BASE CAlCULATION Of ANCHOR FOUNDATIONS USING APPROXIMATEMODEl TESTING

Calcul des fondations d'ancrage à l'aide des modèles approximatifs

by

A.S. KANANYAN,Research Institute of Foundations and Underground Structures, Gosstroy URSS

M.I. NIKITENKO, Yu.A. SOBOLEVSKY, V.N. SUKHODOEVByelorussian Polytecnic Institute

SOMMAIRE

Cette communication présente les résultatsd'une similitude particulière dite des modèlesapproximatifs. Des modèles géométriquement sem­blables pour des ancrages, pour des ancrageschampignons, pour des plaques enterrées placéesdans le sol réel ont été réalisés pour étudier lacapacité portante des ancrages. La loi de la forcelimite et celle du déplacement limite en fonctionde l'échelle a été dégagée et extrapolée jusqu'auréel.

Cette rnéthode permet l'élaboration des abaquesen coordonnées adimensionnelles répétées par lesrésultats de nombreux essais sur modèles àdiverses échelles. Une telle approche minimise lenombre des essais en vraie -grandeur.

l t is rather difficult ta make analytical calculationsof bearing capacities and deformations of anchor foun­dation bases, owing to the absence of axial symmetryand non-linear deformations.

That is why it is advisable to use an approximatemodeling in order to determine the bearing capacityand anchor foundation deformity. In the 50 s theby D.E. Poishin. According to the concept, geome­trical dimensions of the foundation were modelled withthe dynamic similarity kept, , and the soils the sameboth for the. model and the prototype [1].

The systemizing of test results is done in non­dimensional coordinates which gives 'the opportunityto minimize and sometimes to eliminate the effect ofthe model on the final results determining the bearingcapacity and natural foundation base deformation [2],[3], [4].

The models of the anchor foundation parts suchas slabs, inclined piles, cross-bar cylinders, mushroom­like and bored anchors were tested and the resultantdata were represented in non-dimensional coordinates[5], '[6], [7], [8]. The methods of each modelloadingwere taken to be equal according to the requirements ofthe kinematic and dynamic similarity. The anchorswere subjected to pulling' force step by step and \verekept till stabilization of displacement in the point ofload application was achieved. .

69

SUMMARV

The conditions of approximate ,model testingare used to determine the bearing capacity anddef6rmity of anchor foundations bases. The ideaof approximate model testing is to mQdel geome­trical dimensions of foundations keeping dynamicsimilarity, the soil being the same both for modeland the prototype. The models of anchor foun-odation structures such as slabs, inclined piles,cross-bar cylinders, mushroom-like and bored an­chors were tested and the resultant data wererepresented in non-dimensional coordinates. Theempirical method of the calculation of the anchorbearing capacity and deformity should be used.

This method offers the possibility of plottinqcoincidence diagrams in terms of non-dimensionalcoordinates after conducting several model testsin various scales. Such an approach mini,mizes thevolume of full scale tests.

During every model test no less than 10 experimentalvalues for the diagram «load-displacement» were obtain­ed as the steps of loading were nearly 1/10 of theirmaximum value. The tests were considered finishedwhen either a sudden loss in bearing capacity withsoil deformation or increasing displacement took place

. without additional loading.

The last loading step when the anchor displa­cement stabilization set in was taken as a maximumNlim , while the displacement Dlim corresponded to thisloading. The loading Nlim was prior to the maximumvalue of pulling force.

The test results of different anchor foundation struc­tures in sand and clay soils indicated that the depen­dence «load-displacement» is non-linear as thecompaction and displacement deformation of base soiltakes place simultaneously, one of the types predomi­nating at the beginning and at the end of loading.

The «load-displacement» curves for different modelsand prototypes have in absolute values quite a differentcharacter, without giving the opportunity to generalizethe dependence function for the «base-foundation»system. The diagram of the above dependencies inabsolute values by test data does not provide their truesignificance even qualitatively. Thus, for instance,diagram curvature depends on the choice of scales ofdisplacement and loading values. The natural dispers­ing of deformation experimental' values for this or that

load in repeated tests influences the diagram cur­vature as well. The estimation of such diagrams,taking into account the variety of soil conditions,becomes more difficult for foundation models and pro­totypes of various constructions and dimensions.

When the diagram of «load-displacement» depen­dence is compiled in relative values, we have quiteanother picture. The ratio of acting loads Ni t6 theirmaximum value NuIt marked on the abscissa· axis in theunique system of non-dimensional coordinates and thecorresponding relations between Di and Dlim displa­cements are marked on the ordinate axis. Such asystemizing of test results makes it possible to comparethe dependences for anchor foundations of differentscale and to get equations of relative parameterconnections.

Vi Ni u N-U == f -N or Ci == f (Ci) (1)

Hm Hm

The tests diagrams in non-dimensional coordinatewere plotted in accordance with the anchor foundationstructures in the scale range from 1: lOto 1: 1 accord­ing to the tests in sand and clay soils (fig. 1, 2).The analysis of the diagrams showed their characte­ristics as follows:1. The diagrams are characterized by convexity Which

shows the non-linear nature of, anchor foundation

base deformation and the growth of displacementsduring the next steps of load application.

2. The vague diagram curvatureshows the foundationproperties: the abrupt curve corresponds to shallowanchor foundations, soft soils having low mechanicalcharacteristics; the fIat curving corresponds to deeperfoundation bedding and compact soils with muchbetter mechanical characteristics.

3. The diagrams remain just the same for anchorfoundation models both over the whole scale rangeand in a part of the range and this operis wideopportunities for extrapolation of test results.

4. The diagram curvature is not affected by the dimen­sions and the shape of foundations as well as theangle of pull-out, though these parameters influencethe absolute values of maximum displacements andefforts.

5. The comparison of test results of pulling out ram­med piles and cylindrical anchors put into leadingwells shows that the curvature of «load-displace..ment» non-dimensional diagram is more abrupt inthe first case than in the second one.

The accuracyof base calculations under approximatemodel testing conditions depends greatly on the defi­nition of the foundation displacement maximum values.1t is reasonable therefore to lessen the .loading stepsbefore foundation bearing. capacity limit is achieved.

1

- 1

1.0

10

OB0.6

0.6

0.4

040.2

0.2

~ ~e~ cr""

~I"o

~"

l~ ,

:4 ~.,..e1"A

;

d==04m + /1.a6m x ...O.9m 0 f1.0 m I::t. v,,",

1.2 m e' ........

~

C,v1.0 a]

0.6

(J4

02

1.0D.~0.6

0.2

a2 fJ:::Oo.100 x

0.4 15°0'30 0

<D

400A

0.0 50o~

60°l- e:::)

"0.8 7Do D ~

80°Ç/$ sand~'!

1.0 ~0.2 0.4

ct

a.a 1.0

08 1.0

0.6Olt

0/,.

02

0.2..

0.41---+---1

.PijÂ

o.~l-----1~ sund h:: lB"" 2,4m.J.OIJt 40m-<J1---+----+ r::: 1550k.9;",J 0 + A .

1.0 ct 1=1700k9j",3 11 )( Â ~

al

1161----+----+

xÂ

0.6jand cLay

a h h=2om=C(}ns'~~

o.22m QJm. • a=11m A t-----i~

O.R O.SSm o.75m fJ 1.7m. x f--~.U O.69m OS4m. 0 2.2m v

CU 0.98m 1J1m G) 2.6rn +

1.0 i 1.10m 1.50m A

f)

0.4

~ .~xA~~êI Ci

N• .A

v -4•0 ~ A ~

cf .~

M1:10 e "'io A

1=5 A 0

1:2 x -A~1:1 0 xf3~~D}/N ~

~ ,/"WJ l '''''W")

Cl"':)Il

~~ iCi sand ~d=o.55~

1.0el

0.2

08

0.6

C)

A

si/tg sandysoiLs

sand/11:2 x

u M1:5 +10 Cl 1'11:10.

ri;

02 t--t---+--+---+-+--~-lIIIL---+---+--.......j

04

OB

Oô

Fig. 1. - Average «load-displacement» dependence in approximate values foranchor foundations a) right-angled inclinedslabs with 80 X 500 mm in average-sized sand; b) cross-bar cylinders when' being piled into the average-sized sand; c) roundslabs in sand of average size and density; d) inclined piles in fine sand of average 'density and in hard dusty sandy loam;e) cross-bar cylinders when using the principle method of boring into the sand of average size and density; f) mushroom­like foundations in sand of average size and density and in a hard clay.

70

As the summarizing of available data shows, onemust be sure that the test is conducted properly inarder ta minimize the dispersing of results, i.e ta seeif all the adopted methods of model testing and theaccuracy of effort and displacement measurements areobserved carefully till the limit of foundation bearingcapacity is achieved. The soil for model testing musthave similar physical and mechanical characteristics.Fig. 3, 4, 5, 6, show diagrams of maximum values ofstabilized pulling forces Nlim and the correspondingdisplacelnents Ulim depending on anchor model scale.

Dependence Nlim == f (S) is curved and has powerfunction character, but the dependence Ulim == f (S)is almost linear, which simplifies the extrapolation ofthe foundation model test results.

This almost linear character of the dependence ofmaximum stabilized displacement followed by pullingout the anchors will remain the same even for largerprototypes. Such a conclusion is based on the thoughtthat anchor soil base lies above the footing. «Load­scale» dependences are also convenient to represent in aunique system of non-dimensional coordinates for aUthe anchor foundation structures. The scale ratios orratios of, linear dimensions of prototypes and models

. are marked on the abscissa axis and correspondingratios of their maximum loads are marked on theordinate axis. Any fou~dation s,cale, natural dimen­sions included, can be taken as a single one in tiscoordinate system, other S'cales being prototypes.

04- 0.6 0.8 1.0

C·N

l-

X

X•

x0

"0 x

Fig. 2 - Average «Ioad-displacement» dependences in ap­proximate values 'for inclined anchors in soft sandymorainic Ioam.

o.B x S 1:10 L=:08m, Lk=OJm,dIC=1.6cmv 1.5:10 1.2 0.45 2..4+ 2:10 16 0.6 J.2

, Ciu • 3:10 2.4 0.9 't.B

0 4:10 J.2 1.2 6.'1-10

06

0.4

0.2 r-----r-----r---t----+---+--++-~~--+----+-~

10aB0.60401

Nlilfl"-' tJ

1t N'

1----

~[?mf-----

sand J !-1~1

r1

//

//

li~V s

d)

B

2

4

6

12

10

OZ ,In

08 ,S

C}

101---+----t----.-----H~~

O.21--+----=*--+--+-~-4----1

1.2

s0/,. a5o.J0.20,1

Il)

4-

21---+---~--I-J...--+-----I

6r------+---+--+-----!!..-f---I-.......l..

NlJhL' t12

o silty sandy soiLs1

• sand 110 '1) moreniK "soils 1

'So.n 108602

a)

16t------+-----...----4--I-#+-I

20

~ïn,t1.41----r---+----l-----I---À

Fig. 3. - Average «model-scale-Ioad» dependences for anchor foundations: a) cross-bar cylinders in sand and in themorainic sandy loam; b) inclined paired piles in sand and in dusty sandy loam, single piles in morainic sandy loam; c) roundslabs in sand; d) mushroom-Iike foundations in sand.

71

/v2l---1---+---I----+-~+-----+---+---+--~-----i

",/

1 /6 1------+---+----+---l-------i--r------tV-----t---t-----r-----t

/4 I----+------+-----+------+----+---"v~+---r----r------;

/

as0.40.30.20.1

C{ ,mm/m.

!V

V

/V~

/V

I/v

/V~

V

v V

5

8

6

2

12

16

14

10

Fig. 6. - «ModeI scale-maximum displacement» for in­clined bored anchors in soft sandy morainic loam.

0.5s

0.40.30.2.0.1

Fig. 4. - «Model scale-maximum displacement» for slop­ed boring' anchors in soft sandy morainic loam.

Fig. 5. - Average «model scale-maximum displacement»dependences for anchor foundations. 1) cross-bar cylinders 10

. in sand; 2) cross-bar' cylinders in morainic sandy loam;3) inclined single piles in morainic sandy loam; 4) mush-room-Iike foundations in sand.

v~· V

8 t-----+---+---+--F/+---+------7"'fV,----+--+-----+------'-f

/ ~V/' .-/1V

Nprotsand moreniK/lm.

fIYmodf--- soUs J

Iim. 13==20° A Â /ft= 0° rj -fi =4000 • / E~

~ 0 silty sandy Ilt----~oo , solls

+ sandn=2~lf7

1-- X morenix suUs

1Vt--- t sand

t À=2 v n=26 /1f--- .À=3 'V.......

À=4 L. tr+ sand // ~T- El)

Il ViJ 1

!V / V>~ot illn=~/ VNlini _ n

t---

Nmod- f\/;:è/~V n=2.O

"/Tl.

h~/~V fl~2.15

~~v~ ~

~~~

~~

80

30

70

00

20

50

1.008

moreni/\soils

)(

0.60.40.2

1 2

8.

NNii~t . .Dependences N prat == f (CL) are represented ln fIg. 7,

lim

Fig. 7. - Average «model scale-Ioad» dependences calcu­lated in approximate values for anchor foundations ofdifferent constructions (curved diagrams are compiledaccording to the equation 2 with n having differentvalues).

72

Fig. 8. - «Model scale-Ioading» dependences in approxi­mate values for inclined bored anchors (curved diagram iscompiled according to the equation 2 where n = 2.6).

(3)u prot

~-CU

mod - L

lim

where CL is the ratio of linear dimensions or prototypeand model scales; n is the coefficient depending onanchor foundation. construction and the kind ofsoil. 1ts values for anchor foundation models in sandand clay soils are found to be in the interval from2 to 2.7. It is possible to take n == 2.15 for cylindricaland inclined piled anchors, n == 2.3 for anchor slabsand n == 2.6 for mushroom-like foundations w.ith sornestability of foundation in the first approximation.

Thus, us~ng the principle of approximate similarity,with summarizing the model tests of anchor foun­dation structures in relative values, makes it possibleto introduce the empirical method of calculations ofnatural foundation bearing capacity and deformity. Theessence of this method can be represented in thefollowing way.

Repeated (3 or 5 times) model tests of anchorfoundation of definite construction in correspondingsoil conditions are carried out and approximate modeltesting requirements are observed, the limit of foun­dation bearing capacity being exhausted by pull-out.

The valuesN~~d and U~~d

are determined. Multiplying model test results bytransitional coefficientsaccording to dependencies (2)and (3), the ultimate points of prototype displacementand loading are found in. absolute values. Afterwardsthey are multiplied by non-dimensional coordinates ofintermediate points of the «load-displacement» depen­dence and a diagram is plotted for natural foundation.The diagram gives the opportunity to find correspond­ing efforts or displacements caused by them with thenecessary reliability. The calculated load is determined.by means of permissible displacements.

The principle of the calculation of anchor foundationbases with the use of small-scale models test resultswill be shown in the following example.(2)

42

;vPI'otLim

;V/11od/"im

/7

//v

/v

/J

/ n=16

/~v

v v ç~ 1

40

70

10

20

sa

JO

60

Systemizing the .obtained results it is possible toapproximate them in the following expressions:

N prot

~-Cn

N mod- L

lim

CALCULATION EXAMPLE

1t is necessary to calculate the displacement andstability of the model of the inclined bored anchorfoundation having the following dimensions: full length

3.2 m, the root 6.4 ln in diameter and 1.2 m in length,the inclination of the axis - 200

, the slope angle ofthe boring depth -- 40°) in morainic sandy loam.

SOLUTION

1. Average «load-displacement» dependences were ob­tained for the model which is 4 times less than theanchor being calculated and having equal deflectionfrom horizon and the slope angle depth; tests wererepeated three times in identical soil. The non­dilnensional parameters are given in table 1.

The arithlnetical mean values N~~d and U~~daccording to the testresults were 0.20 t and 0.30 mmrespectively.

2. The maximun1 value of the base bearing capacityof calculated bored anchor and its displacement aredetermined in the following w'ay.

TABLE 1

c~ == NiN 1im

1 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0

1-0-~ 0.02 ~ 0.06 0.08 ~-~ 0.29 0.48 ~

73

Nf(~t = N;'I~d . (~::;) 2.6 = 0.20 ( 3~00 ) 2.6 = 7.3 t

Uprot d Uprot

lim = u~~ . Umod == 0.30 X 4 == 1.20 ·cm

3. Compile the supposed diagram of «load-displace­ment» dependence for the prototype. For this pur­pose multiply maximum' load and displacementvalues by the non-dimensional diagram coefficientsfrom table I. The results are summarized in table 2and the diagram Urrot

= f (Nfrot) is compiled(fig. 9 a, curve 1).

There are diagrams obtained experimentally andgiving the opportunity to compare calculation results(fig. 9 a, curve 2). This very figure shows the compa­rative diagrams for other models of bored anchors(8 1.5: la curves 3.4; 8 2: la - curves 5.6; 8 3:la - curves 7.8) in an identical soil.

Figure 9 b shows comparative diagrams for mush­room-like anchor (a == b == ·110 cm; h == 1.5 m curves1.2; a == b == 96 cm, h == 131 cm - curves 3.4;a == b == 69 cm; a == b == 94 cm - curves 5.6;a == b == 55 cm, h == 75 cm - curves 7.8) in average­sized sand. Calculated (curve 1) and experimentalcurve 2) «load-displacement» dependence for cylin­drical cross-bar anchor with the diameter of 56 cm and300 cm long in morainic sandy loam with the pull­out == 400 are represented in fig. 9 c.

Calculated diagrams are obtained by the testing ofmodels with al: 5 scale. T4us, the- use of approximatevalues, while summarizing the results of approximateanchor foundation model testïng, put in the first placethe consideration of base soil properties and made it·possible to solve a problem almost unsolvable for thepractice of full identity and for analytical calculationmethods.

, 1

TABLE 2

0.73, 1.46 2.19 2~92 3.65 4.38 5.10 5.83 6.56 7.30

1------1-- --- ---~ -------------

Uproti cm 0.01 0.02 0.04 0.07 0.10 0.14 0.23 0.34 0.58 1.20

PO16

10

1

6

~ 12

42

IJj

2.4 l----+-----+----+_---f---4i~--+-----+-t-__t1

lJ,mm2.ô '--_----1__---'-__---l-__--..L-__--'--__~~

2.0 ~--.j__--+---_t_-----\rlt_---t--t-------r_;_1

1.6 I------+--~~+----+_----'-\+_---r--~---r-;____t

12 I-------X-I+------+ll--+----~__+\--+_------'H----~___t

0.8 I------D-~----'X---I----~k_____-~~--+-~-----r-____t

8

~1

642

a]

101---1----

56 1----+1.--+--t----Jl-Hl------\-J.-,..:~---l

U,mm12 '--------4-------L-__----l__-b.l---l

Fig. 9. - Analytical and experimental «load-displacement»dependences:

a) for inclined bored anchor in soft sandy morainic loam;

b) for mushroom anchor foundations in sand;

c) for. cross-bar cylindrical anchors in morainic sandyloam.

8t------+----+-----4---:..~-+----

12 t---~____4_----+---_+__-_I___\_\__-----I

74 'U,cm16~_ __L..____l___ _____l___.....L..

C)

....._---------------------------------- ~- - ~- ~

REFERENCES

[1] POLSHIN (D.E.), JHA (J.). - On modelling ofsoil mechanics problem by V.1. Kurdjumov's me­thod. NIIOSP Proceedings N 55, «Osnovanya efundamenti», Stroyizdat, .Moscow, (1964).

[2] CHIZHIKOV (P.G.). - Load-settlement depen­dencies between model and full size footings.Transportnoje stroitelstvo, No 6 (1967).

[3] JAROSHENKO (V.A.). - Modelling settlementsof footings on sand foundations MIIT Proceedings,No 100, «Mekhanika gruntov, osnovanya i fun­damenti». Transzheldorizdat, Moscow (1959).

[4] KANANYAN (A.S.). - Experimental study of an­chor foundations behavior, NIIOSP Proceedings,No 53, «Osnovanya e fundamenti», Moscow(1963).

75

[5] EKIMYAN' (N.B.). - Generalized affinity techni­que and its application to piles, modelling.NIIOSPproceedings, No 65, «Svainye fundamenti», (1975).

[6] SOBOLEVSI(Y (Ju.A.). - Sukhodoev V.N. Thestudy of cylindrical thrust anchors «Energitiches­koye stroitelstvo», No 12 (150), (1973).

[7] GABLIA (Ju.A.), NIKITENI(O (M.!.), SHASHKO(S.D.). - The tests of new anchor modificationsfor securing bearing stays of overhead power trans­mission lines. «Energeticheskoye stroytelstvo»,No 1 (187), pp. 73-76 (1977).

[8] KANANYAN (A.S.). - Experimental study 'Ofdeformability and stability of anchor foundationbases. Proceedings of the Baltic conference onsoil mechanics and foundation engineering, vol. 3,Gdansk, 22-25 (September 1975).