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Evaluation of Small-Scale Laterally Loaded Non-Slender Monopiles in Sand

Roesen, Hanne Ravn; Thomassen, Kristina; Sørensen, Søren Peder Hyldal; Ibsen, Lars Bo

Publication date:2010

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Citation for published version (APA):Roesen, H. R., Thomassen, K., Sørensen, S. P. H., & Ibsen, L. B. (2010). Evaluation of Small-Scale LaterallyLoaded Non-Slender Monopiles in Sand. Department of Civil Engineering, Aalborg University. DCE Technicalreports No. 91

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ISSN 1901-726X DCE Technical Report No. 91

Evaluation of Small-Scale Laterally Loaded Non-Slender

Monopiles in Sand

H. R. RoesenK. Thomassen

S. P. H. SørensenL. B. Ibsen

Department of Civil Engineering

DCE Technical Report No. 91

Evaluation of Small-Scale Laterally Loaded Non-Slender

Monopiles in Sand

by

H. R. Roesen K. Thomassen

S. P. H. Sørensen L. B. Ibsen

June 2010

© Aalborg University

Aalborg University Department of Civil Engineering

Division of Water and Soil

Scientific Publications at the Department of Civil Engineering Technical Reports are published for timely dissemination of research results and scientific workcarried out at the Department of Civil Engineering (DCE) at Aalborg University. This mediumallows publication of more detailed explanations and results than typically allowed in scientificjournals. Technical Memoranda are produced to enable the preliminary dissemination of scientific work by the personnel of the DCE where such release is deemed to be appropriate. Documents of this kindmay be incomplete or temporary versions of papers—or part of continuing work. This should be kept in mind when references are given to publications of this kind. Contract Reports are produced to report scientific work carried out under contract. Publications ofthis kind contain confidential matter and are reserved for the sponsors and the DCE. Therefore,Contract Reports are generally not available for public circulation. Lecture Notes contain material produced by the lecturers at the DCE for educational purposes. Thismay be scientific notes, lecture books, example problems or manuals for laboratory work, orcomputer programs developed at the DCE. Theses are monograms or collections of papers published to report the scientific work carried out atthe DCE to obtain a degree as either PhD or Doctor of Technology. The thesis is publicly availableafter the defence of the degree. Latest News is published to enable rapid communication of information about scientific workcarried out at the DCE. This includes the status of research projects, developments in thelaboratories, information about collaborative work and recent research results.

Published 2010 by Aalborg University Department of Civil Engineering Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark Printed in Aalborg at Aalborg University ISSN 1901-726X DCE Technical Report No. 91

Evaluation of Small-Scale Laterally Loaded

Non-Slender Monopiles in Sand

H. R. Roesen1; K. Thomassen1; S. P. H. Sørensen2; and L. B. Ibsen3

Aalborg University, June 2010

Abstract

In current design of o�shore wind turbines, monopiles are often used as foundation.The behaviour of the monopiles when subjected to lateral loading has not been fullyinvestigated, e.g. the diameter e�ect on the soil response. In this paper the diametere�ect on laterally loaded non-slender piles in sand is evaluated by means of resultsfrom six small-scale laboratory tests, numerical modelling of the same test setup andexisting theory. From the numerical models p− y curves are conducted and comparedto current design regulations. It is found that the recommendations in API (1993)and DNV (1992) are in poor agreement with the numerically obtained p − y curves.The initial sti�ness, E∗

py, of the p − y curves, is found to be dependent on the pilediameter, i.e. the initial sti�ness increases with increasing pile diameter. Further,the dependency is found to be in agreement with the suggestions in Sørensen et al.(2010). It is found that considerable uncertainties are related to small-scale testing,and the di�erent evaluations clearly indicate that the accuracy of small-scale testingis increased when increasing the pile diameter and applying overburden pressure.

1 Introduction

In the design of laterally loaded monopilesthe p−y curve method, given by the designregulations API (1993) and DNV (1992),is often used. For piles in sand the rec-ommended p − y curves are based on re-sults from two slender, �exible piles witha slenderness ratio of L/D = 34.4, whereL is the embedded length and D is thediameter of the pile. Contrary to the as-sumption of �exible piles for these curvesthe monopile foundations installed todayhave a slenderness ratio L/D < 10, andbehave almost as rigid objects. The rec-ommended curves does not take the e�ectof the slenderness ratio into account. Fur-thermore, the initial sti�ness is consideredindependent of the pile properties such asthe pile diameter. The research within the

�eld of diameter e�ects gives contradictoryconclusions. Di�erent studies have foundthe initial sti�ness to be either indepen-dent, linearly dependent, or non-linear de-pendent on the pile diameter, cf. Brødbæket al. (2009). 123

The aim of this paper is to evaluate thediameter e�ect on the pile-soil interaction.Six small-scale tests on laterally loadedmonopiles in sand have been conducted,cf. Thomassen et al. (2010). The diam-eter e�ect is evaluated by comparing re-sults from these tests with calibrated nu-merical models of the same test setup andexisting theory. Furthermore, p− y curves

1Graduate Student, Dept. of Civil Engineer-ing, Aalborg University, Denmark

2Professor, Dept. of Civil Engineering, Aal-borg University, Denmark.

3PhD Fellow, Dept. of Civil Engineering, Aal-borg University, Denmark.

1

Hanne Ravn

hvid


recommended in the current design regu-lations API (1993) and DNV (1992) arecompared to curves obtained from the nu-merical models. As the foundations for o�-shore wind turbines are sensitive towardsrotation and vibrations, strict demands forthe sti�ness of the foundation are induced.Therefore, the diameter e�ect is evaluatedwith focus on the initial sti�ness of thep− y curves.

2 Laboratory Test Setup

Six quasi-static tests on two closed-endedaluminium piles with a wall-thickness of5 mm and outer diameters of 40 mmand 100 mm, respectively, have been con-ducted. The piles had a slenderness ra-tio, L/D, of 5 corresponding to embeddedlengths of 200 mm and 500 mm. The pileswere installed in 580 mm fully saturatedsand. The aim of the tests was to obtainload-de�ection relationships for the piles.Therefore, the piles were loaded laterally370 mm above the soil surface, and the de-�ection of the pile was measured at threelevels, cf. Fig. 1.

Figure 1: Setup for measuring the lateral deflection ofthe pile at three levels. The measurements are givenin mm.

In order to minimize errors such as smallnon-measurable stresses and a non-linearfailure criterion, the tests were conductedin the pressure tank shown in Fig. 2. The

Figure 2: The pressure tank installed in the Geotech-nical Engineering Laboratory at Aalborg University,Denmark.

e�ective stresses in the soil were increasedby placing an elastic membrane on the soilsurface sealing the soil from the upper partof the pressure tank. When increasingthe pressure in the upper part of the tankthe membrane was pressed against the soilleading to an increase of the stresses in thesoil. The lower part of the tank was con-nected to an ascension pipe ensuring thatthe load was applied as contact pressuresbetween the grains only, i.e. an increase ofthe e�ective stresses. The tests were con-ducted at stress levels of 0 kPa, 50 kPa,and 100 kPa.

The soil parameters were determined fromcone penetration tests in accordance to Ib-sen et al. (2009). A detailed descriptionof the laboratory tests can be found inThomassen et al. (2010).

2

H. R. Roesen, K. Thomassen, S. P. H. Sørensen and L. B. Ibsen

3 Numerical 3D Models

The six laboratory tests are modelled inFlac3D, which is a commercial explicit �-nite di�erence program. Because of axissymmetry in the tests, only half the testsetup is modelled. The modelling pro-gramme is chosen to match the testingprogramme in Thomassen et al. (2010), cf.Tab. 1.

Table 1: Modelling programme for the FLAC3D mod-els.

D L/D P0

[mm] [-] [kPa]

Model 1 (Test 1) 100 5 0Model 2 (Test 2) 100 5 50Model 3 (Test 3) 100 5 100Model 4 (Test 4) 40 5 0Model 5 (Test 5) 40 5 50Model 6 (Test 6) 40 5 100

The generation of the models and the �-nite di�erence calculations are carried outstepwise as described in the following.

3.1 Geometry of the 3D Models

The model geometry is set to match thecondition in the pressure tank. There-fore, the outer boundaries are given asthe volume of the soil mass in the tank,i.e. a diameter of 2.1 m and a soil depthof 0.58 m. The soil and pile are gener-ated by use of prede�ned zone elements towhich di�erent material models and prop-erties can be assigned. Each zone elementis automatically discritised into �ve tetra-hedron subelements, which are �rst order,constant rate of strain elements. Becauselarge variations in strain and stresses oc-cur in the soil near the pile a �ner zonemesh is generated in this area.

In order to model a correct pile-soil inter-action an interface is generated betweenthe pile and the soil by use of standardFlac3D interface elements. The elements

are triangular and by default two inter-face elements are generated for each zoneface. The interfaces are one-sided andattached to the soil. The constitutivemodel for the interface is de�ned by a lin-ear Coulomb shear-strength criterion thatlimits the shear force acting at an inter-face node after the shear strength limit isreached.

Firstly, the soil is generated, secondly, theinterface is generated and attached to thesoil elements and, thirdly, the pile is gen-erated. Initially, the pile grid is generatedseparately and later moved into the soiland in contact with the interface. Hereby,it is possible to group the pile elementsand specify pile nodes for the computationof bending moment. As a simpli�cation,the piles are modelled as solid cylindersin contrast to the closed-ended pipe pilesused in the laboratory tests. The solidpiles are modelled with a reduced modulusof elasticity and reduced density based onequivalence with the pipe piles used in thelaboratory tests, cf. Sec. 3.5. The zonegeometry for the 100 mm pile is shownin Fig. 3. In Sørensen et al. (2009) con-vergence analyses were conducted and thegeometries used in this article are in agree-ment with the analyses. Note that theshown coordinate system is in agreementwith the coordinate system employed forlaterally loaded piles in the design regu-lations and does not represent the systemused in Flac3D.

Figure 3: Zone geometry in the models with the100 mm pile.

3


3.2 Boundary and Initial Condi-

tions

When the geometry is generated theboundary and initial conditions are as-signed. At the outer perimeter of the soilthe element nodes are restrained in the y-and z-direction, cf. Fig. 3. At the bot-tom surface of the model the nodes arerestrained in all directions. Because onlyhalf the laboratory setup is modelled thenodes at the symmetry line are restrainedin the z-direction.

The initial stresses are initialised based onthe density of the material, the gravita-tional loading, and the overburden pres-sure. The horizontal stresses are gener-ated by use of a K0-procedure in whichK0 = 1− sinϕtr.

3.3 Calculation Phase

In order to prevent stress concentrationsnear the pile the model is brought to equi-librium with both the pile and the soil hav-ing the material properties of the soil. Fur-ther, the pile is assumed smooth by set-ting the interface friction equal to zero.Hereafter, the pile and interface are as-signed the material properties for the pileand interface, respectively, cf. Sec. 3.5.Again, the model is brought to equilib-rium. This second equilibrium ensures acorrect generation of the initial interfacestresses. When equilibrium is reached alldisplacements are reset to zero.

The lateral load is applied as lateral veloc-ities at x = −370 mm. The velocities areapplied to the nodes at the centre of thepile corresponding to y = 0. Hereby, noadditional bending moment is introducedin the pile. In order to avoid a dynamicresponse of the system the velocity is ap-plied in small increments.

During the calculations the total lateralforce, H, the displacement, y, and the

stresses, σ, along the pile are recorded.The bending moment, M , and soil pres-sure, p, are calculated based on therecorded stresses in the pile and the in-terface, respectively, cf. Sec. 3.6.

3.4 Material Models

To describe the constitutive relations inthe soil an elasto-plastic Mohr-Coulombmodel is employed. As the soil is consid-ered cohesionless no tension forces are al-lowed. Thus, tension cut-o� is employedin the model. The yield function of themodel de�nes the stress for which plastic�ow takes place and is controlled by a non-associated �ow rule. The piles are mod-elled by use of an elastic, isotropic model.

3.5 Material and Interface Prop-

erties

The soil properties in the six models arede�ned equal to the �ndings of the sixlaboratory tests, cf. Tab. 2. (Thomassenet al., 2010)

Table 2: Soil properties determined by the six labora-tory tests and employed in the FLAC3D models. Theelasticity moduli written in parentheses are found bymeans of the numerical model.

ϕtr ψtr γ′ E0

[o] [o] [kN/m3] [MPa]

Model 1 53.7 19.6 10.3 (4.0)Model 2 50.3 19.0 10.4 38.24Model 3 47.7 18.3 10.4 55.61Model 4 54.4 20.4 10.4 (2.0)Model 5 50.4 19.1 10.4 38.6Model 6 48.0 18.6 10.4 57.2

For the tests without overburden pressurethe low stresses lead to large uncertain-ties in the calculation of the initial tan-gential elasticity modulus, E0. Thus, inthe numerical models without overburdenpressure E0 is calibrated as described inSec. 3.7. Due to the small variations in ef-fective stresses through the soil layer the

4


soil parameters are assumed to be constantwith depth for all the models. A cohesion,c, of 0.1 kPa and Poissons ratio, ν, of 0.23are applied for the soil in all six models.

Because the piles are modelled as solidcylinders instead of hollow piles, as theones used in the laboratory, an equivalentbending sti�ness and density is required.Based on this equivalence a reduced elas-ticity modulus, Esolid, for the modelledpiles are found.

Esolid =Ehollow · Ihollow

Isolid(1)

I is the second moment of inertia, and thesubscripts hollow and solid denote the pa-rameters derived for the pipe piles in thelaboratory tests and the parameters em-ployed in Flac3D, respectively. In thesame way the density is equated with thecross-sectional area. The elasticity mod-ulus and density of the pipe piles are setto the values for aluminium; 7.2 · 104 MPaand 2700 kg/m3, respectively.

The interface properties are calibrated bymeans of the numerical models as de-scribed in Sec. 3.7. When using the inter-face properties listed in Tab. 3 the load-de�ection curves are found to be similarto the curves obtained in the laboratorytests.

Table 3: Interface properties calibrated by means ofthe numerical models. E0 is the initial tangential elas-ticity modulus of the soil, cf. Tab. 2.

Friction ϕint 30◦

Cohesion cint 0.1 kPaDilation ψint 0◦

Normal sti�ness kn 100× E0

Shear sti�ness ks 100× E0

3.6 Calculation of the Pile Ben-

ding Moment and Soil Resis-

tance

The bending moment of the pile at a givenlevel is calculated by use of Naviers for-

mula, Eq. 2. In order to eliminate the ave-rage vertical stress, corresponding to theaxial force acting on the pile, the bendingmoment in each level is calculated by twopoints (y,z) = (±D/2, 0).

M =σxx,i · Izz

yi(2)

σxx,i is the vertical normal stress at pointi, Izz is the second moment of iner-tia around the z-axis, and yi is the y-coordinate for the point, cf. Fig. 3. Thesoil resistance per unit length along thepile, py, is computed directly by integrat-ing the stresses in the interface nodes alongthe interface circumference C.

py =∫TydC (3)

Ty is the y-component stress in a node ipositioned in the interface.

3.7 Calibration of the Numerical

Models

The calibration of the numerical models isbased on a comparison between the mod-elled load-de�ection curves and the load-de�ection curves obtained from the small-scale tests in the laboratory.

For the models without overburden pres-sure E0 is calibrated in relation to the ini-tial sti�ness of the load-de�ection curves.In Figs. 4 and 5 the calibrated curves forP0 = 0 kPa are shown. In the �gures itis seen that the capacity of the calibratedmodels exceeds the capacity of the labora-tory tests. This indicates that the internalangle of friction, ϕtr, inserted in the mod-els is overestimated. ϕtr is based on theCPT's conducted prior to each laboratorytest. At low stress levels ϕtr varies signif-icantly with the stresses and it is di�cultto determine ϕtr with su�cient accuracy.

The agreement between the capacity inthe calibrated and the measured load-de�ection relationship are found to in-crease with increasing pile diameter and

5


0 10 20 30 40 500

200

400

600

800

1000

1200

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 100 mm, P0 = 0 kPa

MeasuredCalibrated

0 10 20 30 40 50 600

10

20

30

40

50

60

70

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 40 mm, P0 = 0 kPa

MeasuredCalibrated

Figure 4: Calibrated and measured relationshipsat three levels above the soil surface for the test100 mm with P0 = 0 kPa.

Figure 5: Calibrated and measured relationships atthree levels above the soil surface for the 40 mm pilewith P0 = 0 kPa.

0 10 20 30 40 500

5000

10000

15000

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 100 mm, P0 = 50 kPa

MeasuredCalibrated

0 10 20 30 40 500

200

400

600

800

1000

1200

1400

1600

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 40 mm, P0 = 50 kPa

MeasuredCalibrated

Figure 6: Calibrated and measured relationships atthree levels above the soil surface for the 100 mmpile with P0 = 0 kPa.


increasing overburden pressure, cf. Figs. 4to 9. Thus, the best agreement is foundfor the 100 mm pile with an overburdenpressure of 100 kPa, cf. Fig. 8.

Considerable uncertainties are related tothe test results for the 40 mm pile,cf. Thomassen et al. (2010). This canalso be concluded from the calibrationof the model with the 40 mm pile andP0 = 100 kPa as signi�cant disagreementbetween the calibrated and the measuredvalues are found, cf. Fig. 9. This dis-agreement is explained by a disturbanceof the soil prior to the test as described inThomassen et al. (2010).

The calibration of the six models clearlyindicates that the accuracy in small-scaletesting is increased when increasing thepile diameter and applying overburdenpressure.

4 Evaluation of Results

from the Numerical Mod-

els

Prior to the evaluation of the bending mo-ment and de�ection of the pile a conver-gence of the stresses in the numerical mod-els is checked by a comparison between the

6


0 10 20 30 40 500

0.5

1

1.5

2

x 104

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 100 mm, P0 = 100 kPa

MeasuredCalibrated

0 10 20 30 40 500

500

1000

1500

2000

2500

Hor

izon

tal l

oad

[N]

Deflection [mm]

D = 40 mm, P0 = 100 kPa

MeasuredCalibrated

Figure 8: Calibrated and measured relationships atthree levels above the soil surface for the 100 mmpile with P0 = 100 kPa.


0 0.5 1 1.5 2 2.5

x 104

0

1

2

3

4

5

6

7

8x 10

6

Mom

ent,

M, [

Nm

m]

Horizontal load, H, [N]

D = 100 mm, P0 = 100 kPa

Flac: NavierReal: M=He

Figure 10: Comparison of the applied moment (ap-plied load H multiplied with the load eccentricity, e,with the computed bending moment at soil surface forthe 100 mm pile with P0 = 100 kPa.

applied moment and the computed ben-ding moment, cf. Fig. 10. In all the mod-els the computed bending moment is inagreement with the applied moment.

4.1 Evaluation of Bending Mo-

ment and Lateral De�ection

In Figs. 11 and 12 the bending momentdistribution along the piles below the soilsurface is shown. For both models the pre-scribed displacement at x = −370 mm is35 mm. In the �gures it is seen that themaximum bending moment occurs at dif-ferent locations depending on the overbur-

den pressure. When overburden pressureis applied, the point of maximum bendingmoment is located closer to the soil sur-face. This indicates that the relative in-crease in soil resistance with overburdenpressure is most signi�cant at the soil sur-face.

In Figs. 13 and 14 the lateral de�ectionwith depth at three di�erent overburdenpressures is shown. The prescribed de�ec-tion at x = −370 mm is 35 mm. Belowthe soil surface the de�ection is recordedin 21 levels for the 40 mm pile and 26 lev-els for the 100 mm pile. Above the soilsurface the de�ection is recorded in twolevels: x = −200 mm and x = −370 mm.

When applying overburden pressure thepile exhibits a more �exible behaviourthan without overburden pressure, cf.Figs. 13 and 14. This is in accordancewith Poulos and Hull (1989), who pro-posed a criterion for the pile-soil interac-tion in which an increase in the soil sti�-ness compared to the pile sti�ness will leadto a more �exible behaviour of the pile.When applying overburden pressure thee�ective stress level increases, leading toan increase in the soil sti�ness.

Although the piles behave more �exiblewhen overburden pressure is applied, theprimary de�ection is caused by rigid body

7


−2 0 2 4 6 8 10

x 106

0

100

200

300

400

500

Dep

th, x

, [m

m]

Moment, M, [Nmm]

D = 100 mm

P0 = 0 kPa

P0 = 50 kPa

P0 = 100 kPa

−2 0 2 4 6 8 10

x 105

0

50

100

150

200

Dep

th, x

, [m

m]

Moment, M, [Nmm]

D = 40 mm

P0 = 0 kPa

P0 = 50 kPa

P0 = 100 kPa

Figure 11: Bending moment distribution at differentoverburden pressures for the 100 mm piles. The hor-izontal lines indicate the depth of maximum moment.

Figure 12: Bending moment distribution at differentoverburden pressures for the 40 mm piles. The hori-zontal lines indicate the depth of maximum moment.

−2 0 2 4 6 8 10 12

−400

−300

−200

−100

0

100

200

300

400

500

Dep

th, x

, [m

m]

Deflection, y, [mm]

D = 100 mm, y|x=−370

= 10 mm

P0 = 0 kPa

P0 = 50 kPa

P0 = 100 kPa

Initial deflection

−2 0 2 4 6 8 10 12

−400

−300

−200

−100

0

100

200

Dep

th, x

, [m

m]

Deflection, y, [mm]

D = 40 mm, y|x=−370

= 10 mm

P0 = 0 kPa

P0 = 50 kPa

P0 = 100 kPa

Initial deflection

Figure 13: Lateral deflection with depth for differentoverburden pressures for the 100 mm piles.

Figure 14: Lateral deflection with depth for differentoverburden pressures for the 40 mm piles.

rotation, which is evident because only asingle point of rotation and a negative de-�ection at pile toe is present, cf. Figs. 13and 14.

4.2 Evaluation of Diameter ef-

fect on the p�y Curves

The p − y curves from the models with40 mm and 100 mm piles without overbur-den pressures are compared at three di�er-ent depths; 20 mm, 40 mm and 60 mm, cf.Fig. 15.

At the depth of 20 mm the ultimate soilresistance for the 100 mm pile is higherthan for the 40 mm pile. At the depth

of 40 mm the opposite is the case. Forthe depth of 60 mm it seems the curve forthe 40 mm pile is approaching the ultimatesoil resistance for the 100 mm pile. Whichof the two curves that reaches the highestultimate resistance is not possible to pre-dict because of the limited displacementapplied. Based on Fig. 15 the diameter isnot thought to have a signi�cant in�uenceon the ultimate soil resistance.

From Fig. 15 it can be seen that the ini-tial sti�ness of the curves are dependent onthe pile diameter, i.e. the larger pile diam-eter the higher initial sti�ness. This is incontrast to API (1993) and DNV (1992)in which the initial sti�ness is considered

8


0 5 10 15 200

2

4

6

8

10

12

Soil

resi

stan

ce, p

, [N

/mm

]

Deflection, y, [mm]

P0 = 0 kPa

D40

, x = 20 mmD

40, x = 40 mm

D40

, x = 60 mmD

100, x = 20 mm

D100

, x = 40 mmD

100, x = 60 mm

0 10 20 30 40 50 60 70 800

100

200

300

400

500

600

700

Soil

resi

stan

ce, p

, [N

/mm

]

Deflection, y, [mm]

P0 = 50 kPa

D40

, x = 20 mmD

40, x = 40 mm

D40

, x = 60 mmD

100, x = 20 mm

D100

, x = 40 mmD

100, x = 60 mm

Figure 15: p − y curves at three different depthsfor models with 40 mm and 100 mm piles andP0 = 0 kPa.

Figure 16: p − y curves at three different depthsfor models with 40 mm and 50 mm piles andP0 = 100 kPa

independent on the pile diameter. Thedependency of the diameter on the initialsti�ness is further evaluated in Sec. 7.

For the models with overburden pressurethe three p − y curves at same levels areshown in Figs. 16 and 17. As in the mod-els without overburden pressure the initialsti�ness of the p− y curves is found to bedependent on the pile diameter.

4.3 Evaluation of the p�y Curves

Dependency on Stress Level

In Figs. 18 to 20 the soil resistance alongthe 100 mm pile is shown for a pre-scribed de�ection of 10 mm and 35 mmat x = −370 mm, respectively. The soilresistance is calculated at 24 levels alongthe pile and are shown for the pressures0 kPa, 50 kPa, and 100 kPa. In Figs. 21to 23 the p− y curves for the 100 mm pileat the 24 levels are shown for the di�er-ent overburden pressures. In the currenttheory concerning the initial sti�ness, E∗py,e.g. DNV (1992); API (1993); Lesny andWiemann (2006); Sørensen et al. (2010),E∗py is found to increase either linear ornon-linear with depth. Therefore, the ex-pected results from the obtained p − ycurves would be an increase in the E∗py

with depth as well.

0 10 20 30 40 50 60 70 800

100

200

300

400

500

600

700

800

900

1000So

il re

sist

ance

, p, [

N/m

m]

Deflection, y, [mm]

P0 = 100 kPa

D40

, x = 20 mmD

40, x = 40 mm

D40

, x = 60 mmD

100, x = 20 mm

D100

, x = 40 mmD

100, x = 60 mm

Figure 17: p − y curves at three different depthsfor models with 40 mm and 100 mm piles andP0 = 100 kPa.

Fig. 18 shows that the soil resistance in-creases with depth from the soil surface toa depth of approximately 150 mm. Thisincrease is in agreement with the expectedvariation. When evaluating E∗py of thep − y curves in the same depth intervalE∗py is constant with depth, cf. Fig. 21. Inthe depth interval between 150 mm andthe rotation point of the pile, at approxi-mately 340 mm, the soil resistance is seento decrease with depth. Concurrently, E∗py

is seen to decrease with depth in the sameinterval.

9


−30 −20 −10 0 10 20

0

100

200

300

400

500

Dep

th, x

, [m

m]

Soil resistance, p, [N/mm]

D = 100 mm, P0 = 0 kPa,

y|x=−370

= 10 mm

y|x=−370

= 35 mm

Figure 18: Soil resistance along the 100 mm pile withP0 = 0 kPa.

−200 −100 0 100 200

0

100

200

300

400

500

Dep

th, x

, [m

m]


D = 100 mm, P0 = 50 kPa,

y|x=−370

= 10 mm

y|x=−370

= 35 mm


−300 −200 −100 0 100 200 300

0

100

200

300

400

500

Dep

th, x

, [m

m]


D = 100 mm, P0 = 100 kPa,

y|x=−370

= 10 mm

y|x=−370

= 35 mm


−5 0 5 10 15 20 25−30

−25

−20

−15

−10

−5

0

5

10

15

20

Soi

l res

ista

nce,

p, [

N/m

m]

Deflection, y, [mm]

D = 100 mm, P0 = 0 kPa

x = 20 mmx = 40 mmx = 60 mmx = 80 mmx = 100 mmx = 120 mmx = 140 mmx = 160 mmx = 180 mmx = 200 mmx = 220 mmx = 240 mmx = 260 mmx = 280 mmx = 300 mmx = 320 mmx = 340 mmx = 360 mmx = 380 mmx = 400 mmx = 420 mmx = 440 mmx = 460 mmx = 480 mm

Figure 21: p − y curves along the 100 mm pile withP0 = 0 kPa.

−40 −20 0 20 40 60 80 100

−800

−600

−400

−200

0

200

400

600

Soi

l res

ista

nce,

p, [

N/m

m]

Deflection, y, [mm]

D = 100 mm, P0 = 50 kPa



−40 −20 0 20 40 60 80 100

−1200

−1000

−800

−600

−400

−200

0

200

400

600

800

1000

Soi

l res

ista

nce,

p, [

N/m

m]

Deflection, y, [mm]

D = 100 mm, P0 = 100 kPa



10


Below the point of rotation, where the pileexhibit a negative de�ection, a negative in-crease in the soil resistance is present. Be-low the point of pile rotation E∗py is foundto increase with depth.

In the models with overburden pressure,cf. Figs. 19 and 20, the soil resistance ismainly seen to decrease with depth fromthe soil surface to the point of pile rotationat approximately 310 mm. When evaluat-ing the p− y curves shown in Figs. 22 and23 E∗py is found to decrease with depth tothe point of pile rotation. The soil resis-tance below the point of rotation is seento increase negatively with depth and E∗py

increases. The �ndings imply that E∗py isdependent on the state of stress. Simi-lar �ndings are found when evaluating the40 mm pile. At the point of no rotationthe soil pressure is zero and it is thereforedi�cult to evaluate E∗py near this point.

The obtained results should be consid-ered with reservations due to the fact thatthe soil sti�ness is modelled constant withdepth. Secondly, a more advanced consti-tutive model, in which the variation of thesti�ness with the de�ection is taken intoaccount, could have been used. Hereby,the sti�ness of the soil would increase atsmall de�ections, leading to an increaseof the initial sti�ness of the p − y curvesinstead of the decrease of E∗py at smallde�ections as observed in Figs. 18 to 23.Thus, in future research a further evalua-tion of E∗py is recommended. The evalua-tion should consist of laboratory tests onpiles instrumented with strain gauges, andnumerical modelling with more advancedconstitutive models employed.

5 Comparison of Test Re-

sults and Theory

To compare the test results to the rec-ommendations given by the design regula-tions, API (1993) and DNV (1992), a tra-

ditional Winkler model is made in Mat-

lab by using the �nite element toolboxCalfem. Furthermore, the model is usedto evaluate di�erent expressions for the ul-timate soil resistance.

5.1 Evaluation of Tests with

Overburden Pressure

To model the tests with overburden pres-sure, P0, the formulation for the ultimatesoil resistance must be able to take P0

into account. Hansen (1961) and Geor-giadis (1983) both proposed a formulationin which the overburden pressure is takeninto account. Hansen (1961) incorporatedthe overburden pressure directly in the ex-pression for the ultimate soil resistance atmoderate depth. The approach by Geor-giadis (1983) was developed to incorporatedetermination of the ultimate soil resis-tance for layered soils in a Winkler model.This is done by introducing an equivalentsystem with �ctive depths, x′, for each ofthe soil layers. In this paper the approachis used to employ an equivalent systemwith a �ctive depth of the sand layer todescribe the e�ect of the overburden pres-sure.

0 5 10 15 20 25 300

5000

10000

15000

Pile head deflection [mm]

Hor

izon

tal l

oad

[N]

D = 100 mm, P0 = 100 kPa

TestGeorgiadisHansen

Figure 24: Load-deflection relationships measuredat the level of the hydraulic piston (x = −370 mm)obtained from the tests and the Winkler model ap-proach with the two expressions for the ultimate soilresistance accounting for the overburden pressure in-corporated. D = 100 mm. P0 = 100 kPa. The ini-tial modulus of subgrade reaction, k, is set to 40000kN/m3.

11


0 5 10 15 20 25 300

500

1000

1500


Hor

izon

tal l

oad

[N]

D = 100 mm, P0 = 0 kPa

TestAPIHansenUpper bound, α = φ

trUpper bound, α = φ

d

0 5 10 15 20 250

10

20

30

40

50

60


Hor

izon

tal l

oad

[N]

D = 40 mm, P0 = 0 kPa

TestAPIHansenUpper bound, α = φ

trUpper bound, α = φ

d

Figure 25: Load-deflection relationships measuredat the height of the hydraulic piston (x = −370 mm)obtained from the tests and the Winkler model ap-proach with the three different expressions for the ul-timate soil resistance incorporated. D = 100 mm.P0 = 0 kPa. The initial modulus of subgrade reac-tion, k, is set to 40000 kN/m3.

Figure 26: Load-deflection relationships measuredat the height of the hydraulic piston (x = −370 mm)obtained from the tests and the Winkler model ap-proach with the three different expressions for theultimate soil resistance incorporated. D = 40 mm.P0 = 0 kPa. The initial modulus of subgrade reac-tion, k, is set to 40000 kN/m3.

In Fig. 24 the load-de�ection relationshipobtained by the two di�erent methodsare compared to the test results for the100 mm pile with P0 = 100 kPa. The �g-ure shows that when employing the formu-lation given by Hansen (1961) the lateralload is signi�cantly underestimated. Theapproach given by Georgiadis (1983) giveslarger lateral load, but still, the load is un-derestimated. Thus, neither of the formu-lations are able to take the e�ect of theoverburden pressure into account in a sat-isfactory way.

5.2 Evaluation of the Ultimate

Soil Resistance

As none of the evaluated methods for in-corporating the overburden pressure pro-duced satisfactory results the evaluation ofthe ultimate soil resistance is based on thetests without overburden pressure. Theexpression for the ultimate soil resistancerecommended by API (1993) is comparedto two upper bound expressions given inGwizdala and Jacobsen (1992) and Jacob-sen (1989), respectively, and a lower bound

solution given by Hansen (1961). The dif-ference of the four expressions is the shapeof the wedge formed in front of the pile,which is de�ned by the angle α. In API(1993), which is based on the formulationderived by Reese et al. (1974), α = ϕtr/2.For the upper bound formulations α = ϕtr

and α = ϕd, the latter given by Eq. 4. Forthe lower bound formulation α = 0.

tanϕd =sinϕpl · cosψ

1− sinϕpl · sinψ(4)

ϕd is the reduced angle of friction takingthe energy loss into account in the kine-matic admissible solution. ϕpl = 1.1 · ϕtr

is the plane angle of friction. The four ex-pressions are incorporated in the Winklermodel and the obtained load-de�ectioncurves are shown in Figs. 25 and 26 to-gether with the test results.

For the 100 mm pile with P0 = 0 kPa, cf.Fig. 25, the ultimate soil resistance givenby the horizontal asymptote of the curveis overestimated by both upper bound so-lutions. However the solution with the re-duced angle of friction is seen to give thebest estimate of the two. The lower boundsolution is seen to underestimate the ulti-

12


−1 0 1 2 3 4 5 6

x 105

−500

−450

−400

−350

−300

−250

−200

−150

−100

−50

0

Moment [Nmm]

Dep

th [m

m]

D = 100 mm, P0 = 0 kPa, y|

x = −370 = 35 mm

APIFLAC

−0.5 0 0.5 1 1.5 2 2.5 3

x 104

−200

−180

−160

−140

−120

−100

−80

−60

−40

−20

0

Moment [Nmm]

Dep

th [m

m]

D = 40 mm, P0 = 0 kPa, y|

x = −370 = 35 mm

APIFLAC

Figure 27: The moment curves obtained by meansof the Winkler model approach with the ultimate soilresistance calculated by the design regulation for-mulation incorporated and the numerical model forD = 100 mm and P0 = 0 kPa

Figure 28: The moment curves obtained by meansof the Winkler model approach with the ultimate soilresistance calculated by the design regulation for-mulation incorporated and the numerical model forD = 40 mm and P0 = 0 kPa

mate soil resistance. The expression givenin API (1993) predicts a lower capacitythan the upperbound solutions but stillthe capacity is overestimated compared tothe test results.

For the 40 mm pile the test results andthe ultimate soil resistance determined ac-cording to API (1993) is found to be inbetter agreement, cf. Fig. 26. However,the deviation between the results for the100 mm and the 40 mm pile must be seenin relation to the uncertainties when con-ducting the tests, where the largest un-certainties are related to the 40 mm pile,cf. Thomassen et al. (2010). Nevertheless,from the four expressions evaluated the ex-pression given in API (1993) is found togive the best estimate of the ultimate soilresistance even though the results deviatesfrom the laboratory tests.

6 Comparison of Design

Regulations and Numer-

ical Models

To establish whether the recommenda-tions in the design regulations API (1993)and DNV (1992) gives good estimations

of the pile-soil interaction for non-slenderpiles the design method and model resultsare compared. Again, only the resultsfrom the tests without overburden pres-sure are compared.

6.1 Evaluation of Bending Mo-

ment Distribution

The bending moment curves obtainedfrom the numerical models are comparedto the bending moment calculated bymeans of the Winkler model approach us-ing the formulation for the ultimate soilresistances given by API (1993).

In Figs. 27 and 28 the moment curvesfor the 40 mm and 100 mm piles, respec-tively, are shown. Both curves are shownfor a prescribed de�ection of 35 mm atx = −370 mm. For both piles it canbe seen that the maximum moment ob-tained by the numerical models is locatedapproximately 1/5L below the soil sur-face. The maximum moment obtainedfrom the Winkler approach is located ap-proximately 2/5L below the soil surface.The maximum moments found by the nu-merical models are higher than the onesobtained by the Winkler model approach.

13


0 5 10 150

2

4

6

8

10

12

Deflection, y [mm]

Soil

resi

stan

ce, p

[N

/mm

]D = 100 mm, P

0 = 0 kPa

xAPI

= 20 mmx

API = 40 mm

xAPI

= 60 mmx

FLAC = 20 mm

xFLAC

= 40 mmx

FLAC = 60 mm

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Deflection, y [mm]

Soil

resi

stan

ce, p

[N

/mm

]

D = 40 mm, P0 = 0 kPa

xAPI

= 20 mmx

API = 40 mm

xAPI

= 60 mmx

FLAC = 20 mm

xFLAC

= 40 mmx

FLAC = 60 mm

Figure 29: p−y curves for three depths from the nu-merical model and the design regulation formulationfor the 100 mm pile with P0 = 0 kPa.

Figure 30: p−y curves for three depths from the nu-merical model and the design regulation formulationfor the 40 mm pile with P0 = 0 kPa.

The maximum curvature of the moment-curves indicates the maximum soil pres-sure. At pile toe it can be seen that themoment obtained by means of API (1993)is curved whereas the modelled momentcurve has no curvature. This indicatesa di�erence in soil pressure and pile be-haviour. Due to the di�erences betweenthe measured and calculated moment dis-tributions it is recommended that testsare carried out on piles instrumented withstrain gauges in order to evaluate the cor-rect behaviour of the pile.

6.2 Evalutation of p�y Curves

The p − y curves recommended in thedesign regulations API (1993) and DNV(1992) are compared to the p − y curvesobtained by the numerical models. For thetwo tests without overburden pressure thecomparison is shown in Figs. 29 and 30 forthree di�erent depths.

The �gures show that the ultimate soil re-sistance recommended by API (1993) issigni�cantly lower than the resistance ob-tained by the numerical models, most sig-ni�cant for the 40 mm pile, cf. Fig. 30.This large di�erence is believed to oc-cur because the capacity in the numerical

models are overestimated compared to thetest results. Hence, the di�erence emergefrom uncertainties when determining thesoil parameters for low stress levels. InFig. 30 the initial sti�ness of the p − ycurves from the numerical models is seento be in agreement with the calculated ini-tial sti�ness from the curve at a depth of40 mm. In Fig. 29, however, the initialsti�ness of the p − y curves from the nu-merical models is in agreement with thecalculated initial sti�ness from the curveat 60 mm. Because the initial sti�nessfound by the numerical models are seen tobe constant with depth, in the evaluateddepth interval, and because of the di�er-ence in Fig. 29 and Fig. 30 it is di�cultto draw any clear conclusions in relationto the recommendations other than theagreement between the curves are poor.

7 Evaluation of Initial Sti�-

ness

In API (1993) and DNV (1992) the ini-tial sti�ness of the p− y curves, E∗py givenby Eq. 5, is assumed to vary linearly withdepth.

E∗py =dp

dy|y=0 = k · x (5)

14


0 5 10 15 20 25 30 350

100

200

300

400

500

600

700

800

900

1000

1100


Hor

izon

tal l

oad

[N]

D = 100 mm, P0 = 0 kPa

TestAPINon−linear

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

45


Hor

izon

tal l

oad

[N]

D = 40 mm, P0 = 0 kPa

TestAPINon−linear

Figure 31: Load-deflection relation ships measuredat the height of the hydraulic piston (x = −370 mm)obtained from the tests and the Winkler model ap-proach with the expressions for the ultimate soil re-sistance with both linear and non-linear formulationof the initial stiffness incorporated. D = 100 mm.P0 = 0 kPa. The initial modulus of subgrade reac-tion, k, is set to 40000 kN/m3.

Figure 32: Load-deflection relation ships measuredat the height of the hydraulic piston (x = −370 mm)obtained from the tests and the Winkler model ap-proach with the expressions for the ultimate soil re-sistance with both linear and non-linear formulationof the initial stiffness incorporated. D = 40 mm.P0 = 0 kPa. The initial modulus of subgrade reac-tion, k, is set to 40000 kN/m3.

k is the initial modulus of subgrade re-action and x is the depth below soil sur-face. k is according to the design regula-tions dependent only on the relative den-sity of the soil and, thus, independent ofthe pile properties.

Because of strict demands for the maxi-mum rotation of the wind turbines andthe resonance in serviceability mode theinitial sti�ness of the p − y curves are ofgreat importance. Therefore, it is of in-terest to �nd a correct expression for theinitial sti�ness in order to �nd the correctpile de�ection. Sørensen et al. (2010) pro-posed a non-linear formulation for the ini-tial sti�ness, cf. Eq. 6, based on numericalsimulations of full-scale monopiles in sand.

E∗py = a

(x

xref

)b( D

Dref

)c

ϕdtr (6)

a is a factor determining E∗py for(x,D,ϕtr) = (1 m, 1 m, 1 rad) andthe constants (b,c,d) = (0.6, 0.5, 3.6),a = 50000 kN/m2. xref and Dref are ref-erence values both of 1 m.

Similar to API (1993) the initial sti�nessincreases with increasing internal angle of

friction, however, with a slightly di�erentvariation. Contrary to API (1993) theinitial sti�ness increases with increasingpile diameter and varies non-linearly withdepth when using Eq. 6.

7.1 Comparison of Load-

De�ection Relationships

Eq. 6 is inserted in the formulation for thesoil resistance given in API (1993) and em-ployed in the Winkler model. Thereby,the load-de�ection relationships shown inFigs. 31 and 32 for the two piles withoutoverburden pressure are obtained.

For the 40 mm pile, cf. Fig. 32, it is dif-�cult to determine, which of the formula-tions gives the best �t to the test results asthese results are positioned in between thetwo. Moreover, because of the large uncer-tainties for this test, the results may notbe representative for the correct pile-soilbehaviour.

The uncertainties for the test results withthe 100 mm pile are smaller, and the re-sults are considered more accurate. Fig. 31

15


shows that the formulation by API (1993)overestimates the lateral capacity. Whenusing the non-linear formulation for theinitial sti�ness the lateral capacity is closerto the measured results, however, stilloverestimated. For the initial part of thecurves, the non-linear expression is seento be in better agreement with the resultsobtained in the laboratory tests and there-fore the non-linear expression is believedto give the best estimate of the variationof the initial sti�ness.

7.2 Comparison of p�y Curves

In order to evaluate the diameter e�ect thenon-linear formulation, Eq. 6, for the ini-tial sti�ness is evaluated against the initialsti�ness found from the p− y curves fromthe six numerical models. The factor c isevaluated by the ratios:

E∗py|D=100

E∗py|D=40=(D100

D40

)c

(7)

The initial sti�ness of the numerically ob-tained p − y curves, cf. Figs. 15, 16, and17, is found by linear regression of thedata until a de�ection of approximately0.2 mm. The slope of the linear regres-sion is assumed representative for the ini-tial sti�ness, and the obtained values forthe six models are shown in Tab. 4.

Table 4: The initial stiffness in N/mm2 read of thep − y curves obtained from the FLAC3D-models forthe two piles at different overburden pressures, cf.Figs. 15, 16, and 17.

0 kPa 50 kPa 100 kPa

E∗py|D=100 2.9 42.3 79.2E∗py|D=40 1.3 30.0 48.9

Table 5: Ratio of the initial stiffness of the p − ycurves obtained in the numerical models for the dif-ferent overburden pressures.

0 kPa 50 kPa 100 kPa

E∗py|D=100

E∗py|D=40 2.3 1.4 1.6

With c = 0.5, as proposed by Sørensenet al. (2010), the right side of Eq. 7 givesapproximately 1.6. If this value of c is cor-rect the ratio on the left side of the equa-tion should give values of approximately1.6 as well. In Tab. 5 the ratios of theinitial sti�ness from the numerical modelsare given. It can be seen that the ratiofor the models without overburden pres-sure deviates the most. The ratios for themodels with overburden pressure indicatesthat c = 0.5 is an appropriate value for thediameter e�ect on the initial sti�ness. Theresults in Tab. 5 indicate that larger un-certainties are related to the tests withoutoverburden pressure and, hence, low stresslevels in the soil.

8 Conclusion

In this paper the diameter e�ect onthe pile-soil interaction is evaluated bymeans of results from small-scale labora-tory tests, numerical models of the sametest setup, and existing theory. In total sixtests were carried out on piles with outerdiameters of 40 mm and 100 mm, respec-tively, and a slenderness ratio L/D of 5.In four of the tests overburden pressuresof 50 kPa and 100 kPa were applied. Thetests were modelled in the numerical �nitedi�erence program Flac3D, and the mod-els were calibrated against the obtainedload-de�ection relationships from the lab-oratory tests. From the numerical modelsp−y curves for the six tests were obtainedand used in a comparison with the recom-mended curves in the current design regu-lations. From the evaluations, the follow-ing conclusions can be drawn:

From the numerical models the recordedde�ection along the pile when subjected tolateral loading showed an increase in �ex-ible behaviour when overburden pressurewas applied. However, the primary de�ec-tion of the piles were caused by rigid bodyrotation.

16


To take the overburden pressure into ac-count in the Winkler model approach for-mulations proposed by Hansen (1961) andGeorgiadis (1983) was evaluated. How-ever, none of the formulations producedresults in agreement with the test results.

By means of the Winkler model approachthe formulations for the ultimate soil resis-tance given by API (1993), Hansen (1961),Gwizdala and Jacobsen (1992), and Ja-cobsen (1989) were compared to the load-de�ection relationships obtained from thelaboratory tests without overburden pres-sure. The comparison showed that the for-mulation given by the current design regu-lation API (1993) provided the best agree-ment to the test results even though theultimate resistance was overestimated.

Based on a comparison of the p− y curvesfor the two pile diameters it was foundthat the initial sti�ness, E∗py, is dependenton the pile diameter, i.e. the initial sti�-ness increases with increasing pile diame-ter. Further, the p− y curves obtained inthe numerical models indicated that E∗py

is dependent on the stress state as E∗py in-creases with increasing soil pressure alongthe pile and decreases with decreasing soilpressure.

The dependency of the diameter was eval-uated by means of E∗py obtained in thenumerical models and by the non-linearformulation suggested in Sørensen et al.(2010). The models with overburden pres-sure indicated that a value of c = 0.5 forthe diameter dependency is an appropriatevalue. By employing the formulation ina Winkler model approach the non-linearformulation was compared to the tests re-sults and it was found that this formula-tion was in better agreement with the re-sults than the formulations given in API(1993) and DNV (1992) where E∗py is as-sumed independent of pile diameter.

From the calibration of the numericalmodels, the evaluation of p−y curves, and

the evaluation of E∗py it was found thatconsiderable uncertainties are related tosmall-scale testing and the di�erent evalu-ations clearly indicates that the accuracyin small-scale testing is increased when in-creasing pile diameter and applying over-burden pressure.

9 Acknowlegdements

The project is associated with the EFPprogramme �Physical and numerical mod-elling of monopile for o�shore wind tur-bines�, journal no. 033001/33033-0039.The funding is sincerely acknowledged.

Bibliography

API (1993), Recommended Practice for

Planning, Designing and Constructing

Fixed O�shore Platforms � Working

Stress Design, American PetroleumInstitute.

Brødbæk, K., Møller, M., Sørensen, S.and Augustesen, A. (2009), `Evaluationof p-y relationship in cohesionless soil',DCE Technical Report No. 57 .Aalborg University.

DNV (1992), Foundations, Det NorskeVeritas. Classi�cation Notes No. 30.4.

Georgiadis, M. (1983), `Development ofp-y curves for layered soils',Proceedings of the Conference on

Geotechnical Engineering pp. 536�545.

Gwizdala, K. and Jacobsen, M., eds(1992), Bearing capacity and

settlements of piles, AalborgUniversity. ISBN 87-88787-10-9.

Hansen, J. B. (1961), `The UltimateResistance of Rigid Piles AgainstTransversal Forces', Bulletin No. 12 .Geoteknisk Institut.

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Ibsen, L. B., Hanson, M., Hjort, T. andThaarup, M. (2009), `MC-ParameterCalibration for Baskarp Sand No. 15',DCE Technical Report No.62 .Department of Civil Engineering,Aalborg University.

Jacobsen, M. (1989), Lærebog i

videregående Geotektik 1, Brud i Jord.

Lesny, K. and Wiemann, J. (2006),`Finite-Element-Modelling of LargeDiameter Monopiles for O�shore WindEnergy Converters', Geo Congress .

Poulos, H. and Hull, T. (1989), `The Roleof Analytical Geomechanics inFoundation Engineering', FoundationEngineering: Current principles and

practice, 2 pp. 1578�1606.

Reese, L. C., Cox, W. R. and Koop, F. D.(1974), `Analysis of Laterally LoadedPiles in Sand', O�shore Technology

Conference . Paper Number OTC 2080.

Sørensen, S., Ibsen, L. and Augustesen,A. (2010), `E�ects of diameter oninitial sti�ness of p-y curves forlarge-diameter piles in sand'. AalborgUniversity.

Sørensen, S., Møller, M., Brødbæk, K.,Augustesen, A. and Ibsen, L. (2009),`Numerical Evaluation ofLoad-Displacement Relationships forNon-Slender Monopiles in Sand', DCETechnical Report No. 80 . AalborgUniversity.

Thomassen, K., Roesen, H. R., Ibsen, L.and Sørensen, S. (2010), `Small-ScaleTesting of Laterally Loaded,Non-Slender Monopiles in Sand', ShortCandidate Project.

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Recent publications in the DCE Technical Report Series Brødbæk, K. T., Møller, M., Sørensen, S. P. H. and Augustesen, A. H. (2009) Review of p-y relationships in cohesionless soil, DCE Technical Report No. 57, Aalborg University. Department of Civil Engineering. Sørensen, S. P. H., Møller, M., Brødbæk, K. T., Augustesen, A. H. and Ibsen, L. B. (2009) Evaluation of Load-Displacement Relationships for Non-Slender Monopiles in Sand, DCE Technical Report No. 79, Aalborg University. Department of Civil Engineering. Sørensen, S. P. H., Møller, M., Brødbæk, K. T., Augustesen, A. H. and Ibsen, L. B. (2009) Numerical Evaluation of Load-Displacement Relationships for Non-Slender Monopiles in Sand, DCE Technical Report No. 80, Aalborg University. Department of Civil Engineering. Thomassen, K., Roesen, H. R., Ibsen, L. B. And Sørensen, S. P. H. (2010) Small-Scale Testing of Laterally Loaded Non-Slender Monopiles in Sand, DCE Technical Report No. 90, Aalborg University. Department of Civil Engineering.

ISSN 1901-726X DCE Technical Report No. 91

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