2009 Andersen_Bearing Capacity Under Cyclic Loading - Offshore, Along Th(01)

Bearing capacity under cyclic loading — offshore,along the coast, and on land. The 21st BjerrumLecture presented in Oslo, 23 November 20071

Knut H. Andersen

Abstract: Cyclic loading can be important for the foundation design of structures, both offshore, along the coast, and onland, and for the stability of slopes. This is illustrated by several examples. The paper discusses how soil behaves undercyclic loading, both for structures and for slopes, and shows that the cyclic shear strength and the failure mode under cy-clic loading depend strongly on the stress path and the combination of average and cyclic shear stresses. Diagrams withthe cyclic shear strength of clay, sand, and silt that can be used in practical design are presented. Comparisons betweencalculations and model tests indicate that foundation capacity under cyclic loading can be determined on the basis of cy-clic shear strength determined in laboratory tests.

Key words: cyclic shear strength, bearing capacity, clay, sand, silt, design diagrams.

Resume : Le chargement cyclique est important pour la conception de fondations de structures, autant en mer, sur la coteet sur la terre, et pour la stabilite des pentes. Ceci est illustre a l’aide de plusieurs exemples. Cet article discute du compor-tement du sol soumis a un chargement cyclique, pour la structure et les pentes, et demontre que la resistance au cisaille-ment cyclique et le mode de defaillance sous chargement cyclique dependent fortement du cheminement des contraintes etde la combinaison des contraintes en cisaillement moyennes et cycliques. Des diagrammes de resistance au cisaillementcyclique pour l’argile, sable et silt, qui peuvent etre utilises pour la conception, sont presentes. Des comparaisons entre lescalculs et les essais modelises indiquent que la capacite de la fondation soumise a un chargement cyclique peut etre deter-minee a partir de la resistance au cisaillement cyclique obtenu par des essais en laboratoire.

Mots-cles : resistance au cisaillement cyclique, capacite portante, argile, sable, silt, diagrammes de conception.

[Traduit par la Redaction]

IntroductionBearing capacity under cyclic loading governs the founda-

tion design of offshore installations and cyclic soil behav-iour has received significant attention over the last 30–40 years. However, there are also installations and slopesalong the coast and on land where it is important to considerthe effects of cyclic loading on bearing capacity.

At the Norwegian Geotechnical Institute (NGI), the be-haviour of soils under cyclic loading started in the early1970s in connection with the first exploitation of oil andgas in the North Sea. Dr. Laurits Bjerrum, NGI’s director atthat time, saw the geotechnical challenges in connectionwith the foundation design of the fixed platforms that wereto be constructed, and he enthusiastically involved NGI in

practical foundation design and research in this area (e.g.,Bjerrum 1973). Since then, the cyclic behaviour of soil hasbeen an important topic at NGI.

This paper first gives examples of cases where cyclicloading is important for foundation design. Then it explainshow soil behaves under cyclic loading, and diagrams withcyclic shear strength of clay, silt, and sand that can be usedin practical design are provided. Finally, comparisons of cal-culated to measured bearing capacity in model tests showthat bearing capacity under cyclic loading can be reliablypredicted based on cyclic strength from laboratory tests.

Examples of cyclic loadingThe first gravity platform in the North Sea was the Eko-

fisk oil storage tank in Fig. 1, which was installed in June1973 (Clausen et al. 1975). The tank was designed for a100 year storm with a maximum wave of 24 m. In additionto the maximum wave, the foundation had to withstand theforces from a large number of other waves in the storm.These forces may generate excess pore pressure and degradethe soil prior to the impact of the maximum wave.

Since the installation of the Ekofisk tank, a large numberof gravity platforms have been installed in the North Seaand other parts of the world. In several cases, the platformshave been designed for severe storms with a maximum100 year wave in excess of 30 m. One example is the FriggTCP2 Condeep platform in Fig. 2.

Received 14 May 2008. Accepted 14 January 2009. Publishedon the NRC Research Press Web site at cgj.nrc.ca on 1 May2009.

K.H. Andersen. Norwegian Geotechnical Institute (NGI),Sognsveien 72, P.O. Box 3930, Ullevaal Stadion, Oslo 0806,Norway (e-mail: [email protected]).

1This paper represents the written version of the 21st BjerrumLecture. While it has been edited for the present publication, itretains the general structure of the original lecture, which wasintended for a general geotechnical audience. The BjerrumLecture is presented in Oslo in alternate years by theNorwegian Geotechnical Society with the support of theBjerrum Memorial Fund (Laurits Bjerrums Minnefond).

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Can. Geotech. J. 46: 513–535 (2009) doi:10.1139/T09-003 Published by NRC Research Press

In recent years, gravity platforms have also been designedto serve as liquified natural gas (LNG) terminals. These ter-minals have been situated closer to land than the installa-tions for oil and gas production. Geotechnically, this haspresented new challenges with soil profiles consisting ofmixed layers of loose silt, sand, and soft clay often signifi-cantly less uniform than encountered offshore.

Essentially, all offshore installations will experience waveloading and need to be designed for cyclic loading. In addi-tion to the gravity platforms mentioned above, this includespiled installations, anchors, and skirted installations. One ex-

ample is the Snorre tension leg platform (TLP), which in1991 was the first tension leg installation to be anchored bymeans of suction anchors (Christophersen et al. 1992)(Fig. 3). Due to the novelty of the suction anchor concept atthat time, extensive studies were made to ensure that thefoundation design methods were sound. This included field-model testing that is described towards the end of this paper.Suction anchors have since been extensively used to anchorvarious types of floating installations; an example is shownin Fig. 4. By the end of 2004, about 500 suction anchorswere installed at 50 different offshore locations worldwide

Fig. 1. Ekofisk oil storage tank, installed in the North Sea in June 1973 (from Clausen et al. 1975; # 1975 Offshore Technology Confer-ence).

Fig. 2. Frigg TCP2 Condeep platform in the North Sea (adapted from Andersen and Høeg 1991).

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in water depths reaching more than 2000 m (Andersen et al.2005).

Structures along the coast may also be subjected to severewave loading. Such structures include harbours, breakwaters,and storm-surge barriers. One example is the Oosterscheldestorm-surge barrier in the Netherlands that was completed in1986 (Fig. 5).

Many wind turbines are now placed offshore (Fig. 6), andtheir foundations need to be designed for cyclic loadingfrom both wind and waves. Even if placed on land, they doof course need to be designed for cyclic wind loading.

On land there are also situations with cyclic loading. Thisincludes design of road and railway embankments and cutsto withstand the effects of traffic-induced cyclic loading(Fig. 7). In seismic areas, earthquakes may cause foundation

failures of buildings and bridges (Fig. 8) and induce slopefailures (Fig. 9). Cyclic loading from traffic and earthquakeshave lower cyclic load periods (*1 s) than wave loading(*10–20 s) and this needs to be taken into account.

Ice loading can cause cyclic loads on structures that areplaced in the sea. The Great Belt bridge in Denmark, for in-stance (Fig. 10), was designed for cyclic loading from icesheets that break when they float past and impact on thebridge piers (Andersen et al. 1991). Andersen et al. (1991)reported that the breaking of the ice sheets would cause animpulse that would set the bridge piers in motion with a fre-quency determined by their resonance periods. This wouldlead to a two-frequency cyclic loading on the soil beneaththe piers (Fig. 10). The importance of ice loading on off-shore structures will increase as oil and gas productionmoves into arctic areas.

Fig. 3. Snorre TLP platform installed in the North Sea in 1991.

Fig. 4. Suction anchors installed at the Horn Mountain field in theGulf of Mexico in 2002 (photo by E.C. Clukey, BP America Pro-duction Company).

Fig. 5. Oosterschelde storm-surge barrier. (www.deltawerken.com/Deltaworks, photo by the Ministry of Public Works, Transport andWater Management (the Netherlands)).

Fig. 6. Offshore wind turbines (www.vestas.com).

Fig. 7. Vibrations from traffic (photo by Christian Madshus, NGI).

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What happens to soil subjected to cyclicloading?

General behaviourCyclic loading may reduce the bearing capacity of a soil

and the bearing capacity under cyclic loading may be lowerthan the capacity under monotonic loading. This is illus-trated by the results of model tests of a gravity platform onclay in Fig. 11. The model has a submerged weight, W’, andis loaded with a cyclic horizontal load, Hcy, a distance zabove the sea floor. The results show that the displacementsunder cyclic loading increase with the number of cycles andbecome larger than the displacements under monotonic load-ing at the same load. The model develops excessive dis-

placements and fails at a cyclic load that is lower than thefailure load under monotonic loading.

In this paper, the failure load and the shear stress at fail-ure under monotonic loading will be called static capacityand static shear strength, respectively.

The reason why the cyclic capacity may be smaller thanthe static capacity is that the cyclic loading tends to breakdown the soil structure and cause a tendency for volumetricreduction in the soil. If the conditions are undrained, volu-metric changes will be prevented by the low volumetriccompressibility of the water. The normal stresses that werecarried by the soil will then be transferred to the pore waterand the effective stresses in the soil will decrease accord-ingly. This is illustrated by the effective stress paths formonotonic and cyclic soil elements in Fig. 12.

The development of pore pressure and shear strain withtime for a soil element subjected to undrained cyclic loadingwith a constant cyclic shear stress is illustrated in Fig. 13. Theload cycles with a single-amplitude shear stress, tcy, around aconstant shear stress, ta. The cyclic loading generates a porepressure characterized by a permanent pore-pressure compo-nent, up, and a cyclic pore pressure component, ucy. The in-creased pore pressure reduces the effective stresses in thesoil, resulting in increased permanent, gp, and cyclic, gcy,shear strains with time.

The stress–strain behaviour of a soil element under thecyclic loading in Fig. 13 is illustrated in Fig. 14.

Effect of average shear stress and test typeThe soil beneath a structure is subjected to various stress

conditions where the average and cyclic shear stresses andthe type of loading (e.g., triaxial versus direct simple shear,DSS) vary from one point to another. This is illustrated inFig. 15, which shows a simplified image of the stress condi-tions along a potential failure surface beneath a gravitystructure under cyclic loading.

The behaviour of soil elements under various loading con-ditions is illustrated in Figs. 16 and 17 with results from lab-oratory tests on Drammen clay, a marine clay with aplasticity index of Ip = 27%.

The first two tests in Fig. 16, Figs. 16a and 16b, showthat the response to symmetrical cyclic loading is differentin DSS and triaxial tests. In the DSS tests, the shear straindevelops relatively symmetrically, apart from the first quar-ter cycle. In the triaxial test, the shear strain is nonsymmet-rical with a permanent shear strain of the same magnitude asthe cyclic shear strain. This is related to the strength aniso-tropy under triaxial loading, with an extension strength thatis smaller than the compression strength.

The third test, Fig. 16c, has a shear stress where the aver-age and the cyclic components are the same. The result is ashear-strain development with dominant permanent shearstrain and small cyclic shear strain that does not increasesignificantly with number of cycles.

Figure 17 shows that the cyclic behaviour is not governedby the maximum shear stress (tmax). The three tests in Fig. 17have the same maximum shear stress, but different averageand cyclic shear stress components. The test with ta = 0 failsafter 10 cycles, whereas the tests with ta = 0.5tmax and ta =0.85tmax have developed only small shear strains after 2500

Fig. 8. Earthquake damage to buildings (photo by Amir Kaynia,NGI).

Fig. 9. Earthquake-induced landslide, El Salvador (U.S. GeologicalSurvey, photo by Ed Harp, USGS).



cycles, and the test with the highest ta has the smallest shearstrains.

These examples illustrate that the cyclic behaviour de-pends on both average and cyclic shear stresses, and thatthe behaviour is different in triaxial and DSS tests. Thenext section describes how this knowledge can be utilizedto establish design diagrams for practical applications.

Number of cycles to failure as function of average andcyclic shear stresses

Given the importance of the average and cyclic shearstress components for the cyclic behaviour, the results froma large DSS and triaxial cyclic testing programme on plastic

Drammen clay (e.g., Andersen et al. 1988) were plotted asfunction of average and cyclic shear stresses.

The plot for DSS tests on normally consolidated clay ispresented in Fig. 18. Fig. 18a shows the results from onemonotonic and nine cyclic tests. The location of the variouspoints is determined by the average and cyclic shear stressesunder which the tests were run, and the numbers along eachpoint give the number of cycles to failure, Nf, and the per-manent and cyclic shear strains at failure, gp/gcy. Failurewas defined as either a permanent or a cyclic shear strain of15%. The shear stresses in Fig. 18 are normalized with re-spect to the static shear strength, su, in a DSS test run tofailure with a constant rate of shear strain of *4.5%/h.

Fig. 10. Ice load history for Great Belt bridge piers (photo by Henrik Sendelbach; commons.wikimedia.org/wiki/File:Storeb%C3%A6lts-broen_from_Sj%C3%A6lland.jpg).

Fig. 11. Results of model tests with monotonic and cyclic loadingon gravity platform on clay (adapted from Dyvik et al. 1989).

Fig. 12. Effective stress paths for undrained tests with monotonicand cyclic loading. up, permanent pore-pressure component; s’, ef-fective normal stress; t, shear stress. ta, average shear stress; tcy,single-amplitude cyclic shear stress.

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By inspection of the data in Fig. 18a, it was possible todraw contours through points with the same number ofcycles to failure. This gave the contour diagram in Fig. 18b.Curves that define the failure mode, i.e., the permanent andcyclic shear strains at failure, are drawn in addition.

The contour diagram defines the number of cycles to fail-ure as a function of average and cyclic shear stresses. Thediagram also defines the failure mode; i.e., the combinationof permanent and cyclic shear strains at failure, gp and gcy.The diagram shows that the failure will occur as large cyclicshear strains when the average shear stress is small, and aslarge permanent shear strains when the average shear stressapproaches the static shear strength. For average shearstresses between zero and the static shear strength, the fail-ure mode will be a combination of permanent and cyclicshear strains.

A contour diagram similar to the one for DSS tests isgiven for triaxial tests in Fig. 19. The diagram is establishedbased on a number of cyclic triaxial tests, each with differ-ent average and cyclic shear stresses, such as for the DSStests. The diagram in Fig. 19 shows that the triaxial testswill fail with large cyclic shear strains for a range of aver-age shear stresses about halfway between the compressionand extension static shear strengths. For average shear

stresses approaching the compression shear strength, thefailure mode will be dominated by large permanent com-pression shear strains, whereas for average shear stresses ap-proaching the extension strength, the failure mode will bedominated by large permanent extension shear strains.Strains in compression are defined as positive and strains inextension are defined as negative in Fig. 19 and later fig-ures.

The intersection of the contours with the ta–axis and thelocation of the contours for values of ta approaching thestatic undrained shear strength depend upon the duration ofta because of the undrained creep that occurs under highaverage shear stress. In the diagrams in this paper, the con-tours have been drawn to intersect the horizontal axis at theundrained shear strength in standard laboratory tests. If theduration of ta deviates from the approximately 2 h time tofailure in a standard monotonic laboratory test, this can becorrected for when applying the diagrams by using a shearstrength corrected for load duration when denormalizing ta/su. The shear strength correction can be based on the data inFig. 20, which shows the shear strength of several clays as afunction of time to failure.

Cyclic shear strengthThe diagrams in Figs. 18 and 19 show the combinations

of average and cyclic shear stresses that will cause failurein a given number of cycles. In a stability analysis, oneneeds to know the maximum shear stress that can be mobi-lized. As illustrated in Fig. 21, the maximum shear stressthat can be mobilized is the sum of average and cyclic shearstresses at failure, i.e.,

½1� tf;cy ¼ ta;f þ tcy;f

where tf,cy is the cyclic shear strength, ta,f is the averageshear stress at failure, and tcy,f is the cyclic shear stress atfailure. ta,f is composed of the initial consolidation shearstress, t0, plus the change in average shear stress, Dta, dueto an additional average load or redistribution of averagestresses, i.e.,

Fig. 13. Pore-pressure and shear strain as function of time underundrained cyclic loading. u, pore pressure; g, shear strain; t0, initialconsolidation shear stress.

Fig. 14. Stress–strain behaviour under cyclic loading.

Fig. 15. Simplified stress conditions along a potential failure sur-face in the soil beneath a gravity structure under cyclic loading. H,resultant horizontal load; h, height above seafloor of resultant hori-zontal load.



½2� ta;f ¼ t0 þ ta

For clays, Dta would normally be undrained, but for sands,Dta may be drained.

Equation [1] means that the cyclic shear strength for agiven number of cycles to failure can be established by sim-ply adding average and cyclic shear stresses for variousgiven values of average shear stress in the diagrams inFigs. 18 and 19, and then plotting this sum as a function ofthe average shear stress. This is done as illustrated for DSStests in Fig. 22 and for triaxial tests in Fig. 23. The reasonfor the discontinuity in the curves for triaxial tests inFig. 23 is that the average stress has opposite sign for com-pression and extension. Compression is defined as a failuremode where the permanent shear strain is positive, and ex-tension is defined as the failure mode where the permanentshear strain is negative.

The cyclic shear strength diagrams show that the cyclicshear strength can be higher than the static shear strength,as tf,cy/su > 1 for a low number of cycles in some cases.This is because the clay strength is rate dependent (e.g.,

Fig. 20). As the cyclic tests are run with a load period of10 s and the monotonic tests are brought to failure in about2 h, the cyclic strength may thus be higher than the conven-tional static shear strength.

The diagrams in Figs. 22 and 23 provide the data requiredto define the cyclic shear strength for the various stress con-ditions shown in Fig. 15.

All the diagrams in this paper assume that Dta is appliedundrained. A diagram showing the effect of applying Dtadrained is presented for normally consolidated Drammenclay in Andersen (1988). The effect of drained versus un-drained Dta for very dense sand in presented in Andersenand Berre (1999).

The diagrams also assume that the soil is undrained dur-ing a cycle. If it is possible for drainage or pore-pressure re-distribution to occur during a cycle, as it may be for sand insome cases, one should consider limiting the cyclic strengthto the drained shear strength.

Equivalent number of cyclesThe diagrams in Figs. 22 and 23 give the cyclic shear

strength for cases with a constant cyclic shear stress duringthe cyclic load history. In a storm, however, the cyclic shearstress is likely to vary from one cycle to the next. Theequivalent number of cycles of the maximum cyclic shearstress, Neqv, that would give the same effect as the real cy-clic load history must therefore be determined to be able touse the diagrams.

Procedures to determine Neqv are presented by Andersen(1976) and Andersen et al. (1992). The procedures useshear-strain or pore-pressure contour diagrams of the typepresented in Figs. 24 and 25. The diagrams are establishedfrom the same tests as used to establish the diagrams inFigs. 18 and 19. The diagrams in Figs. 24 and 25 are forDSS tests with an average shear stress of ta = 0. Similar di-agrams can be established for other average shear stressesand for triaxial tests. Various such diagrams are given inAndersen (2004).

For undrained conditions, Neqv may be determined by the‘‘strain accumulation’’ procedure where the cyclic shear

Fig. 16. Stress–strain behaviour under various cyclic loading conditions.

Fig. 17. Results from cyclic triaxial tests with the same maximumshear stress, tmax.

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strain is used as a memory of the cyclic effect by keepingtrack of the cyclic shear strain during the cyclic load history.

For sands or situations where drainage can occur during a

storm, it is necessary to account for the effect of drainage.The equivalent number of cycles, Neqv, can then be deter-mined by keeping track of the permanent pore pressure ac-cumulated during the cyclic load history, accounting for thesimultaneous generation and dissipation of the excess porepressure. Andersen et al. (1994) describes the pore-pressureaccumulation procedure and how the pore-pressure dissipa-tion can be taken into account.

In principle, the pore-pressure accumulation procedurecould also be used for clays. In practice, however, accuratelaboratory measurement of pore pressure is more difficult toperform in clays than in sand. As drainage is not likely to oc-cur during the cyclic load history in clays, it may be prefera-ble to use the cyclic strain-accumulation procedure for clays.

Fig. 18. Number of cycles to failure and failure mode as a function of average and cyclic shear stresses for cyclic DSS tests on normallyconsolidated Drammen clay. (a) Results from one monotonic and nine cyclic tests; (b) contour diagram with the same number of cycles tofailure based on the data in part (a). ta,f, average shear stress at failure; tcy,f, cyclic shear stress at failure; su

DSS, static DSS shear strength.

Fig. 19. Number of cycles to failure and failure mode as a function of average and cyclic shear stresses for cyclic triaxial tests on normallyconsolidated Drammen clay. gp, permanent shear strain; su

C, static compression shear strength.

Fig. 20. Static shear strength of several clays as a function of time tofailure (adapted from Lunne and Andersen 2007). tf, time to failure.

Fig. 21. Definition of cyclic shear strength, tf,cy.



Fig. 22. Cyclic DSS shear strength. Normally consolidated Drammen clay.

Fig. 23. Cyclic triaxial compression and extension shear strengths. Normally consolidated Drammen clay.

Fig. 24. Cyclic shear strain as function of number of cycles (DSStests with ta = 0 on Drammen clay with overconsolidation ratio(OCR) = 1). svc’, vertical effective consolidation stress.

Fig. 25. Permanent pore pressure as function of number of cycles(DSS tests with ta = 0 on Drammen clay with OCR = 1).

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Cyclic strength diagrams for practicalapplications

Importance of databasesDiagrams with cyclic shear strength of clay, silt, and sand

that have been established from DSS and triaxial laboratorytests are presented in this and the preceding sections. Thedata are compiled from NGI files and from published litera-ture sources that are included in the list of references at theend of the paper. The literature sources are Lee and Seed(1967); Mulilis et al. (1975, 1977a, 1977b); Wong et al.(1975); Silver et al. (1976); Seed et al. (1977); Lee andVernese (1978); Ishihara and Takatsu (1979); Vaid andFinn (1979); Finn (1981); Vaid and Chern (1983); Siddiqi(1984); Sakai and Ochiai (1986); Tatsuoka et al. (1986a,1986b, 1988); Toki et al. (1986); Tanaka et al. (1987); Hata-naka et al. (1988); Hyodo et al. (1991, 1994, 1996); Yoshimiet al. (1994); Evans and Zhou (1995); Vaid et al. (1999);Koseki and Ohta (2001); Oda et al. (2001); Hosono andYoshimine (2004); Kokusho et al. (2004); Park and Byrne(2004); Porcini et al. (2004); Sivathalayan and Ha (2004);Triantafyllidis et al. (2004); Wijewickreme et al. (2004);Koseki et al. (2005); Wijewickreme and Sanin (2005); andHyde et al. (2006).

The diagrams can be used to determine parameters forfeasibility studies before site-specific data are available.The diagrams can also be used as guides when specifyingand interpreting site-specific cyclic laboratory tests. Thiswill help to reduce the required number of site-specific cy-clic tests and to evaluate their quality. Many of the diagramspresented in the paper have already successfully servedthese purposes in practical projects.

For final design, the parameters from the diagrams shouldbe verified by site-specific laboratory tests.

Diagrams for normally consolidated Drammen clay werepresented in the preceding section. These diagrams have theformat that the diagrams should ideally have. Additional di-agrams for clays are presented in the first part of this sec-tion. Thereafter, diagrams for sands and silts are presented.A database similar to the one for Drammen clay is availablefor very dense clean Baskarp sand (Andersen and Berre1999). Baskarp sand is, however, more angular than mostnatural sands and may give strengths and moduli on thehigh side. The diagrams for silts and sands are less completethan for clay due to a lack of a general systematic testingprogramme similar to the ones on Drammen clay and Bas-karp sand.

The main diagrams are for normally consolidated soilswith moderate or no preshearing. The effect of overconsoli-dation and (or) preshearing can be evaluated from additionaldiagrams that show the effect of these parameters.

All the diagrams in this paper are from stress-controlledcyclic tests with a 10 s load period on noncemented soils.

Cyclic shear strength of claysFigures 18, 19, 22, and 23 present diagrams for normally

consolidated Drammen clay. The cyclic shear strength for anumber of other normally consolidated clays are comparedwith Drammen clay in Figs. 26 and 27. There is a tendencyfor the normalized cyclic shear strength to increase with in-creasing plasticity index.

Diagrams for overconsolidated Drammen clay with over-consolidation ratios of 4 and 40 can be found in Andersen(2004).

Cyclic shear strength of sands and silts

Sample preparationHigh-quality samples of sands and silts that are represen-

tative of the in situ conditions are difficult to obtain. Incases where ‘‘intact’’ samples have been disturbed signifi-cantly, one often reconstitutes the samples, but this may notgive samples that are fully representative of the in situ con-ditions.

Silver et al. (1976) and Mulilis et al. (1977a) have shownthat the cyclic shear strength of sands and silts depends onthe sample preparation method. Vaid et al. (1999) showedthat water-deposited sand closely simulated static and cyclicbehaviour of frozen sand samples of natural alluvial and hy-draulic fill. They also found that loose samples prepared bymoist tamping gave a weaker response than water-deposited

Fig. 26. Normalized average and cyclic shear stresses for Nf = 10 inDSS tests, for different normally consolidated clays (adapted fromAndersen 2004).

Fig. 27. Normalized average and cyclic shear stresses for Nf = 10 intriaxial tests, for different normally consolidated clays (adpatedfrom Andersen 2004).



samples. Høeg et al. (2000) showed results for the staticshear strength of silty sand tailings, with lower staticstrength for samples prepared by wet tamping than for‘‘intact’’ samples at the same void ratio.

In several cases, however, samples prepared by wet tamp-ing have given similar strengths as ‘‘intact’’ samples. This issupported by Fig. 28, which compares the cyclic triaxialshear strength of samples reconstituted by wet tamping with

the strength of high-quality frozen samples. A few resultsfrom water-deposited and water-vibrated samples do not de-viate significantly from wet tamping and frozen samples.The tests on reconstituted samples are from various sourcesand thus not on the same soil as the frozen samples. Thedata in Fig. 28 show that the samples reconstituted by wettamping have similar cyclic shear strengths as the frozensamples. These data thus indicate that wet tamping maygive a reasonably realistic in situ cyclic shear strength. Asshown later, wet tamping also seems to give similar cyclicshear strengths as ‘‘intact’’ samples (Fig. 29), whereas drytamping seems to give a tendency for lower strengths thanwet tamping and ‘‘intact’’ samples (Figs. 29 and 30).

A fines content of more than a few percent will make re-constitution more difficult, especially if the fines also con-tain clay. Use of ‘‘intact’’ samples may then be possible andpreferable, even if such specimens will also be disturbed. Itis uncertain whether the disturbance may give a cyclicstrength that is too high or too low. This will depend on therelative density. If samples have to be reconstituted, theyshould be prepared wet, by tamping or water deposition, un-less the in situ soil has been deposited under dry conditions.

The samples should be presheared if the soil is subjectedto drained preshearing prior to and (or) during the main de-sign event. Herein, preshearing means cyclic loading accom-panied by drainage during or after the cyclic loading. Forlarge offshore gravity platforms on dense sand, preshearinghas typically been estimated to be about 400 cycles at tcy/s 0vc = 0.04, as this has been estimated to occur during thebuild-up period of the design storm or during smaller stormsprior to the design storm. In earthquake areas, the soil mayhave experienced smaller earthquakes during its history. Pre-shearing will increase the cyclic shear strength. Preshearingmay also reduce the effect of the sample preparationmethod, but this has not been systematically studied.

Effect of consolidation timeThere seems to be a long-term effect of the consolidation

time of reconstituted samples, even for clean sand. Tatsuokaet al. (1986a) found that the cyclic strength in isotropically

Fig. 28. Cyclic shear stress to reach g = 3.75% after 10 cycles inisotropically consolidated triaxial tests on different sands as a func-tion of relative density. Comparison of in situ frozen samples andsamples prepared by wet tamping, water deposition, and water vi-bration.

Fig. 29. Shear strength for 10 cycles of symmetrical cyclic loading(ta = 0) in DSS tests on different sands and silts with relative den-sity (Dr) < 65% as a function of vertical consolidation stress.

Fig. 30. Shear strength for 10 cycles of symmetrical cyclic loading(ta = 0) in DSS tests on different normally consolidated sands as afunction of relative density.

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consolidated triaxial tests on air-pluviated Toyoura sandwith no fines content increased by 15%–20% after 68 days,for relative densities of both 50% and 80%. Tatsuoka et al.(1988) found that the cyclic shear strength of isotropicallyconsolidated triaxial tests on water-vibrated Sengenyamasand with 2.4% fines and a relative density, Dr, of 80% in-creased by about 25% after 64 h and 40% after 68 days.Mulilis et al. (1977b) found that the cyclic strength of iso-tropically consolidated triaxial tests on air-pluviated Monte-rey No. 0 sand with no fines at Dr = 50% was essentially thesame after 20 min and 1 day consolidation, whereas it in-creased by 12% and 26% after 10 and 100 day consolidationtimes, respectively. The cyclic strength in DSS tests at NGIon air-pluviated Oosterschelde sand with no fines and Dr =62%, however, gave the same cyclic shear strength after16 h and 4 day consolidation.

For conventional projects, it may be impractical to repro-duce the long-term effect in the laboratory, but the consoli-dation stress should act overnight for samples with somefines content. The effect of a longer consolidation timemust be evaluated by judgement and experience as refer-enced above. The experience above is from reconstitutedsamples with no preshearing, and one should be aware thatthe effect is likely to be less on intact samples and on sam-ples with preshearing.

Cyclic shear strength in symmetrical DSS loadingThe cyclic DSS shear strength for 10 load cycles of dif-

ferent normally consolidated sands prepared by wet and dryreconstitution is plotted in Fig. 30.

The cyclic shear strength depends on the shear strain usedto define failure, especially for densities above Dr = 65%.Failure is defined as large shear strains of g = 7.5%–15%for most of the points in Fig. 30, but in a few cases failureis defined at a lower strain. This includes the data point forBaskarp sand at tcy/s 0vc = 1.2, which is for g = 3% andwhich would plot even higher if a higher failure strain hadbeen used.

The samples with Dr < 85% in Fig. 30 have been pre-sheared with 400 cycles at tcy/s 0vc = 0.04 or less. The sam-ples with Dr ‡ 85% have been presheared with 400 cycles attcy/s 0vc between 0.075 and 0.1.

The plot in Fig. 30 shows that the cyclic shear strengthincreases with relative density, especially for relative den-sities above Dr = 65%. The cyclic shear strength is less de-pendent on relative density below Dr = 65%. The plot inFig. 30 contains results from tests on both wet and dry re-constituted samples. The results from the tests on sampleswith dry reconstitution generally tend to plot lower thanthose with wet reconstitution. Based on the earlier discus-sion, one should disregard the results from reconstituted dryspecimens.

Figure 30 contains data from tests with consolidationstresses in a range of s 0vc = 10–710 kPa. The cyclic shearstrengths for relative densities Dr < 65% was plotted inFig. 29 as function of consolidation stress to see what effectthe consolidation stress may have. Figure 29 also containsdata for normally consolidated Drammen clay and someloose to medium-dense silty soils that were not included inFig. 30 because of the problems of assessing relative densitywith silty soils. Some of these tests were run on ‘‘intact’’

samples. The samples in Fig. 29 have been presheared with400 cycles at tcy/s 0vc = 0.05 or less.

As seen earlier, the samples that were reconstituted drytend to give the lowest cyclic shear strengths, and these arebelieved to underestimate the in situ shear strength. The‘‘intact’’ samples and the samples reconstituted wet tend togive similar results. It is interesting to note that the cyclicshear strength of normally consolidated Drammen clay plotsin the high range of the sand and silt data. There is a ten-dency for sand to have smaller cyclic shear strength thanclay, and the cyclic shear strengths are generally lower thanthe cyclic shear strength of Drammen clay. This is in linewith the results for clays in Figs. 26 and 27, which seem toindicate that the cyclic shear strength decreases with de-creasing plasticity. Attempts to plot the cyclic shear strengthof sand and silt as a function of grain size or the grain sizeuniformity coefficient did not show any clear trend.

The data in Fig. 29 show that there is some tendency forthe normalized cyclic shear strength to increase with de-creasing consolidation stress. This tendency may be morepronounced below s0vc = 100 kPa, where there is no data forintact samples and samples prepared by wet reconstitution.

Dense soils (Dr > 65%) may also deviate from the trendin Fig. 29 and give a greater increase in strength ratio withdecreasing tcy,f/s0vc. For instance, DSS tests on air-pluviatedFraser River sand with Dr*80% gave about 25% increase intcy,f/s 0vc for s 0vc = 100 kPa compared with tests with s 0vc =200 kPa. Tests with Dr*40%–44% gave a smaller increase(about 10%) in tcy,f/s 0vc when decreasing s 0vc from 200 to100 kPa (Park and Byrne 2004; Wijewickreme et al. 2004).

Calcareous soils may also deviate from the trend inFig. 29. Experience from testing of calcareous silts andsands shows that calcareous soils tend to give similar orslightly higher normalized cyclic shear strength, tcy,f/s 0vc,than the noncalcareous soils in Fig. 29 at vertical consolida-tion stresses above 250 kPa. For lower consolidationstresses, however, laboratory tests have shown a significantincrease in tcy,f/s 0vc with decreasing s0vc for calcareous soils.

Fig. 31. Cyclic shear stress to failure in 10 cycles in anisotropicallyconsolidated triaxial tests with ta = t0 compared with DSS tests.Different normally consolidated sands prepared by wet tamping, asa function of relative density. t0 is about 0.25svc’ to 0.275svc’.



The tests on calcareous soils have generally been on intactsamples from a relatively shallow depth. Reasons for thesignificant increase in tcy,f/s 0vc with decreasing s 0vc may bethat calcareous soil has high angularity, but may also bedue to cementation or overconsolidation, even if they arenot characterized as cemented or overconsolidated.

Cyclic strength in triaxial testsThe cyclic shear stress that will bring anisotropically con-

solidated triaxial samples to failure in 10 cycles is comparedwith DSS tests in Fig. 31. There are only three triaxial tests.One should therefore be cautious about drawing generalconclusions. However, the normalized cyclic shear stress to

Fig. 32. Shear strength for 10 cycles of symmetrical cyclic loading (ta = 0) in DSS tests on different normally consolidated soils, as afunction of water content.

Fig. 33. Cyclic shear stress to failure in 10 cycles in anisotropically consolidated triaxial tests with ta = t0 compared with DSS tests. Dif-ferent normally consolidated sands prepared intact and by wet tamping, as a function of relative density.

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failure, tcy,f/s 0vc, is about 75% higher for the triaxial testswith ta = t0 than for the DSS tests with ta = 0.

Cyclic shear strength and water contentThe cyclic shear stress that gives failure in 10 cycles in

DSS tests with symmetrical cyclic loading is plotted as func-tion of the water content in Fig. 32. The samples preparedby dry reconstitution tend to give the lowest cyclic shearstrength, as in previous figures.

For the intact samples and the samples prepared by wetreconstitution, the normalized cyclic shear strength, tcy,f/s 0vc,increases with decreasing water content, especially as thewater content decreases below a water content of about25%. The effect of the water content is less significantabove 25%.

Some of the scatter in tcy,f/s 0vc below a water content of25% is due to differences in consolidation stress, with a ten-dency for tcy,f/s 0vc to increase with decreasing consolidationstress. The effect of consolidation stress was not large in thetests on sand with a relative density below *65% (Fig. 29),but as mentioned before the effect of the consolidation stressmay be more pronounced at higher relative densities, i.e., atlower water content. Some scatter may also be due to uncer-tainty in the water content for some of the tests, as it wasnot clear in all the literature cases whether the reportedwater content was before or after consolidation. The watercontent after consolidation was used when it was available.

The cyclic shear stress that will bring anisotropically con-solidated triaxial samples to failure in 10 cycles is comparedwith DSS tests in Fig. 33. For the samples prepared by wetreconstitution, the normalized cyclic shear stress to failure,tcy,f/s 0vc, is higher in the triaxial tests with ta = t0 than inthe DSS tests with ta = 0. This is the same tendency seenwhen tcy,f/s 0vc was plotted as a function of relative densityin Fig. 31. The two triaxial tests on intact silt–clay samplesshow the opposite trend, but one should be cautious aboutdrawing general conclusions with the limited number of tri-axial tests available.

Effect of number of cyclesThe cyclic shear stress that will bring DSS samples and

anisotropically consolidated triaxial samples to failure for anumber of cycles different than 10 are plotted in Figs. 34and 35. Figs. 34a and 35a show the cyclic shear stress tofailure normalized to the vertical effective consolidationstress, tcy,f/s 0vc. Figs. 34b and 35b show the cyclic shearstress to failure relative to the cyclic shear stress to failurein 10 cycles. The diagrams contain results from both intactsamples and wet and dry sample preparation. Normally con-solidated Drammen clay is included for reference.

The data show that in DSS tests the cyclic shear stress togive failure in three cycles is about 20% to 40% higher thanfor 10 cycles. The difference between three and 10 cycles tofailure shows more scatter for the triaxial tests. There are nosystematic differences between intact samples and sampleswith wet and dry sample preparation. Drammen clay tends tobe somewhat less sensitivite to the number of cycles to failurefor DSS tests, but is closer to the average for triaxial tests.

The data in Figs. 34 and 35 are for normally consolidatedand close to normally consolidated soils. Less data are avail-able for overconsolidated soils, but the data for a few over-

consolidated soils indicate that they possibly follow thetrend in Figs. 34 and 35.

Effect of average shear stressThe diagrams in Figs. 29 to 35 are for DSS tests with ta =

0 and triaxial tests with ta = t0, where t0/s 0vc*0.25–0.275.The cyclic shear strength is tf,cy = ta,f + tcy,f, and the cyclicshear strength depends on the average shear stress. To fullydefine the cyclic shear strength, one therefore needs dia-grams of the type presented for clays in Figs. 18, 19, 26,and 27. Such diagrams are given for the very dense Baskarpsand in Andersen and Berre (1999) for both undrained anddrained Dta.

In triaxial tests with drained average shear stress, the cy-clic shear strength will depend on the stress path for the

Fig. 34. Cyclic shear stress to failure as a function of number ofcycles. DSS tests with symmetrical cyclic loading (ta = 0) on nor-mally consolidated sands and silts: Dr-range 40%–100%; consoli-dation stress range 85–710 kPa. (a) tcyf/svc’ versus Nf;(b) normalized to cyclic shear stress to failure in 10 cycles.



average load, i.e., whether Dta is applied by changing thevertical or the horizontal normal stress.

In dense soils that dilate under a change in average shearstress, the cyclic shear strength will generally be higher ifDta is applied undrained than if it is applied drained. Insoils that contract under a change in average shear stress,the cyclic shear strength may be lowest when Dta is appliedundrained.

Comparison between DSS and isotropically consolidatedtriaxial tests

The DSS test represents the best simulation of the in situstress conditions for many situations. When DSS tests havenot been available, isotropically consolidated triaxial tests

have sometimes been used to estimate the cyclic shearstrength for DSS stress conditions, even if the isotropicallyconsolidated triaxial tests do not model a representativestress path. Isotropically consolidated triaxial tests generallyshow higher cyclic shear stresses at failure, tcy,f/s 0vc, thanboth the DSS and anisotropically consolidated triaxial testswhen they are normalized to the vertical effective consolida-tion stress (Fig. 36). To correct for this, one may assumethat the strengths of DSS and isotropically consolidated tri-axial tests will be the same when normalized to the octahe-dral effective consolidation stress. A comparison ofavailable data show that normalization to the octahedralconsolidation stress appears to give reasonable estimates ofthe cyclic DSS strength for Dr < 65%. However, the hori-zontal consolidation stress needed to calculate the octahedralstress in the DSS test is uncertain. At higher relative den-sities, normalization to the octahedral consolidation stressseems to overestimate the cyclic DSS strength.

One should generally be cautious about using isotropicallyconsolidated triaxial tests, as the stress conditions in this testare normally not representative of the stress conditions be-neath a structure.

Effect of preshearingSand deposits are often subjected to preshearing, i.e.,

small cyclic shear stresses accompanied by drainage, priorto the main design event, as discussed earlier. Preshearingmay influence the undrained cyclic shear strength of a sand.Figure 37 shows how the undrained cyclic shear strength for10 load cycles depends on the normalized cyclic shearstress, tcy/s 0vc, and the number of cycles during preshearing.The figure contains DSS, shaking table, and triaxial testssubjected to various degrees of preshearing.

In DSS tests, the preshearing may

� improve the seating between the sand and the horizontalend plates

� level out stress concentrations from the consolidation� increase the horizontal effective stress

Fig. 36. Cyclic shear stress to failure in 10 cycles in isotropicallyconsolidated triaxial tests compared with triaxial tests with ta = t0

and DSS tests as a function of Dr. Different normally consolidatedsands prepared by wet tamping.

Fig. 35. Cyclic shear stress to failure as function of number ofcycles. Anisotropically consolidated triaxial tests with ta = t0 =0.21–0.3svc’ on normally consolidated sands and silts: Dr-range35%–96%; consolidation stress range 100–710 kPa. (a) tcyf/svc’versus Nf; (b) normalized to cyclic shear stress to failure in 10 cy-cles.

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� change the soil structureThe volume reduction is generally small during preshear-

ing, and the increase in density is by far not large enough toexplain the increased cyclic resistance. One may expect pre-shearing to have less effect in triaxial tests than in DSStests, as seating and stress concentrations are likely to beless important and the horizontal stress is kept constant intriaxial tests.

The data in Fig. 37 show that

� the cyclic shear stress at failure increases with increasingpreshearing, i.e., both with increasing cyclic shear stressand increasing number of cycles during preshearing

� preshearing has an important effect for both low and highrelative density; no clear trend is observed as function ofDr

� there are less data with preshearing in triaxial than inDSS tests, and the data do not show clear differences be-tween triaxial and DSS tests

� preshearing with 400 cycles at tcy/s 0vc = 0.04 may give acyclic shear strength increase between about 5% and 25%

The effect of preshearing may be the opposite of what ispresented above if the preshearing causes large shear strainsthat may break down the structure, e.g., Oda et al. (2001)and Wijewickreme and Sanin (2005).

The data above are for normally consolidated soil. Pre-shearing may give a less positive effect on overconsolidatedsoil. Cyclic tests on Drammen clay show that preshearing at

a cyclic shear stress of half the static shear strength gives anincreased resistance to subsequent undrained cyclic loadingin normally consolidated clay, but a reduced resistance inclay with an overconsolidation ratio of 4 (e.g., Andersen1988). Similar effects of overconsolidation may also existfor cohesionless soil, but no data have been available foroverconsolidated sand.

Effect of overconsolidationThe in situ soil may be overconsolidated due to removal

of previous overburden, variation in the weight of the struc-ture or preloading by temporary weight or underpressure.Overconsolidation will increase the horizontal effective nor-mal stress, increase the relative density, and possibly changethe structure. These changes will tend to increase the cyclicresistance of the soil.

The effect of overconsolidation on the cyclic shear stressat failure, tcy,f/s 0vc, was compiled for different cohesionlesssoils in Fig. 38. Both loose and dense soils are included.Drammen clay and an empirical equation from Ishihara andTakatsu (1979) are included as references. The equationfrom Ishihara and Takatsu (1979) is applied for two condi-tions: (i) K0-value of 0.5, 0.7, 1.0, and 1.35 for OCR = 1, 2,4, and 8, respectively; and (ii) K0 = 1.0 for all OCRs. Thefirst condition simulates one-dimensional consolidation,such as in the DSS test. The second condition represents iso-tropically consolidated triaxial conditions where K0 does notchange because of overconsolidation.

The data in Fig. 38 show that

� Overconsolidation increases the resistance to cyclic load-ing significantly.

� The effect of overconsolidation on the cyclic shear stressat failure is typically about 50% higher in DSS than intriaxial tests. One reason for this is likely the increase inK0 with OCR in the DSS tests. If the triaxial tests are runby adjusting K0 as function of OCR, one would expectthe same effect of OCR as in the DSS tests.

� The increase in the cyclic DSS strength for the noncohe-sive soils is close to or slightly smaller than the increasemeasured on Drammen clay.

� The empirical equations from Ishihara and Takatsu(1979) give a somewhat greater effect of overconsolida-tion than the data points, but also indicate a differencebetween DSS and isotropically consolidated triaxial tests.

Effect of load periodAll results presented in this paper are from tests with a

10 s load period. There is scatter in the data, but experiencefrom the testing of several offshore clays is that one 100 sload cycle has the same effect as 1.5 to 5 cycles with a 10 sload period. This observation is for clays with a plasticityindex, Ip, in the range of 40%–100%. There is not a cleartrend, but the effect of a longer load period seems to behighest for tests with a high Ip.

The tests on quick clay in the subsequent section showthat one 10 s cycle seems to have the same effect as abouteight 1 s cycles. Cyclic tests on sand seem to indicate nosignificant effect of load period (Lee and Vernese 1978;Tatsuoka et al. 1986a). No systematic data has been found

Fig. 37. Effect of preshearing on undrained cyclic shear stress atfailure in triaxial and DSS tests.



for silt, but it seems reasonable to expect an effect betweenclay and sand, depending on the silt, sand, and clay content.

Cyclic data for displacement analysesData for calculation of cyclic displacements, equivalent

soil stiffnesses for structural dynamic analyses, permanentdisplacements due to cyclically induced shear strains, andpermanent displacement due to dissipation of cyclically in-duced pore pressure are presented in Andersen (2004) forclay and in Andersen et al. (1994) and Andersen and Berre(1999) for sand.

The data are presented in the same format as for cyclicstresses to failure in Figs. 18 and 19, but with contours ofpermanent and cyclic shear strains and permanent pore pres-sure for a given number of cycles instead of contours of thenumber of cycles to failure.

Procedures to calculate the different displacement compo-nents are proposed in Andersen (1991) and Andersen andHøeg (1991).

Capacity calculationThe capacity of a foundation under combined static and

cyclic loading can be calculated by limiting equilibriumanalyses with the procedure proposed by Andersen andLauritzsen (1988). The cyclic shear strength of the clay isdetermined from diagrams such as in Figs. 22 and 23. Thecyclic shear strength at a given point on the failure surface(see Fig. 15) is interpolated between the strengths fromcompression, DSS, and extension tests. The procedure ac-counts for the redistribution of average soil stresses duringcyclic loading and determines whether the failure mode willbe large cyclic displacements, large average displacementsor a combination of the two. The procedure is based on theassumption that the combination of average and cyclic shearstrains is the same along the potential failure surface (straincompatibility) and on the condition that the average shearstresses along the potential failure surface is in equilibriumwith the average loads.

The capacity of piles under vertical cyclic loading can becalculated by modelling the pile–soil interface with nonlinear‘‘t–z’’ springs (Karlsrud and Nadim 1990), where t and z rep-resent mobilized skin friction and vertical displacement, re-spectively, with cyclic and permanent componentsdetermined through strain contour diagrams of the type men-tioned in the section ‘‘Cyclic data for displacement analyses’’above.

Clay slopes under earthquake loading

Special considerations for quick clay and slopessubjected to earthquake loading

For slopes subjected to earthquake loading, the stress con-ditions and the failure mechanism require special considera-tions. A permanent slope will consolidate under a shearstress from its own weight, tc, as illustrated in Fig. 39. Forrelatively steep slopes, this average shear stress may be ofabout the same magnitude as the cyclic shear stress due tothe earthquake. The earthquake has a cyclic load periodabout one-tenth of offshore wave loading.

This section presents preliminary results from an on-goinglaboratory testing programme where such conditions aremodelled. The tests were run on high-quality block samplesof a Norwegian quick clay with a sensitivity of more than75. The samples were normally consolidated with water con-tent of about 39%, clay content of about 40%, plasticity in-dex of about 10%–12%, and an apparent overconsolidationratio due to secondary consolidation less than 1.5. The pre-consolidation stress was obtained from constant rate ofstrain oedometer tests.

Quick clay was used for the testing because new Norwe-gian regulations may require slopes to be checked for earth-quake loading, and some slopes in Norway contain quickclay. There is little experience with the cyclic behaviour ofquick clay and it was believed that quick clay may be morevulnerable to cyclic loading than ordinary clays.

The purpose of the testing was (i) to check cyclic behav-iour under the stress conditions in a slope and (ii) to study ifquick clay behaves differently from ordinary clays.

Cyclic behaviour of quick clay versus ordinary claysThe behaviour of the quick clay under cyclic loading is

compared with normally consolidated Drammen clay inFig. 40. The data in Fig. 40 are for DSS tests with symmet-rical stress-controlled 10 s load cycles. The number ofcycles to failure is slightly lower for the quick clay than forDrammen clay. The relatively small difference may be ex-plained by differences from one soil to another. In particu-

Fig. 38. Effect of overconsolidation on cyclic shear stress at failurefor 10 load cycles in DSS tests with symmetrical loading (ta = 0)and in triaxial tests. CIU, isotropically consolidated triaxial test.

Fig. 39. Simplified stress conditions in infinite slope. sn’, effectivestress normal to the failure surface.

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lar, the quick clay had somewhat smaller clay content (40%)than Drammen clay (45%–55%). Experience has shown thatthe cyclic shear strength may tend to decrease with decreas-ing plasticity (e.g., Figs. 26 and 27). The data thus show thatthe quick clay tested seems to behave similarly to otherclays under cyclic loading.

Effect of load periodThe tests in Fig. 40 were run with a load period of 10 s.

Earthquakes have a period of about 1 s, and preliminarytests on the quick clay with different load periods indicatethat the number of cycles to failure increases about 8 timeswhen the load period is reduced from 10 to 1 s.

Effect of shear stress during consolidationThe undrained shear strength will increase if the clay is

consolidated under a shear stress, as illustrated in Fig. 41.The effect may be smaller in overconsolidated clay andmay depend on plasticity.

The data in Fig. 41 illustrates the importance of consoli-dating the clay under the appropriate stresses, both for mon-

otonic and cyclic testing. If this strength increase isneglected, the stability of a slope under additional undrainedloading may be significantly underestimated. On the otherhand, a laboratory test is normally run to failure in less than2 h, and the slope will remain undrained for a much longerperiod than this after additional loading. The undrainedshear strength may then be reduced by about 20%, accord-ing to Fig. 20. Monotonic tests on the quick clay shearedwith different strain rates agree well with the diagram inFig. 20.

Effect of cyclic loading on static shear strengthA series of tests were performed to see the effect of cyclic

loading on the static shear strength of a slope. Examples ofcyclic tests consolidated with tc/s0vc = 0.16, corresponding toa slope of about 108, are presented in Fig. 42. The figureshows one reference monotonic test and two cyclic teststhat were run with monotonic loading to failure after cy-cling. The monotonic tests were run strain-controlled with arate of shear strain of *4.5%/h.

The reason why the cyclic stress–strain curves go beyondthe monotonic stress–strain curve is that the cyclic tests arerun stress-controlled and that the rate of strain is signifi-cantly higher in the cyclic tests when they develop largestrains than the rate of strain in the monotonic tests.

The cyclic loading was stopped when a permanent shearstrain of gp = 2% was reached in the first cyclic test (DSS8)and when gp = 12% was reached in the other cyclic test(DSS6). The results in Fig. 42 show that the monotonicpeak shear strength is reduced by the cyclic loading andthat the post-cyclic monotonic stress–strain curves rapidlyjoin the virgin monotonic stress–strain curve. Differences inthe monotonic curves are believed to be due to soil variabil-ity. The series of tests consolidated under other shear

Fig. 41. Undrained static DSS shear strength of the quick clay as afunction of normalized consolidation shear stress, tc/svc’.

Fig. 42. Stress–strain behaviour in monotonic, cyclic, and post-cyclic monotonic DSS tests with ta = tc = 20.8 kPa = 0.16svc’. th,horizontal shear stress.

Fig. 40. Number of cycles to failure for quick clay compared withDrammen clay. DSS tests with symmetrical loading (ta = 0) and10 s load period. St, sensitivity.



stresses show better agreement. It thus appears that the post-cyclic static shear strength is governed by the virgin mono-tonic stress–strain curve and the permanent shear strain thatis developed during cyclic loading. Similar results have beenfound on Drammen clay (Andersen 1988), but the behaviouris even more evident for the quick clay due to the more pro-nounced strain-softening.

Tests with symmetrical cyclic loading (ta = tc = 0) showa somewhat different picture, where the post-cyclic mono-tonic stress–strain curve does not reach the monotonicstress–strain curve. This more severe effect of cyclic loadingwas seen both in tests on quick clay and Drammen clay(Andersen 1988).

Effect of cyclic loading on undrained creepA slope subjected to an earthquake will experience both

cyclic and permanent shear strains and displacements. How-ever, the failure mode is not likely to be large cyclic shearstrains and displacements because of the relatively signifi-cant average shear stress in a slope. The cyclic loading willinstead cause large permanent shear strains and displace-ments, as in the tests in Fig. 42. The failure is not likely tooccur during the peak load either, because the duration ofthe peak load is not long enough to accelerate the soilmass. The critical mechanism is therefore likely to be devel-opment of large permanent shear strains and displacementsduring or after the earthquake. The critical period may besome time after the earthquake, before the excess pore pres-sure generated by the cyclic loading has dissipated. Duringthis period, the clay will creep under undrained conditionsand a delayed failure may occur. This is simulated in theDSS tests and illustrated by an example in Fig. 43.

The test in Fig. 43 was consolidated with an averageshear stress of 62% of the undrained static shear strength,corresponding to a slope of about 138. The specimen wascycled to a permanent shear strain of 5% and left with thisaverage shear stress under undrained conditions. It can beseen that the specimen develops shear strains that accelerateand failure occurs after 136 min.

A reference test is included in Fig. 43 to verify that thetest was not unstable after consolidation and that the creepfailure was induced by the cyclic loading. The referencetest was run by just closing the drainage valves after thesame consolidation period as in the cyclic test. The refer-ence test did not develop noticeable shear strains.

The failure mode for a slope subjected to earthquakeloading is thus expected to be delayed undrained creep.Based on the results produced so far, the slope may be ana-lysed by first running a dynamic analysis to determine thepermanent shear strain due to the design earthquake. Thepost-cyclic shear strength may then be determined as theshear stress on the monotonic stress–strain curve at a shearstrain equal to the calculated permanent shear strain. Thisshear strength should be reduced by 15%–25% to accountfor (i) the post-cyclic stress–strain curve reaching the virgincurve at a somewhat larger strain than the permanent straindeveloped during the earthquake and (ii) the time to failurebeing significantly longer than in the monotonic laboratorytest (see Fig. 20).

In a quick clay slope there will be progressive failuremechanisms (e.g., Andresen and Jostad 2004) and this must

be taken into consideration when applying the shear strengthdiscussed above.

Verification of calculated foundationcapacity by means of model tests

The use of laboratory test data, as presented above, to cal-culate the foundation capacity of structures subjected to cy-clic loading was verified by predicting or back-calculatingvarious series of model tests. The calculation method isbriefly described earlier in the paper.

The model tests included:

� Five 1g laboratory model tests of an offshore gravity-base structure with monotonic and cyclic loading on asoft clay (Andersen et al. 1989).

� Twelve 1g laboratory model tests with monotonic andcyclic loading on an offshore tripod gravity platform(Aas and Andersen 1992).

� One monotonic and one cyclic centrifuge test of a gravity-base structure similar to the Ekofisk oil storage tank (An-dersen et al. 1994)

� Two series of large-scale field tests with monotonic andcyclic loading of offshore suction anchors in clays. Oneseries of tests was run with a load inclination of 108with the vertical to simulate anchors for a TLP (Andersenet al. 1993; Dyvik et al. 1993). The other series was runwith a load inclination of 108 with the horizontal to simu-late anchors with more horizontal loading (Keaveny et al.1994).The comparison of calculated and measured capacities are

presented in the references for the various model testsabove. The calculated bearing capacity, type of failuresurface, failure surface location, and failure mode (large per-manent displacements, large cyclic displacements or a com-bination of the two) agreed well with the measurements forall the model tests.

As an example, some details are given for the last of themodel test series referenced above. The model geometry andthe soil are summarized in Fig. 44. The model after it wasbrought to failure is shown in Fig. 45.

Predicted and measured capacities of the monotonic andthe three cyclic TLP tests are compared in Table 1. The

Fig. 43. Development of shear strain in undrained DSS tests withconstant shear stress.

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agreement is very good. The predicted and observed failuresurfaces are shown in Fig. 46. The agreement is also gener-ally good, but there are some differences. However, back-calculations with the observed failure surfaces gave insignif-icant differences in the calculated capacities. The reason forthe difference in failure surface between test 4 and the othertests is that test 4 was subjected to a greater moment.

Summary and conclusions

Cyclic loading can be very significant for the foundationdesign of structures — offshore, along the coast, and onland — and for the stability of slopes.

The soil elements beneath a structure subjected to cyclicloading follow different stress paths. The behaviour undercyclic loading depends strongly on the stress path and it is

important to determine the cyclic shear strength under repre-sentative stress conditions. In practice, this can be done byDSS and triaxial tests consolidated to the appropriate in situstresses prior to cyclic loading and run under representativecombinations of average and cyclic shear stresses.

A convenient way to present the results from the cyclictests is to prepare diagrams where the number of cycles tofailure is plotted as a function of average and cyclic shearstresses. These diagrams should also contain the failuremode, i.e., the combination of permanent and cyclic shearstrains at failure. The diagrams will thus contain the infor-mation required to calculate the capacity of a structure undercyclic loading by a limiting equilibrium method that ac-counts for (i) strain compatibility and (ii) equilibrium be-tween the weight of the structure and the average shearstresses in the soil.

The paper presents diagrams that contain the cyclic shearstrength of clay, sand, and silt that can be used for practicaldesign. These diagrams are useful for feasibility studies be-fore site-specific cyclic data become available and as aguide when specifying and interpreting site-specific cycliclaboratory tests.

Some cases, such as slopes under earthquake loading,may require special considerations and the paper presentssome data on cyclic testing of a quick clay under such con-ditions. One possible failure mode for such cases is un-drained creep initiated by an earthquake. The post-cyclicmonotonic shear strength may also be reduced by the earth-quake loading, making the slope vulnerable to increasedloads or erosion in the period before the earthquake-inducedexcess pore pressures have dissipated.

Comparisons between calculations and model tests indi-

Table 1. Predicted and measured failure loads for the TLPfield-model tests.

Test No. Test type Predicted/measured failure load1 Monotonic 1.002 Cyclic 1.053 Cyclic 1.064 Cyclic 1.01

Fig. 46. Predicted and observed failure surfaces in TLP model tests.(a) Tests 1, 2, and 3; (b) test 4.

Fig. 44. Geometry and key soil data for the large-scale field modeltests of offshore suction anchors. P, applied load.

Fig. 45. TLP model after failure (photo by Rune Dyvik, NGI).



cate that the foundation capacity under cyclic loading can bereliably determined on the basis of cyclic shear strength de-termined in laboratory tests.

AcknowledgementsThe results presented in this paper are based on informa-

tion from joint industry-sponsored research projects, re-search projects funded by the Research Council of Norway,and consulting projects. Numerous colleagues at NGI havecontributed to the results, both in performing and interpret-ing laboratory tests and model tests and by developing theo-retical models. This co-operation is greatly appreciated.Special thanks are extended to Dr. Fritz Nowacki, NGI, forfruitful discussions through many years and projects;Mr. Jan Lampe, NGI, for his high-quality and careful DSStesting; Dr. Amir Kaynia, NGI, for discussions on slope be-haviour under earthquake loading; and Dr. Suzanne Lacasse,NGI, for reviewing and commenting on the paper.

ReferencesAas, P.M., and Andersen, K.H. 1992. Skirted foundations for off-

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