Thorne. C. P., Wang, C. X. & Carter, 1. P. (2004). Geotechnique 54, No.8, 507-517

Uplift capacity of rapidly loaded strip anchors In uniform strength clay

C. P. THORNE*, C. X. WANGt and J. P. CARTER* /

The behaviour of horizontal strip anchors buried in clayis examined in this paper. A brief critique of the variousapproaches suggested for the design of these anchors ispresented, with emphasis placed on estimation of theultimate load that these anchors can withstand whenloaded rapidly in uplift under undrained conditions.Possible mechanisms of failure are reviewed, includingshear and tensile failure within the soil and the develop-ment of suction within the pore fluid, and the results offinite element predictions are compared with experimen-tal data for ultimate loads. The analyses reveal that thebehaviour of strip anchors in uplift is a function of thefollowing non-dimensional parameters: HIB, yHlc andu.lc, where H is the depth of embedment of the anchor,B is the width of the strip anchor, y is the unit weight ofthe soil, c is its undrained shear strength, and u; is themagnitude of the maximum tensile stress that can besustained by the pore water in the soil. It is demonstratedthat the ultimate uplift capacity is dependent on theavailability of water at the surface of the soil and withinthe soil beneath the strip anchor. The analyses also showthat shallow anchors in relatively strong soil tend to failby the development of tensile failure in the soil above theanchor. The ultimate capacity of these shallow anchors isa function of the undrained shear strength of the soil, itsself-weight and the tensile capacity of the pore fluid. Bycontrast, the failure mechanism for deeply buried an-chors where the initial vertical total stress at the plateexceeds 7c involves only localised shear failure aroundthe anchor, and as a result the ultimate capacity effec-tively becomes a function only of the undrained shearstrength of the soil.

KEYWORDS: anchors; design; failure; numerical modellingand analysis; plasticity; pore pressures; suction; shear strength

Nous examinons dans cette etude Ie comportementd'ancres en bande horizontales enfouies dans de l'argile.Nous presentons une breve critique des diverses methodessuggerees pour la conception de ces ancres, en insistantsur l'estimation de la charge ultime que ces ancrespeuvent supporter lorsque ces ancres sont chargees rapi-dement dans des conditions de redressement non drai-nees. Nous passons en revue les eventuels mecanismes dedefaillance, dont la defaillance de cisaillement et detraction dans Ie sol et Ie developpernent d'une succiondans Ie fluide interstitiel, et nous comparons les resultatsdes predictions d'elements finis avec les donnees experi-mentales pour des charges u\times. Les analyses revelentque Ie comportement d'ancres en bandes lors du red res-sement est fonction des parametres non dimensionnelssuivants: HIB, yll/c et ucle, H etant la profondeurd'enfouissement de l'ancre, B etant la largeur de l'ancre,y etant Ie poids unitaire du sol, C etant la resistance decisaillement non draine et uc etant la magnitude de l'eaude pore dans Ie sol. II est dernontre que la capacite deredressement ultime depend de la disponibilite de l'eau ala surface du sol et a l'Interieur du sol sous l'ancre enbande. Les analyses montrent aussi que les ancres en-fouies peu profondernent dans des sols relativement fortsont tendance a etre deficientes a cause du developpernentde defaillance de resistance a la traction dans Ie sol au-dessus de l'ancre. La capacite u\time de ces ancres peuprofondes est fonction de la resistance au cisaillementnon draine du sol, de son poids propre et de la capacitede resistance a la traction du fluide de pore. Par con-traste, Ie mecanisme de defaillance pour des ancresenfoncees profondernent oil la contrainte totale verticaleinitiale depasse 7 c cause uniquement une defaillance decisaillement localisee autour de l'ancre et en raison de lacapacite ultime devient en fait fonction uniquement de laresistance au cisaillement non draine du sol.

INTRODUCTIONThe behaviour of horizontal or near horizontal buried an-chors in vertical uplift loading is important to a number ofengineering applications, including transmission tower an-chors, variable geometry drag anchors, and other forms ofmarine anchor system. This paper provides a brief critiqueof the available approaches to the design of these anchors in~lay when subjected to rapidly applied uplift loading-thatIS, under undrained conditions. Shortcomings of the currentdesign methods are identified, and the results of analyses toallow a more rational design approach are provided.

Figure 1 shows the problem investigated and defines thekey parameters. Most references (e.g. Meyerhof & Adams,

Manuscript received 10 June 2003; revised manuscript accepted 22

Iy2003.'. 'scuss,ion on this paper closes on I May 2005, for further detailsee p. 11.

~;Departrnent of Civil Engineering, The University of Sydney,ftustralia.f"Faculty of Design, Architecture and Building, The University of~hnology Sydney, Australia.

H

p

1_ B -I!Fig. 1. Uplift of a strip anchor

507

508 THORNE. WANG AND CARTER

1968; Davie & Sutherland 1977; Sutherland. 1988) give theultimate uplift capacity of a strip buried in a uniformcohesive soil and loaded under undrained conditions as

Pult = B(Fc + yH)

where Pull is the ultimate resistance in uplift per unit lengthof the strip anchor (kl-l.m), B is the width of buried stripanchor (m), c is the undrained shear strength of the clay(kPa), F is the uplift capacity factor, H is the depth of thestrip below the surface (m), and y is the total unit weight ofsoil (kN/m3). Some references. however. do not include thesoil self-weight term (e.g. Das & Singh. 1994: Forrest et al.,1995).

Rowe & Davis (1982) and Merifield et al. (1999. 200 I)use equation (I) but apply a limiting value for the capacityof a buried strip anchor. That is:

Pult = II A2Bc (2)

Most of the analytical models in the literature, including thelatter two, are based on weightless soil models with theeffect of density superimposed. In their study Merifield etal. (200 I) concluded that the errors incurred by assumingsuperposition are likely to be relatively insignificant forinfinitesimal strain analyses. This paper presents analyses inwhich the soil density and other factors noted below areincluded in the initial analyses, i.e. superposition of the self-weight effect is not assumed a priori.

In this paper the results are presented for the upliftcapacity Nc, defined as

One of the major aims of the paper is to investigate thephenomena of tensile failure in the soil and the developmentof suction pore water pressures, and the influence they haveon the ultimate capacity of strip anchors.

MECHANISMS OF FAlLUREMechanisms offailure for various conditions

Uplift loading produces different stress changes in variousregions of the soil. In the region below the strip anchor thereis a reduction in the total vertical stress, whereas in theregion immediately above the strip there is an increase intotal vertical stress. The surface directly above the striptends to bulge upwards, with the intervening soil acting as aform of beam. This 'beam' action results in a decrease inthe horizontal stress that can lead to tensile stresses. Tensilefailure is unusual in soil mechanics, though several authorshave noted tensile cracking above the plate during loading intests (e.g. Meyerhof & Adams, 1968; Davie & Sutherland,1977; Rowe & Davis, 1982). Rowe & Davis (1982) notedthat because of this cracking their analyses could not beused for shallow anchors. They did not provide alternativesolutions for this situation.

The various mechanisms by which a rapidly loaded anchormay fail in uplift are depicted in Fig. 2. Figs 2(a) and 2(b)are for strips that separate from the soil beneath duringloading, whereas Figs 2(c) and 2(d) are for anchors that havenot separated from the soil beneath during loading.

Figure 2(a) shows a shallow anchor separated from thesoil beneath. In this case the failure occurs as a result ofshearing of the soil along lines directly above the edge ofthe strip (thus lifting the soil above the strip) and of tensilefailure of the soil near the surface as a result of the 'beam'action.

Figure 2(b) shows the mechanism for a deep anchorseparated from the soil beneath: in this case the mechanismof failure is shearing contained within the soil above thestrip without surface effects. With the strip at great depth

Tension~cracks

Tension

.-/-:'l cracks

(I)" Shear~~ Shear

____ J Gap

/~-~/

',- Inverted 'bearing capacity'flow shear failure

(a) (c)

(b) (d)

Fig. 2. Mechanisms of failure in uplift: (a) shallow anchor,separated from soil beneath; (b) shallow anchor, joined to soilbeneath; (c) deep anchor, separated from soil beneath; (d) deepanchor, joined to soil beneath

(3) there is no significant surface expression. and hence the'beam' action is absent.

Figure 2(c) shows the mechanism for a shallow anchorbonded with the soil beneath. In this instance the failure isby tension near the surface resulting from 'beam' action.shearing between the strip and these tensile cracks, andshearing beneath and beside the strip in a form of 'bearingcapacity' failure as the soil beside the strip flows round tobeneath the strip. As will be shown later. the self-weight ofthe soil is less important in this case.

Figure 2(d) shows the mechanism for a deep anchorbonded with the soil beneath. In this instance the soil flowsaround the strip, and the failure is in shear and is containedlocally within the soil. It will be shown that, for this formof failure, the self-weight of the soil has no effect on thefailure load.

Most of the published design methods show the value ofeither For N, as a function of HE. At HIB = 0, the valueof F or N; is typically zero for the unbonded case or 5·14for the bonded case, and increases to a maximum value ofabout 5·5-7·5 for the unbonded case as the anchor becomesburied. The corresponding values for the deeply buriedbonded case are: for strips II A2, i.e. 3n + 2, as inMeyerhof (1951) and Rowe & Davis (1982); and for circles,12-42 and 13·11 for rough and smooth plates respectively(Martin & Randolph, 200 I). Solutions for deep square,circular and rectangular anchors have also been published byMerifield et al. (2003). The value of HIB at which thismaximum value is reached is called the critical depth ratio;it corresponds to the onset of the self-contained failuremodes of Figs 2(b) and 2(d).

Forrest et al. (1995) and Das & Singh (1994) give thecritical depth to diameter ratio for buried circular plates. Das(1978, 1980) provides estimates of the critical embedmentratio for square and circular plates, given by the embedmentdepth divided by the plate size (side length or diameter). Inall these studies this critical depth ratio is given as afunction of the shear strength alone. The former gives thecritical depth to diameter ratio as about 1·2 for c = 5 kPa,increasing to about 3-5 at c = 30 kPa. The corresponding

UPLIFT CAPACITY OF RAPIDLY LOADED STRIP ANCHORS

values quoted by Das and Singh are 3 and 5·7. Das (1978)quotes values between 3 and 7 for circular and square platesover a similar range of strengths. For rectangular anchorsDas (1980) indicates that the critical embedment ratio in-creases approximately linearly from the value for a square toa maximum of 1·55 times the value for a square when theplate has an aspect ratio of 3 or more. It must be kept inmind that Forrest et al. (1995) did not include overburdenpressure in the expression for uplift capacity, whereas thepapers by Das do include it.

These empirical relationships of critical depth to diameterratio with soil strength are plotted in Fig. 3, together withdata from other workers. The differences between the twocurves for circular plates can be ascribed to different platesizes and conditions, though both are from relatively small-scale experiments. It may be significant that Forrest et al.(1995) recommend that plate anchors should be installed toa depth of at least 5 diameters. It is also clear from Fig. 3that neither curve is very reliable for other data.

It will be shown that the concept of a straight-linerelationship up to a 'critical depth' is an oversimplification.In addition, the onset of the 'deep' failure load is shown tobe a function of the size (either H or B), the soil densityand the shear strength, plus the ability of the surface soiland the soil beneath the plate to accept tension.

Factors affecting separationWhen uplift loading is applied the (total) contact stresses

beneath the plate decrease. With rapid loading this results ina decrease in the pressure in the pore fluid. Whether thestrip will separate from the sailor not as a result dependson the physical conditions.

If the underside of the strip is connected to the outsideair, or if the pore fluid cannot sustain tension, the strip willseparate from the soil when the total stress reduction equalsthe initial total stress. Pores containing large proportions ofair, or pore fluids with high dissolved gas contents, may be

11

10

,._._.;'

/;'

;'

.//

/L/ - Das (1978,1980) - rectangles

;';'

;';'

;';'

4&5 ./

m 12"//-m,/ D--'-O

6~.;'. cs

9

8 _

7

6~b5:

5

4

3

~ Forest et al. (1995) - circles

1 - Das & Singh (1994)2 - Davie & Sutherland (1977)3 - Meyerhof & Adams (1968), stiff fissured clay4 - Saba et al. (1989)5 - Datta & Suryawarayana (1994)6 - Forrest et al. (1995)7 - Khing et a/. (1994)8 - Das et a/. (1993)9 - Narasimha & Prasad (1993)10 - Shin et al. (1994)o 0'----1-'-0-----'20--3.L0-......J.40--5LO---l.60--7LO--8..l.0--

c: kPa

2 09

Fig. 3. Test data illustrating the effect of shear strength on thecritical depth ratio for circular, square and rectangular anchors

509

unable to sustain significant tension. This may be an impor-tant consideration for plate anchors embedded in someseabed soils, where gas contents, especially methane, may besignificant.

If the soil is saturated, and the underside of the strip isopen to water at the same hydrostatic level as the porewater, then separation will take plaee when the pressurereduction equals the initial effective overburden pressure.

In a saturated soil where the strip is sealed within the soil.separation cannot occur unless either:

(a) the pore pressures equalise by dissipation of theinduced pore pressures. in which case an undrainedanalysis is invalid, as the loading is no longer 'rapid',or

(b) the pore pressure drops far enough below atmosphericfor cavitation to occur-that is. failure in tension of thepore contents.

Estimates of the rate of dissipation of pore pressurearound a plate can be made by the methods described inBooker & Small (1987) to test the assumption of undrainedbehaviour. Some other relevant information is also containedin Pyrah et al. (1985) and Small et al. (1998). A discussionof the effects of failure in tension of the pore contents isgiven below in the section 'Effect of allowable pore waterpressure tension on uplift capacity'.

Factors affecting soil tensile capacity near the soil surfaceThe concept of soil operating in tension is somewhat

unusual. Finite element analyses in which tension wasallowed showed a drop in total horizontal stress near thesurface of approximately 100-160% of the shear strength.Although unsaturated soils can have some tensile strength intotal stress terms. it is certainly not of this magnitude.Meyerhof & Adams (1968) indicated that tests on soft clayshad given a tensile strength of 40% of the compressivestrength but did not give any further details, and it ispossible that this strength came from negative pore waterpressures. Tests on unsaturated compacted clays gave tensilestrengths in Brazilian tests of 25- 78 kPa, and all the sam-ples in these tests had unconfined compression strengths inexcess of 500 kPa.

In saturated soils the presence of the pore water will allowsome total stress tension to be sustained, and in a trueundrained situation some tensile total stresses should be ableto be accommodated. The tensile stresses caused by uplift ofa strip are, however, right at the surface, and any negativepore water pressures could dissipate almost instantaneouslyprovided there is free water at the surface. As a crack forms,only the soil at the very tip would need to drain for thecrack to propagate. Such dissipation would occur at manyorders of magnitude greater than dissipation for the porepressures in the soil beneath and around the strip, and theview has been taken that pore pressures at the base of acrack from the surface will not drop below initial (hydro-static) values.

ANALYSES UNDERTAKENAnalyses of strip anchors in clay subjected to undrained

uplift loading were undertaken using the finite elementprogram AFENA (Carter & Balaam, 1995). The analysesassumed a thin, perfectly rigid strip, progressively displaceduntil failure occurred. Large-strain analyses were undertakenwith re-meshing using an automatic mesh generation pro-gram developed by Hu & Randolph (1998). Most of theanalyses were carried out assuming a smooth plate. Somecheck analyses with rough plates showed that the differences

510 THORJ'\!E, WANG AND CARTER

were very minor. Two different soil models were used in thisstudy,

In the first model, the soil was represented as a single-phase material, characterised by a shear strength, a tensilestrength, Poisson's ratio, shear modulus and density (unitweight). In these analyses the tensile strength was taken aseither very large or zero. For the analyses with zero tensilestrength, if the minor principal (total) stress reduced to zero,the stresses at that Gauss point were maintained at that samevalue for all subsequent steps in the non-linear analysis.Poisson's ratio was always 0-49 to approximate constant-volume deformation and the ratio of shear modulus to shearstrength (Glc) was 67, except for some analyses that wereundertaken to examine the effect of changing this ratio.

In the second model. the soil was represented as a two-phase material. One phase was the soil skeleton, charac-terised by a shear strength, a tensile effective strength,effective Poisson's ratio, shear modulus and total density(unit weight). The second phase was the pore water, char-acterised by a very large bulk modulus, zero shear strengthand stiffness, and with a limiting value for the negative porepressure allowable. General details of the two-phase methodcan be found in some textbooks (e.g. Naylor et al., 1981). Inthese analyses the soil tensile strength (measured in terms ofeffective stress) was taken as zero, and soil tension was dealtwith in the same manner as for the single-phase soil.Various values were assigned to the limiting negative porepressure. For the pore fluid, if the pore pressure droppedbelow a value of -lie, the pore pressure was maintained atthat value and the bulk stiffness was set to zero. Theformulation can handle effective stress soil strength para-meters, but, for the purpose of this work, a uniform strengthwas required, and so the artifice was used of giving the soila cohesion only. The ratio of shear modulus to shearstrength was kept as 67, as for the single-phase soil.Poisson's ratio of the solid skeleton was taken as 0·25, andfor most analyses the total unit weight of the soil was takenas 20 kN/m3 and the unit weight of the water was taken as10 kN/m3.

Both methods allow failure of the soil in tension. If theminor principal stress drops to zero the soil stresses arefrozen and any requirement for zero volume change ceases,even in the two-phase soil. This is not strictly correct,because the major principal stress could theoretically con-tinue to increase after tensile failure to 2c (or perhaps evenlarger if a truly frictional soil model had been assumed).This is likely to result in some underestimate of the capacityof shallow anchors with low values of yHlc.

In the two-phase soil, if the pore water pressure reducesto below -Ue then the no volume condition ceases and anyfurther stress changes are transferred to the soil skeleton andthe pore pressure is kept at -lie'

Results of analyses are presented for the following cases.

1. Single-phase soil model, total stress tension allowed inall soil elements and tension allowed at the interfacebetween the soil and the underside of the strip anchor.

2. Single-phase soil model, total stress tension allowed inall soil elements but with a no-tension joint immedi-ately beneath the strip anchor.

3. Single-phase soil model with no total stress tensionallowed anywhere in the soil.

4. Two-phase soil model with soil tensile failure if theminor principal effective stress reduces to zero. Abovethe strip no reduction in pore pressure below the initialpore pressure is allowed, whereas below the strip thetotal pore pressure is not allowed to reduce below zero(i.e. cavitation limit, Ue = 0).

5. Two-phase model with the soil above the strip as for

Case 4 but with no cavitation limit for the soil beneaththe strip (i.e. lie large).

6. As for Case 5 but with varying cavitation limits.

Cases I and 2 do not have much physical validity, if any,but are included to allow comparison with other results andto demonstrate the effect of tensile failure on uplift capacity.

Analyses for case I using small-strain theory showed thatthe uplift capacity factor was independent of the soilstrength, normalised as yHlc. Large-strain analyses were alsoundertaken to assess the extent to which work done againstgravity might influence results. Figure 4 shows the results ofcomparing large- and small-strain load deflection curves fora relativelv shallow anchor (HiE = I). For anchors withHI B > 2 the differences were negligible. Even for shallowanchors it was concluded that, although for very weak soilsthe large-strain results showed higher capacities, these highercapacities occurred at very large deformations, and forpractical deformations the small-strain result was consideredacceptable. Likewise, for high-strength soils, slightly lowercapacities were recorded for very shallow anchors, but thedifference was only 8% in the worst case. Large-strainanalvses for case 2 which assumes no bonding between theund~rside of the strip and the soil, but allows tension in thesoil itself, also showed similar differences between large-and small-strain answers, and also showed that the small-strain results were acceptable. The large-strain results didhighlight the brittle nature of failure in higher-strength soils.

These results also showed that the inclusion of a densityterm in the expression for ultimate capacity, as in equation(I), is not required, and that equation (3) is more appropriatefor expressing the anchor capacity. The results of case 2showed that if yHlc < 7, the mechanisms of failure weresimilar to Figs 2(a) and 2(b), whereas for greater values ofyHic the behaviour was identical to that of a fully bondedanchor.

The results of other cases are dealt with in later sections.

APPLICABILITY OF ANALYSES TO FIELD SITUATIONSUnsaturated soils

Many applications of buried anchors involve unsaturatedsoils, including transmission tower anchors and the like. Inmost instances these will be buried in compacted clays,because of the difficulty of installing a horizontal anchorplate in undisturbed soil. Because of the air in the pore fluid,it is reasonable to assume that the soil near the surface willfail in tension if the total stress drops below zero. Beneath

12

10__--::====== ~6~~~========i8

yH/c = 0oal 6ii

4

...... Small deformation analysis2 - Small deformation analysis

--- Rowe & Booker (1979a) elastic solution

OL-----"-----'----'----_--"-_---'-- __ '---------.Jo 5 10 15 20 25 30 35

GslBc

Fig. 4. Load-deflection curves for large and small deformationanalyses of fully bonded, tension allowed soil (case 1), BIB = 1

UPLIFT CAPACITY OF RAPIDLY LOADED STRIP ANCHORS

the plate the soil and plate would part if the total stressdropped below zero, though the extent will depend on theproportion of air and the speed with which air can getaccess to the underside of the strip. Unless other informationis available, for example the results of full-scale tests at thesame site, a reasonable approach is to assume that no totalstress tension can be tolerated beneath the plate. Thus theanalyses of case 3 (the single-phase soil no-tension analysis)would be adopted.

Caution needs to be exercised if the surface is exposed, asdrying tension cracks could reduce the uplift capacity.

Saturated soilIn saturated soils, separation will occur only if the effec-

tive stress beneath the plate drops below zero. This canoccur only if the negative pore pressures beneath the platedissipate (unless cavitation occurs; see below). If dissipationoccurs then the surrounding soil will also have drained, andthe undrained analysis solutions are no longer applicable. On

m Shear failure

~ Tensile failure

(a)

~ Shear failure

~ Tensile failure

(b)

511

the other hand, dissipation of the negative pore pressures inthe tensile zone near the surface could occur much morerapidly, as discussed above.

It is therefore concluded that for design in such circum-stances the results for case 5 (the two-phase soil, large u,analysis) should be used. It is also necessary to check forcavitation. In deep water and weak soils this will not be aproblem, but in other cases a check should be made usingthe methods described subsequently in the section 'Effect ofallowable pore water tension on uplift capacity'.

RESULTS FOR ANCHORS IN A SINGLE-PHASE SOIL(CASE 3)

The distributions of shear and tensile failure in the soilare shown in Figs 5(a)-5(d). Figures 5(a) and 5(b) showresults for relatively shallow anchors with HIB = 1. FigureSea) is for a relatively strong soil, yH/c = 1, whereas Fig.5(b) is for yH/c = 8, which approximates a normallyconsolidated soil. It can be seen that, for the strong soil, the

r-II

~

a Shear failure

~ Tensile failure

(c)

~----~ m Shear failure

I ~ Tensile failure

I

(d)

Fig. 5. Typical failure zones predicted by single-phase, no-tension analysis (case 3): (a) BIB = 1, yHlc = 1;(b) HlB = 1, yHlc = 8; (c) BIB = 6, yHlc = I: (d) HIB = 6, yHlc = 8

512 THORNE, WANG AND CARTER

tensile stresses near the surface cause failure from thesurface to the plate. Thus the failure is all tensile, and theplate separates, whereas for the normally consolidated soilseparation does not occur, and the failure is mostly in shear,although there is some tensile failure near the surface.

Figures 5(c) and 5(d) show deep strips with HIB = 6,again for the same two values of yHle. In these relativelydeep anchors tensile failure still occurs at the surface butdoes not join the failed sections around the strip. For therelatively strong soil the strip separates from the soilbeneath: tensile failure or splitting occurs next to the strip,and shear failure occurs above the strip. In the normallyconsolidated soil only shear failure is predicted to occur nearand immediately above the strip.

These figures demonstrate the importance of the two non-dimensional parameters HIB and yHle in determining theway that failure occurs and hence the load deflection andultimate load behaviour. It was found that the relativestiffness (or 'rigidity index'), Glc, did not affect the anchorplate behaviour to any significant degree; this ratio was 67and Poisson's ratio was 0-49 for all results given in thissection.

The ultimate values for the uplift parameter N; are shownin Fig. 6 as a function of HIB for various values of yHle.Also included are the values for the tension-allowed analysiswith a no-tension joint beneath the strip (case 2). As tensilefailure is included beneath the anchor for both cases, thedifferences between the two sets of curves are caused by thetensile failure near the soil surface. The percentage reductionin ultimate capacity resulting from tensile failure above thestrip depends on yHle, and for most values of HIB rangestypically from 30% at yHle = I to less than 10% wheny Htc = 3 and to less than 5% when y Hlc is 6 or more.

The capacity of the soil above the strip to accept areduction in horizontal stress is also dependent on the initialin-situ value of the ratio of total horizontal and total verticalstresses, denoted here as Kt. Clearly a large value of K,results in higher initial horizontal stresses and hence a great-er capacity to accept horizontal stress reductions before thestresses become tensile. A greater value of K, gives highercapacity: for example, in the cases where K, = 1 and 0,9,the uplift capacity factors for anchors with HIB = I andyHle = 4 are 5·61 and 5·55 respectively. The factors shownin Fig. 6 are for K, = I.

The nature of the load-deflection curve to failure is alsodependent on HIB and yHle. Fig. 7 shows some typical non-dimensional load-deflection curves presented as PIBe

12

4

2 ... Tension allowed. separation allowed (Case 2)yHle = 1 - Single-phase no-tension soil (Case 3)

00'------'-------'-2 -----'3-'-----'-4---5L------.J

6HIB

Fi~. 6. Uplift capacity against HlB for single-phase, no-tensionsoil (case 3) compared with tension-allowed soil with separation(case 2)

10 IK=1 K=3

! K~2 K':'4K ~ 6 K = 10

_------------------------- ill

8 - h~-___,_--------6

2 ,1;.,-'--,-'-' '(Hle = 1Single phase (total stress) tension allowedSingle phase (total stress) no tension

_--'---_R_o_w_e_&_Booker (1979) elasticsol~tiono o 10 15 20 25 30 355

Gs/Bc

(a)

14 _

K~1 K~3 K=612- K=2 K~4 K = 10

=i:=;;.-;;.'-;;"-;' "';;"-;;.'-;;,'-==-='-'--'--'-4-'- ._._.-

ocoQ 6-

--~~-------~----------

Single phase (total stress) tension allowedSingle phase (total stress) no tensionRowe & Booker (19~9) elastic solutio~o "- -'----_----' -'--_--' __ -'-_----.J

o 5 25 4030 3510 15

(b)

Fig. 7. Load-displacement curves predicted by single-phase, no-tension analysis (case 3): (a) HIS = I; (b) HIS = 6

against GslBe, where s is the strip deflection and P is theapplied force. Rowe & Booker (1979) give a method ofcalculating the elastic deflections. and these are also shownin Fig. 7. It is convenient to give the deflection to failure asa ratio K of the deflection at failure to the deflection thatwould occur if the soil had remained elastic up to that load.Table I shows the results for a range of values of HIB andyHle. It should be noted that, with strong soils (yHle = I),sudden failure occurs at relatively low deflections. Forshallow anchors in weak soils (yHie ? 8), very large deflec-tions may be required to attain the ultimate load, as is alsothe case for deep anchors of intermediate strength (2 <yHle < 4).

The distribution of pressure across the strip is importantfor the design of real anchors. The distribution of loadacross the strip is shown in Fig. 8 in non-dimensional formas net vertical pressure normalised by the stress quantity(PIB). Figure 8(a) is for loads of one-third the ultimate, andall the curves are very similar, with significant stress con-centrations near the edge. This is an important considerationin the structural design of an anchor, because most anchorswill work in this range of loading. By contrast, Fig. 8(b)shows the distribution at failure. In this case, the distributionis relatively uniform except for the case of a shallow anchor(HIB = I in strong soil, yHle = I). Fig. 8(c) shows thereduction in stress beneath the anchor at failure for caseswhere the anchor does not separate. It will be seen that inboth cases the reduction is from 6 to 7 times the shear

Table \. Failure deflection ratio. K. predicted by single-phase analyses

UPLIFT CAPACITY OF RAPIDLY LOADED STRlP ANCHORS 513

yHe Tension allowed above plate (case 2) '\10 tension (case 3 )

HE = 1 HIB = 3 HIB = 6 H,B = I H'B = 3 HIB = 6

1 -l 7 16 3 3 32 -l 6·5 14 3 -l 10-l -l 6 10 3 5 96 5 6 4 -l 5 38 8 55 3 7·5 5 3

10 10 5 3 10 5 3

strength. This is similar to the value noted in Rowe & Davis(1982).

RESULTS FOR ANCHORS IN A TWO-PHASE SOIL(CASES 4 AND 5)

As noted above. the analyses for cases 4 and 5 used atwo-phase soil model. All calculations assumed that Pois-son's ratio of the soil skeleton was 0·25, Ko = 1·0, the totalunit weight of soil was 20 kN/m', and the unit weight ofpore water was 10 kNrrn '. The calculations are not espe-cially sensitive to Poisson's ratio but are affected by Ko andthe density insofar as they affect the initial horizontal effec-tive stress. Common to both cases is the assumption thatpore pressure dissipation at the base of a crack starting fromthe surface will be virtually instantaneous, and so tensilefailure will occur when the reduction in horizontal stressequals the initial horizontal effective stress for the materialabove the strip.

Below the strip in case 4 it is assumed that the pore watercannot accept any negative pressure. This means that thestrip will separate from the underlying soil when the totalstress reduction beneath the strip equals the initial totalvertical stress. In practice this is the same assumption aswas made for the soil model for case 3. Below the strip incase 5 it is assumed that the pore water can sustain anynegative pore pressures without failure. In practice thismeans that the strip always stays in contact with the soilbeneath it.

The mechanisms of failure for case 4 are very similar tothose shown in Fig. 5. although the change from tensile toshear failure above the strip occurs at higher values of yHle.Likewise, the mechanisms of failure for case 5 always showshear failure beneath the strip but show similar mechanismsto case 4 above the strip.

Figure 9 shows the ultimate uplift values obtained forcases 4 and 5. It will be seen that, once yHle exceeds 6 to8, there is little difference between the two predictions. Thisis because the value of the total vertical stress change belowthe anchor required to cause shear failure adjacent to andbelow the anchor is less than the initial total vertical stress,so tension does not occur beneath the anchor. At smallervalues of yHle the capacities for case 4 are substantiallybelow those for case 5. An interpolation method to deal withdifferent values of the allowable negative pore pressure, u.,is given in the next section.

It is instructive to compare the ultimate values of PIBe forcase 3 with those for case 4. In effect, in the former casethe clay fails in horizontal tension above the plate when thehorizontal stress reduction is the same as the total over-burden pressure, whereas in the latter case the clay experi-ences failure at half this total stress reduction. This is alsoanalogous to using the case 3 analysis with a K, of 0·5instead of 1·0. The effect where yHle = I (strong soil) is toreduce the ultimate load by about 30% at HI B < 4, reducing

to 14% at HIB = 6. The reduction is under 10% whereyHlc > 3.

The distribution of load across the strip is shown in Fig.lOin non-dimensional form as net vertical total pressurenormalised by PIB. Figure 10(a) is for loads of one-third theultimate, and all the curves are very similar, with significantstress concentrations near the edge. By contrast. Fig. I O(b)shows the distribution at failure. In this case the load isrelatively uniform except for the case of a shallow anchor(HIB = I) in strong soil (yHlc = I). Figure 10(c) shows thereduction in total stress beneath the anchor at failure wherethe anchor does not separate. It will be seen that in bothcases the reduction is from 6 to 7 times the shear strength.All these distributions are very similar to those for thesingle-phase soil (Fig. 8).

The nature of the load-deflection curves for the two-phase soil is similar to those for the single-phase soil. Table2 shows the values of K at failure-s-that is. the ratio of thedeflection at failure to that which would occur at that load ifthe soil remained elastic. It should be noted that, with strongsoils (yH/c = I), sudden failure occurs at relatively lowdeflections. For shallow anchors in weak soils (yH/c?o 8),very large deflections may be required to attain the ultimateload, as is also the case for deep anchors of intermediatestrength (yHle = 4).

EFFECT OF ALLOWABLE PORE WATER TENSION ONUPLIFT CAPACITY

For pure water at normal temperatures (5-25°C) cavitation(boiling) will occur at a pressure of 80-95 kPa below atmo-spheric. In clay soils, it is known that the water boundwithin the clay platelets can withstand much higher negativepressures. It is unlikely, however. that this would apply tothe free water in the voids within the soil, and althoughmore research is required to ascertain the actual behaviour,it is considered prudent to assume that pore water wouldalso cavitate at pressures similar to normal water. The stressdistributions in Figs 8(c) and IO(c) show that where separa-tion does not occur the reduction in total stress below thestrip is of the order of seven times the undrained shearstrength. Thus cavitation can occur if the tolerable poretension plus the initial pore pressure plus the initial effectivevertical stress is less than seven times the undrained shearstrength. In stiff soils this can occur, and it will be necessaryto use a lower capacity if

7c>y'H+uo+uc (4)

where Uo is the initial pore pressure above atmospheric(kPa), Uc is the (absolute) magnitude of the pressure dropbelow atmospheric at which water will cavitate (kPa), and y'is the submerged unit weight of the soil (kN/m3).

If (y'H + Uo + uc) < 7Su then the capacity will be inter-mediate between case 4 and case 5. Based on the analysespresented in the previous section, the reduced capacitycaused by cavitation can either be approximated directly

514

co 2·5e;.~ 2·0:JUl

~ 1·5c,

13t 1·0~

co0::'¥ 1·5:JUl

~o,13 10t~

0

-1

-2co -3e;.~ -4:JUlUl -5~o,

13 -6t~ -7

-8

-90

3·5

THORNE, WANG AND CARTER

HIS ~ 1HIS ~ 1HIS = 6HIS = 6

yHle = 1yHle = 8yHle = 1yHle = 8

3·0

05

oL-_'---------l_----L_---L_-'--_-L_--'---_-"----_.L-_o 0·1 0·2 0·3 004 0·5 0·6 0·7 0·8 0·9 1·0

Distance from centre of strip/(SI2)

(a)

2·5

-

HIS = 1HIS = 1HIS ~ 6HIS ~ 6

yHle ~ 8yHle = 1 ~yHlc = 1 . \yHle = 8 jI I

7'-, "~

2·0

--------_ ...••...... -.-:-.-=---::-:

0·5 _'-'-

oL-_'---------l_----L_---L_-'--_-L_--'---_-"----_.L----.Jo 0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9 1·0

Distance from centre of strip/(SI2)

(b)

HIS = 1 yHle = 8HIS = 1 yHle = 8

0·1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 09 10

Distance from centre of strip/(SI2)

(c)

Fig. 8. Normalised stress distributions across the strip (case 3):(a) one-third ultimate load; (b) ultimate load; (c) net total stresschange beneath strip

from the values given or, for other cases,capacity could be taken as

(UO + Uc - YwH)

Pult = P4 + (Ps - P4) 7 c _ Y H

this reduced

where P4 is the uplift capacity for case 4, and Ps is theuplift capacity for case 5.

~

.: ..• . 43

.2 -

19. ..... .'6.: . ..' .

10

.... --_ .

..........

8

43

22

- Two-phase analysis. Uc = 0 (case 4)

o LI . --,",_"_T_w_o--,'P_h.Lf_s8L,_no_,_t8_nLpi_on_a_n_a.LIY--,s,i_s,_u-",c_=_I_ar.I9_e.'-(c_a_se----'-5),

o 234 5 6HIB

Fig. 9. Uplift capacity for no-tension, two-phase soil, Uc

(case 4) and u, = large (case 5)o

Equation (5) becomes unstable near the point where yHapproaches Tc, as both the numerator and denominator inthis equation approach zero, so some judgement is required.

Figure 11 shows a comparison of the results of finiteelement analyses as compared with the approximate predic-tions of equation (5). It can be seen that generally goodagreement is obtained.

(5)

COMPARISON WITH EXPERIMENTAL RESULTSMost of the experimental data in the literature are for the

uplift of circular or square plates. Two sets of data for stripswere found. Rowe & Davis (1982) described experiments on6 mm brass strips, 13-38 mm wide and 64-190 mm long.They indicated that there was little change in results oncethe aspect ratio (LIB) exceeded 5, and that results for loweraspect ratios were slightly larger. The soil was a kaolin clayand was consolidated with an overburden pressure of200 kPa before unloading and testing, resulting in an averageundrained shear strength of 50 kPa. Because of this prepara-tion there would have been considerable initial horizontalpressures in the soil at the time of testing. Tension crackswere noted at HIE values of less than 2·5. Figure 12 showsa comparison of calculations, made assuming an allowablereduction in horizontal stress at the surface of 50 kPa, withthe experimental results. The test results are shown in Fig.12 compared with calculations assuming that (I) the soil cantake unlimited tension, and (2) the soil can sustain a 50 kPareduction in horizontal stress. This latter series showed onlyvery small tension cracks for HIB = 3 or more. It will beseen that the test results lie reasonably on the second linefor shallow strips but nearer the first for higher values ofHIB. It is noted that in the paper the opinion was given thatthe rods attached to the strip to apply the uplift loadingaccentuated the surface cracking.

Khing et al. (1994) reported results for a buried strip,76 mm wide by 152 mm long and 13 mm thick, buried inclay with a liquid limit of 43%, placed in a relatively wetcondition to give an average shear strength of 10·2 kPa. Thestrip was sat on top of a Plexiglas box to prevent anycontribution to the capacity by underlying soil. The soil waskneaded into place to exclude air bubbles. This placementmethod would have resulted in continual passive failure inthe clay, with the result that the initial horizontal stress wasclose to twice the undrained shear strength. With such ahigh initial horizontal stress, tensile failure at the surfacewould not be expected. Figure 13 shows the experimentalresults together with those for calculations allowing tension

3·5

UPLIFT CAPACITY OF RAPIDLY LOADED STRlP ANCHORS 515

30HIB = 1HIB = 1HIB = 6HIB = 6

'(Hie = 1'(Hie = 8'{Hie = 1yHle = 8iil 25

~~ 20:J<Il<Il~Q. 1·5rout 1.0~ ..~~

:..:.........:..-=--.:--~.:....;:=-::-:.-.;.. ...;.... - .. .:..:.....-:

0·5

oL.-_____l~----l.~---L~__'_~....L~..L_~_'___~L.______l~___'o 0·1 0·2 03 04 05 0·6 0·7 0·8 0·9 1·0

Distance from centre of strip/(BI2)

(a)

2·5

HIB = 1HIB = 1HIB = 6HIB = 6

yHle = 1·(Hle ~ 8':Hle = 1'(Hie = 8

2·0

iil~~ 15:J<Il

gJa.ro 10ot:§;

. I'.=-', ;-J\:'.I'-'.-.--';~~>:: f~,~.t'l-

0·5

oL-~L._~'----~'----_____l'---------'~-----'~-----'-~-----'-~---L~---..Jo 0·1 0·2 03 0·4 0·5 0·6 07 0·8 0·9 1·0

Distance from centre of strip/(BI2)

(b)

0

-1

-2iilit -3W -4:J<Il<Il

'" -5a.roo -6t:§;

-7

-8

-90

HIB = 1 yHle = 8HIB ~ 6 yHle ~ 8

0·1 0·2 0·3 04 0·5 0·6 0·7 0·8 0·9 1·0

Distance from centre of strip/(BI2)

(c)

Fig. 10, Normalised stress distributions across the strip (case 4):(a) one-third ultimate load; (b) ultimate load; (c) net total stresschange beneath strip

to develop in the soil and plate separation (case 2), andthere is reasonable agreement, although the experimentalresults are rather higher, as might be expected given theirrelatively low aspect ratio. The box beneath the strip wouldtend to inhibit failure at greater HIB values because the soilcould not move around to beneath the strip so readily.

CONCLUSIONS(a) The analyses described in this paper show that the

behaviour of strips in uplift is a function of the non-dimensional parameters HIB, vH!c and u.lc. Theserepresent the effects of depth of burial, the relativeeffects of overburden pressure and shear strength, andthe capacity of the pore fluid to accept tension. Atnormal temperatures water can accept pressures in theregion of 80-95 kPa below atmospheric withoutvaporising, It is probable that this will also apply towater in macropores within a saturated soil, althoughmore research is required to investigate this behaviour.Gas in solution could also limit the effective value of!Ie·

(b) The ultimate uplift capacity is dependent also on theavailability of water at the soil surface and beneaththe strip. Some guidelines for this are provided in thesection 'Applicability of analyses to field situations',and in the discussion on separation in the subsection'Factors affecting separation'. Designers need to con-sider the particular circumstances of their problem.

(c) In shallow anchors, failure in tension occurs from thesurface downwards. The stronger the soil, the morelikely is tensile failure, and the deeper the strip has tobe before tensile failure does not occur.

(d) When anchors are deeply buried the failure pattern is alocalised shear failure around the anchor, and thecapacity becomes a function only of shear strength andis independent of the overburden pressure.

(e) The deflection at failure is very variable, as shown inTables 1 and 2. In stronger soils, tensile failure resultsin low deflections at ultimate collapse, and overloadcould result in sudden failure. By contrast, for shallowanchors in weaker soils, the deflection to failure can bevery high, and if deflections need to be limited,conservative factors of safety are required.

(/) Intuitively, it should be expected that the capacity ofshallow anchors will be significantly affected by themagnitude of horizontal stresses prior to anchorloading. The limited results presented in this studyconfirm this expectation. In compacted clay fills highhorizontal stresses commonly exist after placement, andcan be as high as 2c. These may dissipate with time asthe surrounding soil creeps away or as drying inducestension cracks in adjacent soil. Care is thereforenecessary in interpreting the results of field tests onshallow anchors.

(g) The curves given in Figs 6 and 9 were computed for )'= 20 kN/m3 and )'W = 10 kN/m3 and for K, = I. The

Table 2. Failure deflection ratio, K, predicted by two-phase, no-tension analyses

)'Hlc Ue = 0 (case 4) Ue = large (case 5)

HIB = 1 HIB = 3 HlB = 6 HlB = 1 HlB = 3 HIB = 6I 2 3 3·5 5 4 3·52 3 4 4 6 4·5 3·54 3·5 5 12 8 7 3·56 5·5 5 5 9 7 3·58 10 5 3·5 10 7·5 3·5

10 10 5 3·5 12 7·5 3·5

516

12

10

8

o~ 6>-Q"3

4

2101

0 2

THORNE, WANG AND CARTER

(h) The predictions presented here indicate that reductionsin the uplift capacity can be as much as 30% due totensile failure of the soil (Fig. 6). This effect is mostpronounced for anchors characterised by low values ofthe parameter yH/c.

(i) Model tests in normal gravity have very low values of;'Hc. In addition, many preparation techniques causehigh initial horizontal stresses. Account must be takenofthese factors when applying the results of such teststo full-scale design.

U) In the normal working range of loading, there is asignificant load concentration near the edge of the strip,and this needs to be taken into account in the structuraldesign of strip anchors.

HIB ~ 1 yHle ~ 3HIB = 6 ',Hle = 3Approximation HIB = 1Approximation HIB ~ 6

~------6 8 104

Fig. 11. Effect of the ability of the pore water to accept negativevalues on the uplift capacity, and comparison with predictionsof equation (5)

6 -

5.•....

4

o-J

~ 3.Q= !

i2

Rowe and Davis (1982)-- If ue ~ 50 kPa

Tension allowed, separation allowed

1 -

o ,-I _-'-- -L:__~:__~:__~:__~=____:'_:=____:'_:=____=_o 0·5 10 1·5 2·0 2·5 30 3·5 4·0 4·5 5·0

HIB

Fig. 12. Comparison of calculated values and experimentalresults from Rowe & Davis (1982)

91817

6

o 5~Q"3 4

:rKhing et a/. (1994)Calculated, tension allowed

0 2 3 4 5 6 7HIB

Fig. 13. Comparison of calculated values and experimentalresults from Khing et al, (1994)

effect of changing the soil density is simply reflected inthe corresponding change in the parameter yH/c. Insituations where horizontal tensile failure occurs in thesoil, the ultimate uplift capacity is likely to be sensitiveto K;

12

ACKNOWLEDGEMENTSSome of the work described here forms part of the

research programme of the Special Research Centre forOffshore Foundation Systems, established and supportedunder the Australian Research Council's Research CentresProzrarnme. In addition, a Large Grant from the AustralianRes~arch Council to investigate the finite deformation behav-iour of soils is also gratefully acknowledged .

NOTATIONB width of strip anchor platec shear strength of soilG shear modulus of soilH depth from surface of strip anchor plateK ratio of deflection at failure to that corresponding to elastic

deflection at same loadL length of plate

N, uplift capacity factor for a strip anchorP force on anchor in uplift

PUll ultimate force on anchor in upliftP, maximum value of Pull for case 4P, maximum value of Pult for case 5

s deflection of plate110 initial pore pressure at platelie maximum drop below atmospheric pressure that pore fluid

can accommodatey bulk unit weight of soil

y' submerged unit weight of soil

REFERENCESBaba, H. U, Gulhati, S. K. & Datta, M. (1989). Suction effect in

plate anchors in soft clays. Proc. 12,h In'. Con! Soil Mech.Found. Engng, Rio de Janeiro 1,409-412.

Booker, 1. R. & Small, 1. S. (1987). The time deflection behaviourof a rigid under-reamed anchor in a deep clay layer. Int. JNumer. Anal. Methods Geomech. 11, 269-281.

Carter. 1. P. & Balaam, N. P (1995). AFENA: Users' manual.Centre for Geotechnical Research, Department of Civil Engi-neering, University of Sydney, Australia

Das, B. M. (1978). Model tests for uplift capacity of foundations inclay. Soils Found. 18, No.2, 17-24.

Das, B. M. (1980). A procedure for estimation of ultimate capacityof foundations in clay. Soils Found. 20, No. I, 77-82.

Das, B. M. & Singh, G. (1994). Uplift capacity of plate anchors inclay. Proc. 4th Int. Offshore and Polar Engineering Conf., Osaka1, 436-442.

Das, R. N., Shin, E. c., Das, B. M., Puri, V K. & Yen, S. C.(1993). Creep of plate anchors in clay. Proc. 3rd Int. Offshoreand Polar Engineering Conf., Singapore 1, 538-543.

Davie, 1. R. & Sutherland, H. B. (1977). Uplift resistance ofcohesive soils. J Geotech. Div., ASCE 103, No. GT9, 935-952.

Datta, M. & Suryanarayana, C. V (1994). Elimination of suctionbeneath plate anchors in model tests: a comparison of twomethods. Proc. 4th Int. Offshore and Polar Engineering Conf.,Osaka 1, 456-459.

UPLIFT CAPACITY OF RAPIDLY LOADED STRIP ANCHORS

Forrest, 1., Taylor. R. & Bowman. L. (1995). Design guide for pile-driven plate anchors. Technical Report TR-2039-0CN, PortHueneme, CA: Naval Facilities Research Center.

Hu. Y. & Randolph, iVl. F. 11998). A practical numerical approachfor large deformation problems in soil. Int. J Numer. Anal.Methods Geomech.22, 327-350 (see also Research ReportG 1226, Department of Civil Engineering, University of WesternAustralia, 1996)

Khing, K. H., Das. B. 1\1. & Yen, S. C. (1994). Uplift capacity ofstrip plate anchors in clay with sloping surface. Proc. 4thInternational Polar and Ottshorc Engineering Cont.. Osaka 1.467--171.

Martin, C. M. & Randolph. M. F. (200 I). Applications of lower andupper bound theorems of plasticity to collapse of circularfoundations. Proc. 10th lilt. Coni. on Computer Methods andAdvances in Gcomechanics. Tucson 2, 1417-1428.

Merifield, R. S., Sloan. S. W & Yu. H. S. 11999). Stabilitv ofplateanchors in undrained elm: Research Report No. 174·02·1999.University of Newcastle. Australia.

Merifield, R. S., Sloan, S W & Yu, H. S. (2001). Stability of plateanchors in undrained clay. Geotechnique 51, No.2, 141-153.

Merifield, R. S., Lyarnin. A. V, Sloan, S. W. & Yu. H. S. 12003).Three-dimensional stability analysis of plate anchors in clay.J Geotech. Geoenviron. Engng, ASCE 29, No. 3, 243-253.

Meyerhof, G. G. (1951). The ultimate bearing capacity of founda-tions, Geotechnique 2, No. 4, 301-332.

517

Meyerhof, G G. & Adams, 1. I. (1968). The ultimate uplift offoundations. Can. Geotech. J 5, No, 4. 225-244.

Narasimha, S. & Prasad, Y. V S. N. (1993). Experimental studieson plate anchors in layered marine soils. Proc. 3rd Polar andOffshore Engineering Conf., Singapore 1, 544-550.

Naylor, D. 1., Pande, G. "I., Simpson, B. & Tabb, R. (1981). Finiteelements in geotechnical engineering, pp. 29-34. Swansea:Pineridge Press.

Pyrah, I. c., Hird C. C. & Tanaka. Y. (1985). Consolidationbehaviour of a single underream anchor. Proc. 5th Int. Coni. onNumerical Methods in Geomechanics . .\"agom. 629-636.

Rowe, R. K. & Booker, 1. R. (1979). A method of analysis forhorizontally imbedded anchors in an clastic soil. Int. J Numer.Anal. Methods Geomech. 3, 187-203.

Rowe. R. K. & Davis, E. H. (1982). The behaviour of anchor platesin clay. Geotechnique 32, No. I. 9-23.

Shin. E. c., Das. R. "I .. Omar, tvl. T., Das. B. \1. & Cook. E. E.(1994). Mud suction force in the uplift of plate anchors inclay. Proc. 5th Int. Offshore and Polar Engineering Conf., TheHague, Netherlands, 1,462-466.

Small, 1. S.. Thorne, C. P & Ta, L. (1998). Effect of pore pressuredissipation on the behaviour of plate anchors in clay. Proc.8th Int. Polar and Offshore Engineering Conf.. Montreal.497-504.

Sutherland H. B. (1988). Uplift resistance of soils. Geotechniquc38, No. I, 493-516.

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OCTOBER 2004 VOLUME LIV NUMBER 8

Contents

507 Uplift capacity of rapidly loaded strip anchors in uniformstrength clayC. P. Thorne, C. X. Wang and J. P. Carter

519 Analyse tridimensionnelle en differences finies del'interaction entre une structure en beton et le creusementd'un tunnel a faible profondeur3-D finite difference analysis of the interaction betweenconcrete building and shallow tunnellingO. Jenck and D. Dias

529 Admissible stress fields and arching in piles of sandR. L. Michalowski and N. Park

Technical Notes539 Microstructure in shear band observed by microfocus x-

ray computed tomographyM. Oda, T. Takemura and M. Takahashi

543 Seismic and static stability analysis for rock slopes by akinematical approachX.-L. Yang, L. Li and J.-H. Yin

551 Soil porosity from seismic velocitiesS. Foti and R. Lancellotta

Discussion555 Proposal for a new plasticity chart

E. Polidori

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The text should be in Enalish or French.Page I should give the follo-ving information:• date paper written.revised• title of paper (maximum twelve words)• full names and qualifications of authors• position affiliation of authors• contact address. telephone and fax numbers. and e-mail

address of principal authorPage 2 should start with an abstract of WO 200 words.Capital letters should be used only for proper nouns. Abbrevia-

tions for units should conform to the latest edition of BS 3S0: Part1. Svmbols should conform to svrnbols and definitions aivcn in thcISS~lFE Lexicon (1981). and be defined where they fi~st occur inthe text and. if numerous. listed in a Notation on a' separate sheetwith special symbols identified and defined.

Equations should be numbered and appear on separate lines in thetext. The development of mathematical expressions should bepresented in appendices with only the relevant equations stated inthe body of the pape~

Reference:References cited in support of conclusions of the authort s) shouldbe to publications alreadx in print and generally available. Where apaper has been accepted for publication elsewhere, but has not yetappeared. the paper submitted to Geotechniquc for approval shouldbe accompanied by a copy of the referenced paper.

References should be indicated in the text bv authors names withthe year of publication in brackets. Details of references should begiven in a list (unnumbered) in alphabetical order of uuthors namesill the following style.

Books. Author's surname. initials. year of publication. title of book.page numbers. place of publication. publisher. e.g.

\\·carnc. S. (1993l. Principles (?( engineering (H:~(/ni~ufi()fl. 2ndcdn. London: Thomas Telford. '

Periodicals. Author's surname. initials. vear of publication. title ofpaper. title of periodical. volume, month or part. page numbers. c.g.

Skempton. A. \\'. 8: Chrirnes, M. (19941 Thames Tunnel: siteinvestigation and geotechnical problems. Geou-chniqn« 44. No. ~.1<.)1-216.

Conference proceeding». Author's surname. initials. year ofpublication, title of paper. title of conference proceedings. placeof conference. volume, page numbers. e.g.

Bolton. 1\1. D. & Sun. H. W. (1991). Bridge abutments and spreadfoundations. Proc. ltnh £111: Coni. Soil vlech.. Florenc-e 1.319-322

TablesTables should be supplied on separate pages at the end of the text.They should be referred to in the text and neither duplicateinformation given in the text nor contain material which would bebetter presented graphically. Tables should have brief columnheadings (including units).

IllustrationsOnly those drawings and photographs essential to the understandingof the text should be included. Colour is not used, and so allillustrations must be suitable for reproduction in black and white.Illustrations should be numbered consecutivelv and referred to inthe text. A list of captions for all illustrations should be supplied ona separate page. Illustrations will not normally be returned afterpublication.

In addition to the printed copies supplied with the text, a set oforiginal illustrations. each marked with the author's name andnumbered, should be supplied in the following form.

Photographs should be supplied as glossy prints at least 125 mm x100 mm in size. They should be sent in stiff packaging andprotected from marking and scratching. The correct orientationshould be indicated.

Line drawings should be on white or transparent material about A4in size. and have thick black lines. They should be sufficiently clearand simple to enable significant reduct inn without loss of detail.Dotted screened areas should be avoided Plans must IUI\e a northpoint and a scale. the axes of graphs must be labelled and numericalvalues must have dimensions. In addition to the dra\\ings suppliedwith the text one copY should be supplied without annotations. Linedrawings may also be supplied as TIFF ur EPS Illes on disk. andsaved at 600 dpi.

Supplcmcntnr: dat«It is the policy of Gcotcchnique that. If appropriate and the authorsare agreed, back-up information to papers should be made availableon the Internet. The suggested format is ASCII or Excel(spreadsheet) files for test data. Exec! tiles I'm tables and graphs.and ASCII files for le x l and code seurnerus sUc'h as subroutinesfrom a program. If appropriate. plea~e suppl\ these files on aseparate 3·5" floppy disk. quoting vour paper number and title.stating clearly what is contained in each tile

CopvrightIt is the author's rcsponsibilir. to obtain pern1l'SIl)n from the owner-of the copyright to reproduce material which ha-. been publishedelsewhere

Approval and publication procedureAll papers for Gcotcchniquc are screened rhmugh the GcotechniqucAdvisorv Panel of the ICE Ground Board.

Papers may fit into one or more of the following categories: II)analysis, (2) experimental. (3) field work. 141 case history or (SIstate-of-the-art review. In each of these categories there can beaspects or combinations of Ia I fundamental properties andbehaviour of soil or rock. rb I s11il or rock engineering and (c') thepractice of geotechnical engineering. enginecring geology. earth-quake engineering or environmental engineering.

Papers should be original. demonstrate qualiiv and be of interestto the readership .. -vnalvsc-, should be rigorou-. and scientificall,correct. In experimcntal papers, technique and apparatus should beclearly described and the data pre,ented in a fonn that woulr' allo«the reader to make an ultcrnati. c interpretation. The problems ofproviding full information for tield programmes <lIT recognized. sohere the emphasis should be on the elarm "I' presentation and onthe usefulness of the rindinus.

The Gcotcchnique Achisc;n Panel app"inh an assessor and t\\Oexternal referees to review the paper for suitahility. Bilsed on theiradvice. the Panel will accept the paper 1'01'. pnblication, recommendit be revised prior to acceptance. or ITlect the paper. if suhstantialrevisions are requested. the revised paper .vi II he treated as ;, ne\\submission and a full review undertaken The referee and ;1s,essorare anonymous. The Panel nominates three puhlished papers tor anICI-: award in the following year.

On acceptance of a pape~' the author \\ill Ix asked t" specil\' si"\kevwords f'JI" indexing purposes. Bet,)rc' publ.c.uion. one set c)f pageproofs will be sent to the principal author onlv. :\0 11<:\\ materialmav be inserted at the time of proof-re.uling. lwcnrv-fi. e clll'les ofthe published paper \\ill he supplied frec' \\1' chIlrge.