MODEl GROUND ANCHORS UNDER GRAVITATIONAlAND CENTRIFUGAl ACCELERATIONS

Modèles réduits d'ancrage au sol en gravité normale ou en centrifugeuse

M.P. BOONJohn Laing ,Construction Ltd., formerly research student University of Manchester, England.

and

W.H. CRAIGLecturer, Simon Engineering Laboratories, University of Manchester, England

SOMMAIRE

On traite de deux séries d'essais dans lesquelsdes plaques circulaires d'ancrage de 25 mm dediamètre, enfouies dans des couches de sable secà l'intérieur d'un conteneur de 0.770 X 0.770 X0.500 m, ont été testées sous un régime decontraintes correspondant aux ancrages in situ.

Les niveaux des contraintes ont été obtenus, soitpar un vide à l'intérieur de la maquette dont lasurface- supérieure était scel.lée par une, membraneen caoutchouc, soit par des forces centrifuges.

On présente des courbes efforts-déplacementspour des plaques d'ancrage verticales, tirées versl,a paroi du conteneur, ainsi que le changement dela distribution de la contrainte normale sur cesparois pour des valeurs différentes de la positionde l'ancrage.

On trouve que la flexibilité du conteneur estcritique- pour le résultat des essais sous vide. Parcontre, les modèles en centrifugeuse où les mouve­ments latéraux sont bloqués, donnent des résultatsplus réalistes.

En utilisant cette technique, on a mesuré desvariations importantes de la force d'arrache-ment,au fur et à mesure que l'ancrage passe d'uneposition horizontale à une position verticale. Lesforces d'arrachement sont inférieures à cellesprésentées normale-mer:tt par d'autres auteurs.

SUMMARV

Two series of model experiments are reportedin which circular plate anchors, 25 mm diameter,buried in beds of dense dry sand within acontainer 0.770 X 0.770 X 0'.500 m, have been testedat effective stress levels appropriate ta fieldanchors.

These stress levels have been obtained by eva­cuating the void space within the container whichwas sealed at the surface by a flexible membraneand exposed to exterrial atmospheric pressure orby the action of inertial accelerations generatedwithin a centrifuge.

Load-deflection data are presented for verticalanchor plates pulled towards the boundaries ofthe- container together with changes in normalpressure distribution at these boundaries for arange of initial anchor positions.

Flexibility of the container is shown to have acritical effect on the results from the evacuatedmodels. .

The· centrifuge models in which boundary deflec­tion is restrained are shown to give' more realisticresults and using this technique significant changesin anchor pull-out load have been measured forvariations in anchor inclination from horizontal tovertical. The pull-out loads have generally beenlower than those predicted by other researchers.

INTRODUCTION

The ultimate resistance to tensile loading of buriedplate anchors in sand has been studied by many au­thors and of the design methods proposed, that develop­ed by Meyerhof and Adams (1968) and Meyerhof(1973) has the widest use, being applicable to anchorsof any shape at any inclination from horizontal tovertical.

Most of the data which have been used to justifythis or any other design method of general applicationhave been provided by small scale laboratory models.However, scale effects in model work on cohesionlesssoils give rise to uncertainty in the extrapolation ofresults to field situations. The reduction of the mobilis-

18

ed angle of friction 0 under increasing mean principalstress levels is weIl known - typically for a densesand a reduction of the order of 5 degrees in 0 perlog cycle of effective stress. Associated with thisreduction is a transition from brittle to plastic failurein soil elements and a trend towards increased displa­cements at failure, relative to model size.

De Beer (1970), Graham (1974) and Aboshi (1975)among others have reported a change from overallshear failure in small models of foundations undercompressive loading, to, punching shear at larger sizesand higher stresses. Mikasa and Takada (1973) haveperformed centrifugaI model tests on both shallow

and deep foundations under compressive loads and_have presented visual evidence of the difference infailure mode of the same model between tests at unitgravity and others at 60 g. Krebs Ovesen (1975) hassummarised the findings of his 6wn centrifuge expe­riments along with those of Mikasa and Takada and ofCherkasov et al. (1970) and has shown that thevariation in model failure loads associated with thedifferent modes of failure at different accelerations isconsistent with substantial reductions in 0 with stresslevel increases. The results of centrifuge tests byYamaguchi et al. (1976) on surface and -shallowfoundations show similar effects.

The implication is that more realistic design infor­mation for tension carrying foundations may be obtain­ed from model experiments carried out at or close tofield stress levels. In this context the centrifuge mode!is an attractive alternative to full scale experimentation.

·The S.E.L. centrifuge has a capacity to acceleràteupto 2,000 kg of soil to 140 g, i.e. an accelerationfactor N == 140, and has been used well within thislimit in a programme of testing model anchors in sandat inclinations from horizontal to vertical. A boltedaluminium container 0.770 m square X 0.500 m deep,with 16 mm walls was used for most of the expe­riments. The container was filled with air dry MerseyRiver sand deposited from a roller spreader. Therange of porosities measured after deposition was0.353 - 0.359 corresponding to a relative density ofapproximately 95%. The anchor plates were 25 mmdiameter, 8 mm thick, attached to steel rods 4.75 mmdiameter and were placed in every case at a depth300 mm, below the upper, level soil surface at an incli­nation which varied from test to test but always coaxialwith the load -to be applied. Full details of the expe­rimental techniques are given by Boon (1975).

TESTS AT UNIT GRAVITY

number of plate anchors initially located· at different­distances from the wall with a suction of 66 kN/m2

applied in each case. The anchor shaft load in theabsence of a -plate was found to be consistently lessthan 0.08 kN. Defining failure arbitrarily at a deflec~

tion of 30% of the plate diameter the failure load isseen, fig. 2, to be sensibly independent of locationrelative to the wall in the range 6 - 12 plate diameters.

In order to carry out preliminary experiments atfield stress levels without using the centrifuge theupper sand surface was covered by a thin rubbermembrane and the void space of -the soil mass wassubjected to a partial vacuum.

-Horizontal anchors were pulled by a pneumatic jacktowards a wall of the container instrumented withtotal stress transducers. The- anchor itself passedthrough a lubricated sleeving at the wall and thejack reaction was taken by a mounting frame of steelsections. Fig. 1 shows load-deflection results for a

1·5

FAILURE LOAD(kN)

xx

2-0 ANCHOR. LOAD(kN)

o

)-4

1-3

x

xx

6 X(TESTS AT.tg)

4

100

8

200

o 150 mm

1 1

x

x

(TESTS AT 19)

- FAILURE LOAD(kN)

o

)-5

1·7

INCLINATION OF ANCHOR ROD TO HORIZONTAL

Fig. 3.

INITrAL ANCHOR DISTANCE FR.OM WALL

Fig.2.

In a further series of tests on inclined anchors theapplied suction was lowered to 57- kN/m2 and thepneumatic jack, suitably mounted on the reactionframe, pulled the anchor rod either through a sleevein the metal -wall or through the rubber membrane.Results, fig. 3, show that the failure load increased asthe inclination from the horizontal increased. Thetest arrangement is shown in fig. 4.

19

300 mm

250 mm

x

~-

(TESTS AT 19)

INITIAL DISTANCE FROM WALL

10 20 ,ANCHOR DISPLACEMENT (mm)

o~

1-5

o~

X~

1-0 0

X

6 wa:

0 :::>-J

X ;{

6u-

0

0·5X

1

rFig. 1.

Fig. 4.

Under the action of the applied suction the boxwalls dcflected inwards by upto 0.4 mm and the totalstresses measured on the boundaries indicated initialK values (K == cr'HI cr'v) of approximately unity. Theresults of the pull-out tests are consistent with. an

initial hydrostatic pressure distribution yielding a bedof essentially uniform strength at aIl depths and thehigher loads on v.ertical anchors are associated withincreased gravity effects in this direction.

TESTS UNDER INCREASED ACCELERATIONS

The SEL centrifuge has a rigid rotor 7.32 m indiameter which moves in a horizontal plane, generat­ing a radial acceleration. In order to keep the freesoil surface perpendicular to the acceleration, as inthe field, this surface must be in a vertical plane andto achieve this with minimal disturbance it is necessaryto fit a thin membrane over the surface and to applya small suction to the sand. mass until sufficient radialacceleration has been generated to hold the' soil înplace.

The model box was packed into a rigid containerand with all four walls fully supported internallythe suctÎon was applied before the whole assembly waslowered into the test position, fig. 5. The suctionwas released when accelerations reached 5 g and theanchors tested under a steady accelerations of 26 g atthe radius of the anchor plate, 2.94 m. Changes inwall pressure over the acceleration increment after

Fig. 5.

1

1

i

1

~ 1

20

kN/m 2

""0 10 10

r---+

0 015 mm 5

B C

WALL PRESSURE CHANGES V ANCHOR M OVE t.1 E NT

~ kN 1m2

+10 tkN/m2 kN/më

40 . 40

a

30 30

A-10

20

kN/m t

40

releasing the suction were consistent with 1< == 0.25.At 26 g the models simulated field anchors 0.65 m indiameter at depths of 7.4 m. 30

Failure loads for a series of 'horizontal' anchorswere again sensibly independent of initial positionwithin the range tested, fig. 6, but the changes inmeasured wall pressure were greatly influenced bythis variable, fig. 7. Detailed study of a single test 20

with the anchor plate initially 8 diameters from the wallshows the development of pressure changes across and

8 161 1 1 1 1

F

o ~_.--J._-~----l---"'-m""

-10

+5

Diameters

10

x

x x)(

0

(TESTS AT 26 9) 1°1

E

~. FAILURE LOAD

(kN)

3·0

2·5 ~

1

2'~

1

100 300 500 mm

INITIAL ANCHOR ·DISTANCE FROM WALLINITIAL ANCHOR DISTANCE

FROM WAL~

+ 150 mm

o 200 mm

)( 250mm

• 500 mm

Fig. 6.

21

~AEYERHOF (1973)

/

GROSS DISPLACEMENT

ANCHOR LOAD (k N)ACCELERATION FACTOR.

t FAILURE LOAD. (l~ N)

2

5

3

11

, 1

1 1 1

10 20 30ANCHOR DEFLECTION 10/0)

2

5g

3

Ig

1 - ('iE5TS AT 26 g.) 1

LIMITED DISPLACEMENT

0 1 1 1 1

0° 30° 60° 90°

INCLINATION OF ANCHOR ROD TO HORIZONTA L

·4

Fig. 9.

Fig. HL

anchor models, pulled vertically in a plane strainconfiguration under different accelerations confirm thatthis zone is considerably reduced in the same manneras observed by Mikasa and Takada (1973) for thecompressive loading situation.

22

u.JV)

<

3 mm

3mm

TESTS AT 26 9

o

/1~\/ \

/ \ ANCHOR/ \ DISPLACEMENT

/ \1 ~IOmm

7·5mm

100

U­oa..o..-

PRESSURE CHANGE(kN/m')

PRESSURE TRANSDUCERS AT ANCHOR LEVEL

UJl?oILl

U­o

...J

...J<~

PRESSURE CHANGE(kN/m2 )

o ~-----+---:::;;::o~~::""--"-'---+---­

300 :.--

20

20

down the wall, fig. 8. The changes are symmetricalacross the wall at the anchor level but are substan­tially higher below the anchor than above.

Limited results for tests on inclined anchors alsocarried out with N == 26, fig. 9, show a significantreduction in pull-out loads at inclinations of 45° and90° from those measuied on horizontal anchors. Thisfigure also shows the failure loads predicted by ~he

method of Meyerhof (1973) for a mean unit weightunder centrifugaI acceleration of 415 kN/m3 and aunique angle of friction of 41° measured in triaxialcompression, for Mersey River sand at an appropriatemean stress level. In every case the prediction exceedsthe observed failure Joad and 'while the difference canbe reduced by considering anchor loads at displa­cements greater than the plate diameter a considerablediscrepançy remains.

40

PRESSURE TRANSDUCERS ON CENTRAL AXIS.

The prediction, developed from the results ofMeyerhof and Adams (1968) assumes implicitly a limitto the zone of soil involved in the failure, based onobservation of model tests at low stresses under unitgravity. However, this zone may be significantlyreduced in size at higher stress levels wit4 a subse-.quent lowering of the failure loads. No direct obser­vation of the size of the 3-D zone of sail movementaround circular .plate anchors in the centrifuge hasbeen possible, but observations on identical strip

Fig. 8.

20

Fig. 11.

la

JL--------'--I~I...la 100ACCELERATION FACTOR (N)

In order to assess directly the effect of changes instress level on the failure of an anchor a 25 mm bar152 ,mm long was pulled vertically, in il plane strainconfiguration in a box also 152 mm wide, from adepth of 340 mm t'owards the surface of a bed ofRiver Mersey sand at the same initial density as usedpreviously. The test was repeated at a number ofdifferent accelerations in the range 1 - 54 g. Forease of comparison fig. 10 shows the measured anchor

loads divided by the acceleration factor as a functionof the anchor deflection. Defining failure at a deflec­tion of 10% of the width in these tests the dependenceof the parameter Nqu and associated values of 0, givenby the analysis of Meyerhof (1973), on accelerationfactor N is clear, fig. Il and table 1.

TABLE 1

Acceleration Mean av Nqu0

0 p .s.(DeducedFactor (kN/m2) (Observed) Meyerhof) (Tong)

1 3 19.4 50.0 51.55 15 8.7 39.0 48.0

Il 32 5.5 32.5 46.032 93. 3.8 26.5 43.554 157 3.3 23.0 42.5

Table 1 shows the mean vertical stress in the sandin each test before loading the anchors and the valuesof 0 indicated for this material at the appropriaterelative density from the plane strain element testsof Tong (1970) with mi!lor ,principal stress of thismagnitude. Allowing for this variation in frictionangle the range of Nqu values predicted would be onlyone third of that observed. The difference appearsto arise from the fact that the factors given byMeyerhof are based upon failure modes observed onlyin small model tests at unity gravity, i.e. low stresses.As Mikasa and Takada (1973) have shown, these willexaggerate the volumes of soil in the failure zoneassociated with geometrically', similar models at higheraccelerations and stress levels.

CONCLUSIONS

The design of field anchors in sand, based on dataobtained from laboratory model experiments at low stresslevels will be in error on account of the difference instress level between the two situations. Adjustment ofthe design for changes in the angle of friction assessedin element tests at appropriate stress levels may partlyeliminate the error but this will not necessarily take

account of differences in failure mode if the design isstill based on model test results with correct frictionangles but incorrect stress levels. The centrifugemodelling technique provides a means of obtainingdesign data from models subjected to the failuremodes appropriate to the correct stress levels.

REFERENCES

ABOSHI (H.). - «On the deformation and failure ofsand underneath deep founda,tions», Proc. 2ndAustralia and New Zealand Conference onGeomechanics, pp. 185-189 (1975).

DE BEER (E.E.). - «Experimental determination or"the shape factors and the bearing capacity factorsof sand», Geotechnique, Vol. 20, pp. 387-411(1970).

BaON (M.P.). - «Load tests on model groundanchors», M.Sc. Thesis, ~niversity of Manchester(1975).

CHERKASOV (1.1.) et al. - «Influence of gravity onthe mechanical properties of soils», Soil Mech.and Foundation Eng., January, pp. 25-31 (1970).

GRAHAM (J .).' - «Plasticity solutions to stabilityproblems in sand», Canadian Geotechnical Jour­nal, Vol. Il, pp. 238-247 (1974).

KREBS OVESEN (N.). - «CentrifugaI testing appliedto bearing capacity problems of footings on sand»,Geotechnique, Vol. 25, pp. 394-400 (1975).

23

MEYERHOF (G.G.). - «Uplift resistance of inclinedanchors and piles», Proc. 8th Int. Conf. on SoilMech. and F.E., Vol. 2.1, pp. 167-172 (1973).

MEYERHOF (G.G.) and ADAMS (J.I.). - «Theultimate uplift capacity of foundations», CanadianGeotechnical Journal, Vol. 5, pp. 425-444 (1968).

MIKASA (M.) and TAKADA (N.). - «Significance ofcentrifugaI model tests in soil mechanics», Proc.8th Int. Conf. on Soil Mech. and F.E., Vol. 1.2,pp. 325-333.

TONG (P.Y.L.). - «Plane strain deformation ofsands», Ph.D. Thesis,University of Manchester(1970).

YAMAGUCHI (H.) and al. - «On the influence ofprogressive failure on' the bearing capacity ofshallow foundations in dense sand», Soils andFoundations, Vol. 16, N° 4, pp. 11-22 (1976).