The Bearing- Capacity of Eccentrically Loaded

8/17/2019 The Bearing- Capacity of Eccentrically Loaded

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Jw 955 181

The

Bearing Capacity

of

Eccentrically Loaded

Foundations on Sandy

Soils

By

W.

Eastwood , B.Eng., Ph.D ., A.M.I.C.E., A.M.1.Struct.E.

Introduction

I

the past it has been usual when designing eccentri-

cally loaded footings t o assume that the pressure

distribution across the base of thefooting wouldbe

linear and that the maximum valuef the pressure must

be limited to that permissible under a centrally loaded

footing.

Recently, however, Meyerhofl has suggested that a

more valid approach s to treat the eccentricallyoaded

foundationas if it were centrally loaded buthada

width equal to the actual width less twice the eccen-

tricity see fig.

1 .

The results

of

experiments on small

scale model footings are reported which appear to con-

firm this hypothesis. For footings on sand theMeyerhof

theory gives somewhat maller ultimate oads han

the older theory except at small eccentricities.

At the time that paperwas published the author was

investigating theeffects of eccentricity on stripootings

on sand. His experiments on larger scale models than

Meyerhof’s gave results which are not in agreement with

that author’s findings, and the object of this paper is

to report the resultsof these experiments and to postu-

late a possible reason for the disagreement.

The author’s tests have lso indicated that there may

not be an ultimate oad in the accepted sense if the

footing is completely restrained from slipping sideways.

The load increases indefinitely with increasing penetra-

tion of the footing.

FOOTIN

‘A’

FOOTIN

‘B‘

Fig.

1

Eccentrically loaded Footing ‘A’ assumed to be equivalent to centrally loaded Footing

‘B’

DETAILSOFAPPARATUSAND

INVESTIGATION

All theests werearriedutnandn

timber box braced with steel. The size of the box was

10

ft. x ft. x t. deep.

The footings tested ere cut from olled steel channel

and were either 6, 8 or 10 in. wide. Grooves in which

the knife-edge loading device was located were cut at

various eccentricities seeFig. 2). The thickness of the

channel under he knife edgewas so small that he

eccentricity was not appreciably affected by the tilt of

the channel under the eccentric test load. The eccen-

tricitiesusedwere up to b/6 i.e. loading within he

middle-third) except for the 6 in. wide footing. In this

case themaximumeccentricity wasalmostb/4, i.e.

loading well outside the middle-third.

Fig. 2 l so shows the method of applying the load.

To ensure that the footing could tilt endways or side-

ways without

any

restraint from the loading arrange-

ment, hevariouspinned oints were ncorporated.

The length A B

was

dso made fairly large

12

in.) so

that, if the footingmoved aterally elative to he

loading beam during a test the inclination

through he oading arrangement would

of the thrust

changeonly

a negGgible amounr from ;he vertical.

It

was found

in he ests hat at the ime heultimate oad was

reached hischange of inclinationwasnevergreater

than about io nd generally was much less.

It

had been noticed in an earlier investigation th at

even with

a

centrally applied load there was often a

measurable lateral movement before the ultimate load

was reached.Witheccentric oading it was thought

that this lateral movement might be considerably in-

creased nlessome restraint were applied. In n

actualstructure heremay be little

or

no estraint

against ateral movement as n he case of a footing

at the bot tom of a relatively slender column, or he

structure may be s stiffened that lateral movement

wouldbe insignificant. Accordingly, it wasdecided

to repeatall he ests usingwo separate oading

arrangements, one with lateral restraint of the footing

and one without see Fig. 2).


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82

The

OADINC BEAM

I

PINNED JO NT

FOOTINC

ERLL R E S T R A I N

Fig.

2.

Loading rrangement

The sand used in the tests had a grading curve as

shown in Fig.

4

It was placed in 9 in. layersand

compacted o refusal bya Kango hammer.The

average density obtained was 108 lb. per cu. ft. After

each test the sand was dug over to a depth of

18

i n

i.e. greater han hemeasureddepth of disturbance

of

the sand in a test) and recompacted. The compac-

tion was continued until a straight screed run along

the top edges of the box produced negligible scrapings.

As the weight of sand in the box was unchanged the

mean density of the sand was also constant from one

test to another.

The lateral slip of the footing was measured contin-

uously during he ests by means of micrometer dial

gauges.A 3 n. ongpointer, part of which can be

seen attached to the far end of the footing in Fig. 3,

moving over a stat ionary scale gave the angle of tilt

of t he footing, a correction being applied to the scale

reading to take account of the vertical settlement.

During a test the footings were driven into the sand

at

approximately

1

in. perminute,measured at he

point of application of the load.

R SULTS

OF

T STS

a) Mode

of

Failure

i )

Footings not restrained against lateral movement

In the tests in hich the footings were not restrained

against ateral movement the oad ncreased steadily

withettlement ntil slip surfaces were suddenly

developed.

his

development of slipurfaces was

quite audible and the load instantly dropped to about

half

its

ultimate value. When the footing was driven

still further nto he sand he loadslowly ncreased

again,

but in general the ultimate load had not been

redeveloped at several times the set tlements at which

it

was first attained.

F i g

3.

Photograph of test on ooting restrained

against lateral slip


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June 1955

B.S.

SIEVE No.

1

9

8

7

U

6

vl

v

2, SO

W 9

U

l

z

< ‘

30

g

2

1

1

t

O / I 0 1

C R A M

SIZE

mms.

Fig.

4.

Gradingcurveof sandused

n

tests

II.

Z o n e s

of

plastic shear.

Ill. Passive Rankine zones.

so i l i n reg ion

II

m ov es ou t w ards

to

replace

it.

Fig. 5. Comparison of two-way failure assumed in some theories and one-way failure which

occurs

in practice


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184

The StructuralEngineer

Several of the more notable theories of foundations

are based on the assumption that for centrally loaded

foundations ailure occurs by slidingwedgesbeing

formedonboth sides of the footing see Fig. sa ).

Most investigators have found,owever, that in ractice

failure occurs b y sliding to one side only see Fig. 5b).

Thiswasso nevery estexceptone of thepresent

series, the dimension A in Fig. 5b being about 4b on

theaverageforcentral oading.

Althoughonly oneslipsurfacewasformed at the

ultimate load, a further surface did evelop later if the

footing waspushed fa r enough nto hesand.With

central loading this second sliding surface was usually

on the same side f the footing as the first, but in about

25

per cent. of the tests it was on the opposite side.

Witheccentric oading he irstslidingsurface was

invariablyon hesame side as heeccentricity see

Fig.

6),

and

if

the footing was then pushed further into

the sand a second surface was usually formed further

out on thesame side. The outcrops of thesefirst

andsecondsurfaces were roughlyatdistances of b

and up to 4b from the footing respectively, this latter

dimension ending to be less for tests with arge ec-

centricity.

In a t east one of the well-known foundation theories

it is assumed that the footing fails by rotation about

some centreas shown in Fig. 7a. The ilt measure-

ments showed that the rotat ion was always away from

the slip surface as n Fig. 7b. Generally the angle of

tilt when theultimate oad was eachedwasabout

l

for centrally oaded footings, andasmuchas

8

for eccentrically loaded footing, increasing with the

eccentricity.

ii)

ootings

restrained against lateralmovement

There were some important differences in behaviour

when the footings were restrained laterally.

With central oading on the

8

in. and 10in. wide

footings the first sliding surface o orm sometimes

outcropped at approximately one footing width away

on the side towards which the footing tilted, and ome-

times at about three footing widths out n the opposite

side. There was not , however, sudden rop in

bearing power when this first surface formed as is in-

variablyhe case with unrestrained footings. The

load continued to rise as the footing was driven further

into the sand, although a t a decreased rate in general.

Even when further sliding surfaces were formed there

was no drop in the load, and it appears that there is

no clearly defined ultimate load in the usual sense.

Fig.

6.

Position of slip urfaces n ests

ai) FOOTINC

R O T A T I O N

ACCOAOINC TO SOME

THEOPIES.

Fig. 7. Direction of rotation of footings according to

some theories and actual direction

as

observed in tests


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June 1955

185

(b) Ultimate oads

set of conditions is given in table

I

The average ultimate load for three tests with each

f O O l l N C WIDTH IN

Fig

8. Variation of ultimate load with footing width

and eccentricity

of

application (no lateral restraint)

om

LOAD

ECCENTRICITY

Fig. 9. Effect of partially restraining lateral movement

on ultimate load for

6

in. wide footing

Similar behaviour was recordedfor eccentric loading

on the 8 in. and 10 in. wide footings.

Unfortunately, the restraining device was incapable

of preventing atera lmovementcompletely because

of the slight play whichwasnecessary to allowun-

restrictedverticalmovement.Themagnitude of this

lateralmovementvariedbetween

0.01

and

0.025

in.

This s quite small compared with ateral movement

in unrestrained tests generally between 0.1 and 0.2 in.)

but was sufficiently large nevertheless for an ultimate

load to be obtained in the normal way for some of the

6

in. footing ests.Thevalue of theultimate oad

obtained n hese ests was somewhat arger han n

the completely unrestrained tests as will be seen later.

Load

restrained restraint

estraint restrained

estraint

Laterally

o lateral

aterally

o

lateral

aterally

o

lateral

t i c i t y

~

____~

eccen-

18in x oin footing

8in x 8in footing

8in x 6in footing

~ ~

zero

P

.16 1.08

2b/9

2.01

.78 1.43.36

b/6

a

2

.46

2

.20 1.77.63

b/9

3 53

.73 2.52

Q)

b/18

2.72.12 2.06

Q E

Table

1

Average ultimate loads

in

ton per sq. f t for tests

on

sand with

~ ~~

various eccentricities of loading.

The results for the tests without restraint are plotted

in Fig.

8.

I t will be seen that the results for all eccen-

tricities are in accordance with previous investigations

using central oading, he oadperunitarea for a

giveneccentricity atiobeingnotquiteproportional

to the ooting width.

Theresults for the estswithandwithout ateral

restraint for the

6

in. wide footings are compared in

Fig. 9. From this figure it will be seen that the partial

restraintcausedanaverage increase in heultimate

load of about

6

per cent.

Figs.

10

a, b and c compare the variation of bearing

valuewith ccentricitywhichwasobtained in the

testswith hat whichwouldbe expected according

to the Meyerhof theory, and also with the older theory

in which straight line pressure istribution,he

maximum value of which is constant, s assumed. I t

will be seen t ha t for the

8

in. and

10

in. wide footings

the older theory gives bearing values in closer agree-

ment with the exper iments than the Meyerhof theory

throughout the range of eccentricities. With the

6

in.

footing each of the theories agrees more nearly with

theexperimentsovercertain anges,but he older

theoryhasa mallermaximumdeviationand also

has the advantage that itoes not give an over-estimate

for any eccentricity.

DISCUSSION OF

RESULTS

The present tests are obviously insufficient in scope

todrawgeneral conclusions for all ypes of footing.

But heydo ndicate hatundercertainconditions

at least the old-established assumptions may be better

than Meyerhof’s suggested alternat ives. Since the

tests were very similar to some of those carried

ut

by Meyerhof except that they were to a much larger

scale Meyerhof’s footings wereonly 1 in. wide in

general)

a

reason was sought for the apparent differ-

ences in the two sets of results.

A probable eason for the divergence is apparent

from n xamination of Meyerhof’s apparatus nd

method of test. Photographs in his paper show that

the oads wereapplied byanarrangementapproxi-

mately as in Fig. 11.

It

will be seen that as the ooting

tilted under the actionf eccentric load the eccentricity

would also increase.

As

no measurements of the angle

of tilt appear to have been made

it

is probable that

no orrectionwasmade to he eccentricity value.

Thus he ultimate oads obtained will correspond to

greatereccentricities han he eported values. The


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186

he Structzcral

Engineer

0 . 5 1

-4 USUAL THEORY

- TEST RESULTS

O d MEYERHOf

ECCENTRICITY

Figs oa, b, and c.

ECCENTRICITY

Comparison of test results with usual theory and Meyerhof

for 6in., 8in., and loin. wide footings

hypothesis

r

Fig. 11. Change of eccentricity as footing tilted in Meyerhof’s tests


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June,

1955

187

0 6

-

Q

MLYLR Of

THEORY

OOJb o l b Oysb

ECCENTRICITY

Fig. 12. Comparison of Ramelot and Vandeperre s test

results

on

square footings with the usual theory

and the Meyerhof hypothesis

error in theccentricity was probably quite considerable

if the angle of ti lt was as great in Meyerhof's tests as

it was in heauthor's . At ultimate load the value

variedbetween about

0.5

with central loading to

about 6 when the eccentricity was b/6.Thus if the

ratio h/b in Fig. l

l

were say 0.5, the actual eccentricity

atultimate load in

a

test in which it was initially

b/6 would be b/6

4

b/20 approximately.

Ramelot and Vandeperre have also reportedhe

results of some tests on square and circular footings on

sand, usingeccentric loading. Theauthorhas com-

pared their results for square footings with the usual

theoryand he Meyerhof hypothesis. Although foot-

ings of variouswidths were tested, only in the case

of the 30cm. square footing were sufficient repeat tests

made odraw n ccurategraph of ultimate load

against eccentricity for eccentricities

up to

b/6.This

graph is

shown

in Fig.

12.

There s some scatter

of

the points partly because some of them represent only

a single test , but again it will be seen tha t the usual

theory is upheld rather than the Meyerhof hypothesis.

CONCLUSIONS

1 ) The ests carried out by theauthor on strip

footings indicate hat he usualpractice of assuming

that here isa straight line distribution of pressure

under an eccentrically loaded foundation, nd hat

the ultimate value of that pressure

is

the same as that

under a centrally loaded foundation, is sound for

footings on sand nd ccentricities u p to /6. An

alternative hypothesis put forward by Meyerhof, in

which theultimate load for an eccentrically oaded

footing isassumed to be equal o

that

for a footing

of width equal

to

theactual widthminus wice the

eccentricity, does notagree

so

well withsome of the

experiments.

2) Footings on sand which areestrained from

slippingideways have no definite ultimate load

whether centrally or eccentrically loaded, there being

no sudden drop of bearing power when slipsurfaces

are formed. When only partialestraintgainst

lateral movement s allowed, the remay be a well-

defined ultimate load somewhatigher thanhat

obtainedwith no lateral estraint of the footings.

Acknowledgments

Theexperimental workdescribed in hispaper was carried

out

in the University of Aberdeen,with heactivehelpand

encouragement

of

Professor Jack .411en, D.Sc.,M.I.C.E.

References

1)

Mcyerhof, G.

C; 1953) .

The Bearing Capacity

of

Found-

ationsUnderEccentric ndnclinedLoads. P r o c . h i r d

Int

Conf

oil M e c h . a n d F o u n d . E n g i n e e r i n g ,

Vol.

1 . p. 440.

2 ) Ramelot, C. andVandeperre, L. 1950) . T r a v a u x d e

la

Cornrnissiosz d E t u d ee sondat ion s de Py lone s . Compt.

Rend. Rech., I.R.S.1.-4., Brussels,

No.

2 .

The Bearing- Capacity of Eccentrically Loaded

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