A me:ioc o'ce:ermina:iona'-:ie a-.era ear:i oressurecoe "icien: 'orsia': 'ric:ionby DR. TING WEN HUI", MICE

A SIMPLIFIED fundamental approachto estimating the shaft friction of pilesin clay was presented in a Paper, by Bur-land (1973). The approach has manyproblems which were discussed in thePaper. An additional problem is that itdoes not lead to the observation that thedistribution of skin friction along a shaftis generally parabolic as described byVesic (1969). In spite of these difficulties,the "static formula" represents a use-ful starting point in the understanding ofthe bearing capacity of a pile.

In his Paper, Burland assumes as anestimate that K=K„. This author findsthat there is another way of estimatingthe value of K. Consider an element ofsoil adjacent to the pile at depth z belowthe ground level as shown in Fig. 1 (a).An enlarged view of the element isshown in Fig. 1 (b) with the stressesacting on it. Initially, before the installa-tion of the pile, K=K. and t =0. If the pileis now installed and the load on it in-creased until the pile fails, then AC willbecome a failure plane. The maximumvalue of ~ will be ueveloped and theprincipal planes which were AB and ACwill be rotated.

It is assumed as an approximation thatthe vertical stress on AB remains as yzafter shear failure occurs on plane AC.With this assumption and vvith the factthat AC is a failure plane, K can be de-duced as a function of c', lf'nd z. InFig. 2 (a), point B represents the state of

«Associate Professor, Faculty of Engineering,University of Malaya, Koala Lumpur, Malaysia

1 —(2c'/yz) tan 4'(2)

? tan' + 1

For normally consolidated or soft claysc' 0 and equation (2) becomes:

2tant4 + 1

" (3)

An assessment can be made of theresults indicated by equation (3). Burlanddefines p = K tan 4'. According to equa-tion (3) this means that:

tan y'

tant ff' 1(4)

The values of p are plotted in Fig. 3using Burland's plot and compared withhis values of p determined from theassumption that K = K. = 1-sin 4'. Itcan be seen that the values of p rangingfrom .234 to .35 are between the valuesof P = 0.25 and 0.4 observed by Burlandin his Fig 3.

In the case of K)1, the soil element ofFig. 1 (a) is assumed initially to be ata state of rest, with K, the coefficient ofearth pressure having a value greaterthan one. The initial vertical stresses offaces AB and CD are yz. The at rest

stress on plane AC on a Mohr diagramfor K(1. It can be deduced from Fig, 2(a) that:

=Kyztan4 + c ...."(1)

stress conditions on faces AC and CD aredenoted by points E and F respectivelyin Fig. 2 (b).

The pile is now loaded, and a graduallyincreasing shear stress r is applied on faceAC of Fig. 1 (b). This is denoted at anyinstance by F''n Fig. 2 (b). The com-plementary shear stress —s- (EH') is alsoshown in the figure. It is again assumedthat the vertical stress yz, in face CD(Fig. 1 (b) is unaltered by shearing onthe face.

As the shear stress on face AC is furtherincreased, a stage will be reached whenits complementary shear stress on faceCD will reach the peak value —t, (EH" inFig. 2 (b)). This also means that CD (Fig.1 (b)) has become a failure plane. Thevalues f, and K can be simply deducedfrom Fig. 2 (b) as follows:—

= yz tan ff' c'.....(5)

K = 2tan"4'+1+ (2ctan4')/yz (6)

It is noted that equation (5) does notcontain K. If c's taken to be 2.0lb/sq.in. and 4' 28.1's determined by Bis-hop et al (1965) for their London claysample, block (1), at level A, then theshaft friction t-., can be obtained by apply-ing equation (5). The results for f-s thusobtained are plotted in Fig. 4 and com-pared with the lower lim'it of p = 0.8as suggested by Burland in his Fig 5. Itcan be seen that the agreement betweenthe two sets of values are reasonable. Asa further check, the values of K are alsocalculated from equation (6) in twoinstances. It is found that K = 2.31 at

Kyz

+11

CT>i D

A >rZB

KTz

Q U

Fig. 1 (b)

22 Ground Engineering

Fig. 1 (a)

2m and K = 1.72 at 10m and both ofthese appear to be reasonable values.

Although reasonable values of K havebeen predicted by equation (6), the pre-diction necessitates the assumption thatfailure is taking place on a horizontalplane. Further investigat'ion into this prob-lem will be required.

0tr

Kgz

LI

r

gZ-KTZ',--'=VZ

\

Fig. 2 (aj

I

J1

ConclusionIt has been shown that the values of

t-. and K as determined by the author'proposed equations (1), (2), (5) and (6)compare well with the observed valuesdetermined by Burland and may be usedas a method for determining the valueof K. It will be of interest to extend theiruses to other situations.

Referencesf. Bishop, A. W., Webb, D. L., & Lewin, P. I.

"Undisturbed samples of London clay fromAshford Common shaft: strength-effective stressrelationships". Geotechnique Vol. 15, No 1.

2. Borland, J. B., (1973): "Shaft friction of pilesin clay —a simple fundamental approach".Ground Engineering, Vol. 6, No 3, May 1973.

3. Vesic, A. S. (1969): "Load transfer, lateralloads and group action of deep foundations".ASTM Special Technical Publication 444, p6.

Dr. J. B. Burland comments:Dr. Ting Wen Hui assumes that thevertical effective stress adjacent to thepile shaft rema'ins constant equal to yzup to failure. He then derives two expres-sions for the shaft resistance:

yz tan fb'+ c'

2 tan'f'+ 1" (7)

which follows from h'is equations (1) and(2). and is based on the assumption thatfailure takes place along the interface be-tween the soil and the shaft,

Fig. 2 (b)and e, = yz tan ff'+ c'5)

I.O-

0.8

0.6

0.4

0.2

I5'0' I

25'0'ig.

3

l

g 4- K>I

z 6

I 8-40e IfI

clO- Pll e 0.8

l2-Fig. 4

SHAFT FRICTION KN/m0 20 40 60 80 IOO l20 l40

which requires that failure takes placeon a horizontal plane.

It should be noted that, in fact, neitherexpression contains any factor involvingthe initial in-situ horizontal stress in theground, although it appears that equation(7) is to be used for K, ( 1 and equation(5) for K, ) 1.

It is apparent that for any given valuesof g', c'nd yz the shaft friction can takeon only two possible values irrespectiveof the magnitude of the initial horizontaleffective stress in the ground. Also it isnot obvious which expression to use whenK, = 1. A decision one way or the othermakes a big difference to the value of K.No explanation 'is given for rejecting theassumption that AC in Fig. 1 (b) is aplane of failure once K, ) 1. Moreover,having rejected th'is widely held assump-tion, no physical explanation is offered foradopting the horizontal plane as a planeof failure as 'opposed to any other plane.

The writer's approach is consistentwith the simple concepts of rigid bodysliding on which much of our present limitequilibrium theory is based. Moreover, itgives the engineer a simple 'base

line'rom

which he can move in making judge-ments about the influence of such factorsas geological history, installation method,etc. Dr. Ting Wen Hui's contribution isinteresting as it raises the difficult problemof the stress distribution around piles. Thesolution of this problem requires detailedstress measuremerfts and sophisticatedanalytical studies. J.B.B.

April, 1977 23