T } + 4 l b {I}n p p ....... (3)in which { < p p } = pile rotation vector; Jp = polar moment of inertia of pile;{ ' T } = interaction stress vector. c . h = tip rotataion of pile; [AD] = (m +n) by (m + n) pile matrix in which ADij = 1 for j > i, 0 for j < i, and0.5 for j = i; [FEQ] = (m + n) by (m + n ) pile matrix in which FEQjj= Fj for j > i and i n; Pi = A jlJ d3; A j = surface area of element j; and Ij = lever armof interaction stress on element, j.Pile-Soil Compatability and Equilibrium.-For elastic conditions at the pile-soilinterface, { 4 > .l = { 4 > p } and from Eqs. 2 and 3

[LIs ] { 'T }ADFEQ - - Gsr - + 4 > b {I} =0 (4)ndKT o, a;

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1022 O CT OB ER 1 -9 75 GT10in which Gsr = a reference value of soil shear modulus; and K T = torsionalstiffness factor in which

GplpKT = G d 4 ", ".,.,'" 0 0 0 0 0 , (5)srThe value of KT expresses the torsional stiffness of the pile to the soil andhas limiting values of 00 for an infinitely rigid pile, and 0 for a perfectly flexiblepile.In addition to the (m + n)simultaneous equations provided by Eq, 4, equilibriumof the pile requires that

m+n TL F T=-3 "., '.. . . 0 , 0 0 , (6)j=' din which Fj is defined in Eq. 3. Solution of Eqs. 5 and 6 gives the m + nunknown values of T and the value of q , b from which the pile rotations maybe calculated via Eq. 3. Note that for the top element, the rotation thus calculatedis that halfway dowr:. the element. and the rotation of the upper half of thiselement must be added to obtain the rotation at the ground surface. .Allowance for Pile-Soil Slip.-The simplest means of making allowance forslip is to specify a limiting value, T G of the interaction stress at each element.When T reaches or exceeds T G the rotation compatability equation for thatelement (from Eq, 4) is replaced by the condition, T = T G' and the solutionis recycled until 'T -< T a at all elements.The foregoing procedure could be modified to allow for a nonlinear relationshipbetween T and < p , in an analogous manner to that used by Coyle and Reese(2) for laterally loaded piles. However, no data are yet available to enablesuch a relationship to be obtained and it will be assumed herein that T versus< p is linear until T = = T QACCURACY OFANALYSIS

The accuracy of the preceding analysis has been examined in two ways:(1) Examination of the effect of the number of elements on the solution obtained;and (2) comparisons with previous solutions.The effect of the number of elements is summarized in Table 1 for a uniformdiameter pile and for four different values of KT ranging from very stiff (KT= 390,625) to relatively flexible (KT = 78.1). The solution for the stiff pileis only slightly affected either by the number of shaft or base elements; butas K T decreases, the number of shaft elements has increasing influence, althoughthe number of base elements appears then to have virtually no influence (this.arises because very little torque is transferred to the piJebase, as will be examined),On the basis of Table 1, it appears that the use of 10 shaft elements shouldgenerally produce a reasonable result, although a greater number may be desirablefor very flexible piles.In comparing the present solutions with other solutions, the two limiting casesof an infinitel y long rigid pile and a rigid pile of zero length (i .e., a' circularsurface footing) can be considered first. For the former case, the followinganalytical solution may be obtained for the rotation per unit length of pile,

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GT10

0'

llii

TORSIONAL 1023

_ ~olutlon for SurfacG! Plotc!

_-- Numo;rlcol SQlutlon- - Analytical SoluUon forLong Plio;

01 10 100

FIG. 2.-Numerical and Analytical Solution for Rigid Pile',5

Kaldjion (1971)

(a)00 025 050 075 '0Lid

3tred ria "T-O 05 H) '5 a

1.0 (6)

V :;. : 02 --- Author

FIG. 3.-Comparison between Solutions for Rigid Pier: (a) Rotation; (b ) Shear Stresson Shaft; (c ) Shear Stress on Base

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1024 O C TO B ,E R 1 97 5 GT104 > . ; (according to J. R. Booker in a private communication):

T.4 > . =---11 '0 d2sin which TI= applied torque per unit length. A comparison between the solutionsfrom the present analysis and from Eq, 7 is shown in Fig. 2 as a functionof L/ d. The agreement is very close for L/ d > 5, thus indicating that a rigidpile is effectively infinitely long in such cases.For the other limiting case of a rigid circular plate, the analytical solutionfor rotation 4 > is

. (7)

1.5T4>=G d3 .s

. (8)in which T = total applied torque. Using m = 10 annular elements to dividethe base, a factor of 1.51 was obtained as compared with the correct valueof 1.5 in Eq. 8. , Even with five elements, a factor of 1.52 was obtained, thusindicating satisfactory accuracy of the analysis. .Further comparisons were made with the finite element results of KaJdjian(4) who obtained solutions for a rigid cylinder up to L/ d = 1. Fig. 3(a) showscomparisons between the writer's and Kaldjian's solutions for rotation whilecomparisons between solutions for the stress distribution along the shaft andbase for L/ d = 1 are shown in Figs. 3(b) and 3(c). The agreement is generallygood although the rotations obtained by Kaldjian appear to diverge from' thewriter's values for L/ d > 0.5. it is not possible to determine whether thisdivergence is due to inaccuracy in the writer's results or Kaldjian's, althoughthe results in Table 1 suggest that the latter is more likely.PARAMETRIC SOLunONS

For a uniform-diameter pile in a soil with constant shear modulus and pile-soiladhesion, the top rotation, 4 > , of a pile subjected to torque Tmay be convenientlyexpressed asT 1 4 >4>---- G dJ F .s 4> . (9)

in which 1q , = elastic rotation influence factor; G s = soil shear modulus, andF < t> = correction factor for the effects of pile-soil slip. The values of J e t > andF4>are functions of L/d and K T (Eq. 5) and are plotted in Figs. 4 and 5.For very flexible piles (low KT values), [4>is independent of L/d, but as K Tincreases, the effect of LI d becomes more significant, l e t > decreasing as L/ dincreases. The value of l e t > is also virtually independent of v s (as it is for thelimiting cases of a surface footing and an infinitely long pile). The slip correctionfactor, F 4>'decreases as the ratio, TITu. increases, in which Tu = ultimatetorsional resistance of pile (for full pile-soil slip). The effect becomes moremarked as the pile becomes more flexible. The effect of L/ d on F q , may bealmost entirely eliminated by plotting F4>as a function of a modified torsionalstiffness factor, KTe, in which

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GT10 TORSIONAL

10

0'

ValulZs 01Lid1-------

001

FIG. 4.-lnfluence Factor for Rotation of Pile Head; Constant Gs

02 "0'B

AG. 5.-YIeld Correction Factor F",; Constant G, and Til

1025

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1026 O CT OB ER 1 97 5 GT10

K T . = K T ( ~ ) 'For purely elastic conditions, the effect of KT on the distribution of rotationwith depth is shown in Fig. 6. For stiff piles (KT = 104), the rotation is constantalong the pile, but as Ky decreases, the top rotation increases and becomesincreasingly concentrated in the upper part of the pile.

. (10)

;;01 02

Valu(ls of KT

LId =25Vs=O5

llastic conditions)

lO~""_-__'_..,.....-_"'&-_--"__--__'

FIG. 6.-Effect of Pile Flexibility on Rotation Distribution along Pile; Constant G,

FIG. '.-Effect of Pile Flexibility on Proportion of Torque Carried by Base; ConstantG,

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GT10 TORSIONAL 1027

III

The proportion of the applied torque transmitted to the pile base is shownin Fig. 7 as a function of L/ dand KT, again for elastic conditions. This proportiondecreases as pile stiffness decreases or L/ d increases. It is significant thateven for a short rigid pier (LI d = 1), only 9% of the torque is carried bythe base. The advent of pile-soil slip leads to some increase in the torque carriedby the pile base, but this increase is not generally significant. The implicationof Fig. 7 is that the effect of any underlying stiff strata will not be significantin reducing the pile rotation and that even the socketing of a pile into underlying

r. ;~

0001

FIG. B.-Influence Factor for Rotation of Pile Head; Linearly Increasing G srock may not reduce the pile rotation unless the pile is relatively short andstiff; this conclusion is analogous to that found for socketed laterally loadedpiles by the writer (7). Furthermore, the presence of an enlarged base generallywas found to have very little influence on the pile rotation.For a soil having shear modulus and pile-soil adhesion that increase linearlywith depth, the rotation of the top of a uniform diameter pile may be givenby

. . . (11)

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fil'l

1028 O CT OB ER , ,19 75 GT10

FIG. g.-Yield Correction Factor F , ; linearly Varying Gsand T"in which N G = rate of increase of shear modulus with depth (i.e., at depthZ, Gs = N aZ); 1$ = elastic rotation influence factor; and F~ = slip correctionfactor. Values of I~ and F$ are plotted in Figs. 8 and 9. In this case, thepile torsional stiffness factor is

a.s,K' =---T N d 5a

......... (12)

and for F$' the effects of L/ d are removed by introducing a modified factor,i.e,

(25 ) 3K~.~ K~ ~ ............ (13)

MODEL PILE TESTS

A series of small-scale model pile tests was carried out to examine thecharacteristics of pile response to torsion and to investigate the relationshipbetween axial and torsional response of a pile. In particular, it was hoped todiscover how successfully the shear modulus and pile-soil adhesion backfiguredfrom an axial load test on a pile could be used to predict the torsional responseof a pile and thus, more importantly from a practical point of view, how wellsoil parameters backfigured from a torsional test could be used to predict axial'load behavior.Apparatus and Experimental Procedure.-- The apparatus used was similar tothat used by Davis and the writer (3) and Mattes and the writer (5) for tests

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GT10 TORSIONAL 1029on model footings and piles, respectively. It consisted of a three-piece vessel,a central cylindrical piece 12 in. (305 mm) internal diameter containing the soiland piles, a steel base plate bolted to the central piece and through whichdrainage could occur, and a top piece containing water under pressure andseparated from the soil in the center part by means of a rubber membrane.The piles were of solid aluminium, ranging in length from about 6 in. (152mm)-20 in. (508 mm) and in diameter from 0.5 in. (13 mm)-1.5 in. (38 mm).The soil used was a Kaolin (LL = 55; PL = 33) and was placed into thepressure vessel at an initial water content of about 55%. Preliminary consolidationwas carried out to a vertical effective pressure of about 10 psi (68.9 kN 1m 2),using a back pressure of 20 psi (137.8 kN/m2). The pressure was then releasedwithout further drainage, the vessel top removed and the piles installed byjacking under a constant rate of penetration. Four piles were installed in eachtest (two sets of two identical piles), one pile of each set to be tested in torsionand the other under axial load. The vessel was reassembled and the consolidationpressure increased to the final required value. In most tests, this value was35 psi (241 kN/m2) although tests at pressures of 20 psi (138 kN/m2) and54 psi (372 kN 1m 2) were also carried out. After completion of consolidation,the vessel top was removed and testing of the piles was carried out.For the torsional tests, the torque was applied to the top of the pile bymeans of dead weights attached to a horizontal cable wrapped around a 4-in.(102-mm) diameter disk on top of a spindle that in turn was connected to akey that fitted into a slot cut in the top of the pile. The rotation of the pilewas measured by a dial gage mounted on an arm that was bolted to the baseof the loading spindle, the radius of the arm being 4.8 in. (122 rnm). A correctionwas made for the torque due to the spring force of the dial gage. Incrementsof torque were added at intervals of 15 sec until failure of the pile occurred.The axial tests were carried out by adding increments of load to the pilethrough a hanger, the settlement being measured by means of a dial gage; inthis case, the axial force exerted by the dial gage was generally significant.The IS-sec periods were again used between loading increments, and theincrements were planned so that the time to failure would be approximatelythe same as for the corresponding torsion test.To have a consistent definition of "failure" in the subsequent interpretationof the tests, a pile was considered to have failed after it- had rotated through

Z O when tested in torsion and after it had settled 10% of its diameter whenloaded axially.Test Resultsv-c- The model test results are summarized in Table 2. In interpretingthe test results, it was assumed that undrained conditions prevailed during loading(although this may not necessarily have been entirely correct), and the soilwas assumed to be purely cohesive. For the axial load tests, the adhesion tocohesion ratio. ca l Cu' was taken to be 0.65, a value measured in a series ofconsolidated-undrained direct shear tests on an aluminium Kaolin interface. Theshear modulus, G s' of the soil was backfigured from the axial load tests atsmall loads within the linear portion of the load-settlement curve. The methodof calculating G s was as described by the writer (9), assuming the soil Poisson'sratio to be 0.5.Pile-Soil Adhesion from Axial and Torsion Tests.~Fig. 10plots pile-soil adhesion,ca. from torsional and axial tests and shows that there is good correlation between

II1I

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1030 OCTOBER 1975 GT10TABLE 2.-Summary of

Consoli-dated

pressure, 8ackfigured,inpounds ca' in caTest per pounds per torsion/num- L, in d, in square square inch caber inches inches inch Torsion Axial axial

(1) ( 2 ) . (3) (4) (5) (6) (7)IA 10.0 1.0 35.0 1.55 1.51 1.03IB 8.0 0.5 1.58 1.64 0.962A 10.0 1.0 35.0 1.99 2.63 0.762B 9 ..0 1.5 1.06 1.97 0.543A 10.0 1.0 35.0 1.28 2.13 0.603B 8.0 0.5 2.17 2.04 1.064A 8.0 0.5 35.0 2.77 2.55 1.094B 12.0 0.5 2.13 1.87 1.14SA 8.0 0.5 35.0 3.09 3.20 0.975B 12.0 0.5 2.55 2.85 0.89~A 19.75 1.0 20.0 0.56 0.64 0.886B 20.75 0.75 0.65 0.62 1.057A 19.75 1.0 35.0 1.35 1.60 0.847B 20.75 0.75 1.20 1.65 0.738A 19.75 1.0 54.0 2.40 2.53 0.958B 20.75 0.75 2.36 2.45 0.969A 12.0 0.5 35.0 1.83 1.39 1.32lOA 11.75 0.75 35.0 LOS 1.03 1.02ItA 12.0 0.5 35.0 2.09 1.75 1.19liB 12.0 0.5 1.64 1.38 1.1912A 11.75 0.75 35.0 3.79 3.52 1.08Note: 1 in. = 25.4 rom; 1 psi = 6.89 kN/m2; Average, Col. 7 = 0.96 and Average,

the two sets of values. As shown in Table 2, the average ratio of c a fromtorsional tests to that from axial tests is 0.96, with a range of 0.54-1.32. Thevariations between C a values from different tests in which a similar consolidationpressure was used, are probably due to variations in the moisture content andthe nature of the pile surfaces.Comparisons between Calculated and Measured Rotations.-For each test, anaverage value of G s was obtained from the axial load tests and then used tocalculate the rotation of the piles subjected to torsion. It was assumed thatG s was constant with depth and thus the theoretical curves in Fig. 4 wereused. The value of torsion for which the rotation was' calculated was in thelinear range of the observed torsion versus rotation curve (generally up to 1/3-1/2of the ultimate torque). The calculated rotations are shown in Table 2 togetherwith the measured values and the ratio of calculated to observed rotations.Despite' some anomalies in individual tests, the overall agreement is quitereasonable: The average ratio of calculated to observed rotation is 0.88 witha range of 0.31-1.47. In view of the small scale .of the tests and possible

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GT10Model Test Results

. TORSIONAL 1031

Backfigured, Average, GsGs' from from axial Torque, (Calcu-axial test, test, in T, in Mea- Calcu- lated/in pounds pounds per pounds sured lated mea-per square square Average, per 4 > 4 > sured)inch inch KT inch radians radians 4 >(8) (9) (10) (11 ) (12) (13) (14)

189 215 1,758 8.0 0.00129 0.00119 0.92240 2.0 0.00173 0.00171 0.99276 362 1,044 8.0 0.00131 0.00075 0.57447 20.0 0.00119 0.00087 0.73317 292 1,086 8.0 0.00073 0.00078 1.07378 2.0 0.00075 OJJOI IO 1.47294 293 1,290 2.0 0.00127 0.00131 1.03292 4.0 0.00638 0.00197 0.31294 274 J ,380 2.0 0.00096 0.00140 1.46254 4.0 0.00427 0.00210 0.4919 0 168 2,250 20.0 0.00183 0.00238 1.30145 6.0 0.00244 0.00140 0.57273 292 1,294 20.0 0.00167 0.00151 0.90310 8.0 0.00181 0.00117 0.65443 420 90 0 20.0 0.00142 0.00114 0.80396 16.0 0.00135 O'(XH81 1.34264 264 1,430 4.0 0.00477 0.00218 0.46307 307 1,230 4.0 0.00071 0.00077 1.09300 258 1,465 4.0 0.00177 0.00223 1.26215 4.0 0.00452 0.00223 0.49536 536 705 16.0 0.00317 0.00205 0.65

Col. 14 =0.88.

experimental errors in measuring the small rotations involved, this agreementis encouraging and points to the possibility of using axial load test data topredict both working load and ultimate behavior of piles subjected to torsion,or vice versa.A further implication of the agreement obtained in Table 1 is that for estimatesof pile response to torsion in field cases where no other data are available,approximate values of Gs may be derived from values of Young's modulusE; for axial loading; for example, the correlations between Esand C II suggestedby the writer (8).Typical comparisons between calculated and observed torque versus rotationcurves to failure are shown in Fig. 11. The agreement here is generally notgood at load levels approaching failure. This lack of agreement possibly stemsfrom two sources: (1) The increasing effects of shear creep on rotation asthe torque approaches the ultimate value; and (2) the inadequacy of the simpleelastic-plastic response assumed in the analysis in modeling the real shear stressversus rotation characteristics of a single element. Nevertheless, at normal

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1032 OCTOBER 1975 GT105-0

N obz 1Ib/sQ In = 689 kN 1m24-0

~g~ 3-0- = -. . , 0ti 0~ 002-0C 0- xE ' - 0~cu

1-0 2-0 3-0 4{)Co From Torsional Tests (Ibl SQ in)

FIG. 10.-Values of C a from AAial and Torsional Load Tests

T~b_ln)L= 19-75 tn ,d = 10 ln

10

(a)-0025 -0050 '00759 (radians)

T(Ib-in)

20

10

(c)002 004 0069 (radians)

L = 20-75ind = 0-75 in

30

20

(b)-002 004 -006 -o os

g (radians)10

L= 1175ind = 0-75in

C d )004

-M

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GT10 TORSIONAL 1a33working loads when relatively little slip has occurred, the theory appears toadequately predict the torque-rotation behavior of the pile.CONCLUSIONS

Theoretical results from the analysis of a pile subjected to torsion show thatthe length of the pile does not significantly influence the rotation of the pilehead unless the pile is stiff relative to the soil (KT or K ~> 100). In addition,a surprisingly small amount of the torque is transmitted to the pile base, evenfor very short piers or piers having an enlarged base.The theoretical results may be used directly to evaluate the torsional response

of a single pile in a group. Although no calculations have yet been carriedout, it is very likely that interaction between adjacent torsionally loaded pileswill not be significant for normal piles. No measurable affect was observedin the model pile tests. The results also have an application in the interpretationof load tests on torsionally loaded piles.To examine the relationship between the axial and torsional behavior of a

pile, a series of tests were carried out on model piles in Kaolin. These indicatedthat there was a good correlation between the pile-soil adhesion from eachtype of test and that the soil shear modulus ca1culated from axial load testscould reasonably be used to predict the response of piles subjected to torsion,at least at normal working load levels. The results therefore imply that torsionalload tests data may be used to predict the behavior of axially loaded pilesin clay. One limitation of such tests may be that they would need to be carriedout on relatively short or stiff piles so that full pile-soil slip occurs prior tofailure of the pile material itself. While other factors such as soil anisotropyand layering may also create complications in practical cases, the model testsindicate that the use of torsional pile load tests in clay soils is worthy of closerconsideration.ACKNOWlEDGMENTS

The work described in this paper forms part of a general program of researchinto the settlement and deformation of all types of foundations being carriedout at the University of Sydney, Sydney, Australia, under the general directionof E. H. Davis. His comments and advice are greatly appreciated. The workis supported by a grant from the Australian Research Grants Committee. Themodel tests described herein were carried out by R. B. Spry and R. K. Roweas part of their undergraduate thesis work. Acknowledgments are also due toK. L. Larymore for his assistance in the construction of the experimentalapparatus and J. R. Booker for his assistance with various aspects of the theoreticalanalysis.ApPENDIX I.-REFERENCES

1. Broms, B. B., and Silberman, J. 0., "Skin Friction Resistance for Piles in CohesionlessSoils," Sols Soils. No. 10, 1964, p. 33.2. Coyle, H. M., and Reese, L. C., "Load Transfer fo r Axially Loaded Piles in Clay,"Journal of So i l Mechanics and Foundation Engineering, ASCE, V ol. 92 , No. SM2 ,Proe. Paper 4702, Mar., 1%6, pp. ]-26.

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1034 OCTOBER 1975 GT103. Davis, E. H., and Poulos, H. G., "Use of Elastic Theory for Settlement PredictionUnder Three-Dimensional Conditions," Geotechnique, London, England, Vol. 18, No.I, 1968, pp. 67-91.4. Kaldjian, M. J., "Torsional Stiffness of Embedded Footings," Journal of the SoilMechanics and Foundations Division, ASeE, Vol. 97. No. 8M7, Proc. Paper 8241,July, 1971, pp. 969-980.5. Mattes, N. S., and Poulos, H. G., "Model Tests on Piles in Clay," Proceedingsof the First Australia-New Zealand Conference on Geomechan.ics, Vol. 1, 1971, pp.

254-259.6. Mindlin, R. D., "Force at a Point in the Interior of a Semi-Infinite Solid," Physics,Vol. 7, 1936, p. 195.7. Poulos, H. G., "Behavior of Laterally Loaded Piles: III-Socketed Piles," Journalo f the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM4, Proc.Paper 8837, Apr., 1972, pp. 341-360.8. Poulos, H. 0., "Load-Settlement Prediction for Piles and Piers," Journal of the SoilMechanics and Foundations Division, ASeE, Vol. 98, No. SM9, Proc. Paper 8170,Sept., 1972,pp. 379-397.9. Poulos, H. G., "Some Recent Developments in the Theoretical Analysis of PileBehaviour," Soil Mechanics-New Horizons, 1. K. Lee, ed. Newnes-Butterworths,London, England, 1974, pp. 237-279.10. Stoll, U. W., "Torque Shear Test on Cylindrical Friction Piles," Civil Engineering,ASCE, Vol. 42, No.4, Apr., 1972,p . 63-64.

ApPENDIX II.-NOTATION

The following symbols are used in this paper:AD =Ca =clI =d =d b =Es -

F 4 > =F' =4 >Gp -Gs =o; =1 4 - =I' -' ".~ -Jp -

K =K' =TK T e, K ~e =L =m -NG -n =T -t; =e -Vs -

pile matrix;pile-soil adhesion;undrained cohesion;pile shaft diameter;base diameter;Young's modulus of soil;yield correction factor for constant G $;yield correction factor for linearly varying G $;shear modulus of pile;shear modulus of soil;reference value of G s ;rotation influence factor for constant G s ;rotation influence factor for linearly varying G s;matrix of soil rotation influence factors;polar moment of inertia of pile section;pile torsional stiffness factor for constant G s ;pile torsional stiffness factor for linearly varying G s;modified values of K T, K ~;pile length;number of annular base elements;rate of increase of G s with depth;number of elements along shaft;applied torq ue on pile head;ultimate value of T;angle defined in Fig. l(c);Poisson's ratio of soil;

5/11/2018 Poulos HG-1975

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GT10 TORSIONALT = pile-soil shear stress at interface;

T Ii - limiting value of T.< I > = pile head rotation; and

~ b = rotation of pile base.

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