Design Of Axially And Laterally Loaded Piles For The .
Indian Geotechnical Conference – 2010, GEOtrendzDecember 16–18, 2010IGS Mumbai Chapter & IIT BombayDesign of Axially and Laterally Loaded Piles for the Support ofOffshore Wind Energy ConvertersAchmus, M.Professore-mail: achmus@igbe.uni-hannover.deInstitute of Soil Mechanics, Foundation Engineering and Waterpower Engineering/LeibnizUniversity of Hannover, Hannover, GermanyABSTRACTA large number of offshore wind farms is being planned in the North Sea and the Baltic Sea in Europe and will beerected in the coming years. Possible foundation structures for water depths of up to 50m are jacket and tripodstructures, i.e. structures with three or four mainly axially loaded piles, and for moderate water depths alsomonopiles, which are mainly horizontally loaded large diameter piles. A special aspect in design is the questionhow effects induced by cyclic loading of these foundation piles can be considered adequately. For cyclic axiallyloaded piles degradation of pile capacity might occur, and for cyclic horizontally loaded piles stability has to beproved and an increase of permanent deformation over the lifetime is to be expected. The paper in hand presentscalculation approaches for the piles under axial and lateral loading and outlines possible design procedures withconsideration of cyclic load effects.1. INTRODUCTIONIn the North Sea and the Baltic Sea in Europe a vast numberof offshore wind farms are being planned and several havealready been installed in recent years. Up to now, in mostcases wind farms were erected in moderate water depths(less than 20m) and monopile foundations have been builtas support structures for the wind tower and the turbine. Amonopile consists of a single open steel pipe pile of largediameter which is driven into the seabed. Diameters of upto 5m have been realized recently. The tower is connectedto the monopile by a transition piece located above the waterlevel (Fig. 1, left). This type of foundation transfers theloads from wind and waves mainly by horizontal stressesinto the ground and is believed to be suitable for waterdepths of up to 25m.In the German parts of North Sea and Baltic Sea waterdepths of up to 50m exist. For such large water depths steelframe structures (jackets with four legs or tripods with threelegs) can be used, which are supported by four or threepiles located in the edges of the construction (Fig. 1, right).Regarding the lengths of these piles, the axial (compressiveor tensile) loads induced by wind and waves are designdriving.Design methods and experience with offshore pilesexist mainly from structures built by the oil and gas industry.However, the loading conditions for offshore wind millfoundations are different. The vertical loads are muchsmaller than for oil or gas platforms, and thus the horizontalloads are of similar magnitude compared to the verticalloads. This means that the extremely cyclic nature of windand wave forces is much more important than for very heavystructures. Due to that, consideration of cyclic load effectsis extremely important.Regarding monopiles, on one hand the question,whether usual calculation methods (p-y method) can beused for piles of very large diameter, has to be answered.On the other hand it has to be investigated how the systemstability under cyclic loads can be proved and howaccumulated deformations due to cyclic loading can bepredicted. The latter is particularly important, since therequirements regarding the stiffness of such structures arevery strict. A maximum rotation of the pile head of 0.5 isusually demanded.Regarding axially loaded piles an important questionis how the axial ultimate pile capacity can be predictedwith sufficient accuracy. The ß-method commonly used inoffshore design (e.g. API, 2000) is known to either overor underestimate pile capacities, dependent on the boundaryconditions. Recently, CPT-based methods have beendeveloped as an alternative. Another open question is how
94the degradation of skin friction to be expected due to cyclicaxial loading can be accounted for in the design.In the following, calculation approaches for the abovementioned problems are presented and critically assessed.Moreover, problems and possibilities regarding theconsideration of cyclic load effects are presented.M. Achmuspile diameter D and on the angle of internal friction ϕ’of the sand:p us (c1 z c 2 D ) γ ' z(1a)p ud c3 D γ ' z(1b) The first mentioned equation applies to small depths (pus)and the second equation to larger depths (pud), the smallerof both values is to be considered. The influence of theinternal friction angle is described by the factors c1, c2and c3, which are given in API (2000) dependent on theangle of internal friction of the sand. The p-y-curve is described by the following equation: kz y p A p u tanh A pu Fig. 1: Schematic Sketches of a Monopile (left) and a JacketFoundation (right)2. DESIGN OF MONOPILESFor monopiles in sand soils the proof of serviceability underhorizontal loading is usually design-driving. A largestiffness under operational load is demanded in order toensure a natural frequency of the system which is higherthan the main excitation frequency. Also, the deflectionsand rotations at mudline must be small to enable a soundoperation of the wind turbine. Moreover, the allowablepermanent rotation of the monopile system is rather small.p-y MethodThe usual design procedure for foundations of offshore windenergy converters in Germany is given in the GermanischeLloyd rules and regulations (GL, 2005). In theseregulations, concerning the behaviour of piles underhorizontal loading reference is made to the regulation codeof the American Petroleum Institute (API, 2000). TheScandinavian guidelines (DNV, 2004) also refer to the APIcode. In the API code the p-y method is recommended forthe design of horizontally loaded piles.In principle, the p-y method is a subgrade modulusmethod with non-linear and depth-dependent loaddeformation (p-y) charac-teristics of the soil springs. API(2000) describes the construction of p-y-curves for soft andstiff clay as well as for sandy soils. According to API,p-y-curves for sandy soils can be derived as follows: The maximum mobilized soil reaction force per unitlength of the pile pu depends on the regarded depth undersea bed z, the submerged unit weight of the soil γ’, the(2)with A 3.0 0.8 z / D 0.9 for static loading and A 0.9for cyclic loading.Here p is the soil resistance per unit length of the pileand y is the horizontal deflection. The parameter k alsogiven in API (2000) describes the initial modulus ofsubgrade reaction and is dependent on the relative densityID and with that on the angle of internal friction.The Equations (1) and (2) are mainly based oninvestigations of Reese and Cox (Reese et al. 1974). Theytested a 21 m long steel tube pile having a diameter of 61cm under different loads and then evaluated their results.For cyclic tests, a maximum number of 200 load cycleswas realized. The correction factor A according to Equation(2) was adjusted based on the measurements done.In a similar manner, also p-y curve approaches forcohesive soils are given in API (2000) or in the literature.Here, the undrained shear strength and a strain valuedetermined in a UU triaxial test are used as the centralparameters describing the soil behaviour. Static and cyclicloading is also considered by different factors.The application of these methods worked satisfactorilyin offshore practice over many years, whereby the collectedexperiences only refer to piles with diameters up to about 2or 2.5m. According to Wiemann et al. (2004) the subgrademodulus for piles of large diameter is overestimated withthe API method. They suggested a diameter-dependentcorrection factor of the initial subgrade modulus k. Alsothe author of the paper in hand showed that the deflectionsof large-diameter piles under static loading areunderestimated by the API method (Achmus et al., 2007,Abdel-Rahman & Achmus, 2005). Recently, Soerensen etal. (2010) proposed an approach to decrease the p-y curvestiffnesses with respect to the pile diameter.Regarding stability under cyclic loads and theaccumulation of monopile displacements due to cyclic
Design of Axially and Laterally Loaded Piles for the Support of Offshore Wind Energy Convertersloading to be expected over the lifetime of the foundationstructure, the p-y method is not suitable, since the numberof load cycles is not taken into account. As mentioned above,the cyclic load approach was found by execution of atmaximum 200 – and in most cases much less – load cycles.Numerical ModelingA three-dimensional (3D) finite element model wasestablished in order to analyze the behavior of monopiles.The computations were carried out using the finite elementprogram system ABAQUS.The most important issue in geotechnical numericalmodeling is the simulation of the soil stress-strainbehaviour. In the case of monotonic loading, essentialrequirements on the material law are the consideration ofthe non-linear, stress-dependent soil stiffness and theconsideration of possible shear failure. An elasto-plasticmaterial law with Mohr-Coulomb failure criterion was used.The soil stiffness is herein represented by a stiffnessmodulus for oedometric compression ES and a Poisson’sratio ν. To account for the non-linear soil behaviour, a stressdependency of the stiffness modulus was implemented asfollows:E S κ σ at σ σ at λ(3)Herein σat 100 kN/m2 is a reference (atmospheric)stress and σ is the current mean principal stress in theconsidered soil element. The parameter κ determines thesoil stiffness at the reference stress state and the parameterλ rules the stress dependency of the soil stiffness.A typical finite element mesh is shown in Fig. 2. Theinteraction behaviour between the monopile and the sandsoil is simulated using contact elements. The maximumshear stress in the contact area is determined by a frictioncoefficient.Fig. 2: Finite Element Mesh95Effect of Monopile DiameterThe stress-dependency of the stiffness modulus given byEquation (3) is often used in soil mechanics. However, nodirect experience exists on the magnitude of the twoparameters (κ, λ) to be used in the calculation ofhorizontally loaded piles. In order to calibrate theseparameters in connection with the numerical model, firstlymonopiles of smaller diameters were investigated (see alsoAchmus et al. 2008). For diameters of up to 2.5m the p-ymethod is known to give a suitable estimation of piledeflection. Thus the numerical results could be comparedwith the results of the API p-y method for calibration. Thecalculations with the p-y method were carried out by meansof the LPILE program.Fig. 3 left shows the deflection lines for monopileswith different diameters in homogeneous dense sand,derived once by the p-y method and once by the numericalmodel. To ensure a similar pile behaviour, different pilelengths were examined, and typical service loads for thedifferent pile geometries were applied.The stiffness parameters of the numerical model werecalibrated by comparison with the results of the p-y methodfor the pile with a diameter of 1.5m. Thus, the deflectionlines of both methods are almost identical for this case.The results show that for larger diameters the p-y methodunderestimates the pile deflections. For a pile with adiameter of 4m, the deviation is 27% with respect to pilehead deflection. For the pile with a diameter of 7.5m, therespective deviation is 38%.Fig. 3 right compares the numerically obtained piledeflection lines for the D 7.5m pile to the results obtainedby the above mentioned approaches of Wiemann et al.(2004) and Soerensen et al. (2010). The results obtainedhere are in good agreement with the Wiemann approach,whereas the approach of Soerensen et al. predicts an evenlarger diameter effect.Fig. 3: Comparison of the Pile Deflection Lines for DifferentPile Diameters, Calculated by FE and p-y Method
96M. AchmusEffect of Cyclic LoadingIt is known from different experimental investigations thatthe deflections of a horizontally loaded pile increase undercyclic loading. As an example, model test results of Hettler(1981) for flexible piles in homogeneous sand are shownin Fig. 4.In general, the increase of head deflection can bedescribed by the following equation:y N y1 f N ( N )(4)Here yN and y1 are the horizontal pile head deflectionsafter N load cycles and after 1 load cycle (static loading),respectively. fN(N) is a function which describes the increaseof deflections. As long as the cyclic load amplitude is wellbelow the ultimate pile capacity, sedation behaviour can beexpected, which means that the deflection rate decreaseswith increasing number of load cycles. The most commonfunctions of displacement of structures under cyclic loadingthat are found in literature are of the exponential type suchas Equation 5 (e.g. Little & Briaud 1988) and of logarithmictype such as Equation 6 (e.g. Hettler 1981):fN N mf N 1 t ln N(5)(6)Here m and t are empirical degradation parameters.Assuming that these parameters (m and t) are constants,Equations 5 and 6 imply that the function of load cyclenumber is independent of the load amplitude. Peralta &Achmus (2010) found, based on model tests, that theexponential function of displacement increase with respectto number of load cycles better fits the cyclic displacementcurves of almost rigid piles while the logarithmic functionbetter fits the displacement curves of flexible piles.in many projects rigid clamping of the pile in the subsoilunder static extreme loads is demanded. This means that thedeflection line of the pile must have two zero deflectionpoints, i.e. no or negative pile toe deflection (zero-toe-kickcriterion), or it must at least have a vertical tangent (verticaltangent criterion). The background of these requirements isthe more or less intuitive idea that a pile which is clamped inthe soil under extreme load would hardly be significantlyloosened by cyclic load actions. However, for monopiles withvery large diameters and thus large bending stiffnesses, inparticular the zero-toe-kick criterion, but also the verticaltangent criterion lead to very long embedded pile lengths.Thus, the suitability of these criteria has to be proved.Stiffness Degradation MethodThe stiffness degradation method (SDM) developed by theauthor and his co-workers is a method based on acombination of a finite element simulation of the pile-soilinteraction and an evaluation of drained cyclic triaxial tests.In cyclic triaxial tests, the accumulation of plasticstrains with the number of cycles under different loadingconditions can be observed. This increase of plastic straincan be interpreted as a decrease in soil secant stiffness.Assessing the stress conditions in the distinct elements andintroducing the stiffness degradation obtained bycomparison with the cyclic test results in the finite elementmodel yields the accumulated deformations of the pile-soilsystem. This is the basic concept of this model.The numerical model of a monopile foundation undermonotonic lateral load presented above is used as a basisfor cyclic analysis. The degradation stiffness approach toaccount for cyclic loading effects is elucidated in Fig. 5. Ina cyclic triaxial test, an increase of the plastic axial straincan be observed. Assuming the elastic strain to be negligible,Es1and Nth cycle EsN can be presented by the plastic axialstrains after first cycle εacp,N 1 and after Nth cycle εacp,Naccording to the following equation:t h ed e g r a d a t i o nr a t eo fs e c a n ts t i f f n e s sa f t e rf i r s tc y c l eaE sN ε cp , N 1 aE s1ε cp , N(7)Fig. 4: Model Test Results of Hettler (1981)These empirical equations take the number of loadcycles explicitly into account. However, only one parametergoverns the displacement accumulation, and it is more orless unknown how this parameter is affected by soil,geometry and loading conditions.In common practice, substitute design requirementsregarding the pile behavior under monotonic (static) extremeload are used. To limit the deformations due to cyclic loading,Fig. 5: Degradation of Secant Modulus Under Cyclic Loadingin the Pile-soil Model (Schematic)
Design of Axially and Laterally Loaded Piles for the Support of Offshore Wind Energy ConvertersThe accumulation of plastic strains in a cyclic triaxialtest can be estimated from a semi-empirical approach ofHuurman (1996). With that, the degradation of stiffnesscan be described using two material parameters b1 and b2as follows:97models A and B. Poisson’s ratio is assumed to remainconstant in the three discrete finite element models.ab2E sN ε cp, N 1 a N b1 ( X )E s1ε cp, N(8)Here N is the number of load cycles and X is the cyclicstress ratio defined by Huurman (1996) for cohesionlessmaterial as follows:X σ 1,cycσ 1, sf(9)where σ1,sf is the major principal stress at static failure stateand σ1,cyc is the major principal stress for the cyclic stressstate under consideration. The cyclic stress ratio is thusdependent on the confining pressure and on the cyclic stresslevel.From cyclic triaxial test results documented in theliterature, typical regression parameters b1 and b2 werefound for dense sand to be b1 0.20, b2 5.76 and formedium dense sand b1 0.16, b2 0.38 (Kuo 2008).A problem to be dealt with is that the Equations (7)and (8) are valid for triaxial test conditions with isotropicinitial stress conditions and a constant confining pressureσ3 during cyclic loading. In the pile-soil system, the initialstress conditions (before application of the horizontal load)are anisotropic and the minor principal stress in theelements as well as the direction of the principal stressaxes in general change with the application of the load. Toovercome this problem, a characteristic cyclic stress ratioXc is defined here asXC Fig. 6: Schematic Sketch of the Determination of DegradationStiffness in the Pile-soil SystemBy back-calculation of model tests it was shown thatthe method can well capture permanent deformationresponses of a soil element and of a pile-soil system(Achmus et al. 2009, Kuo 2008).In Fig.7, calculation results are depicted for a monopilewith a diameter of 4m embedded in dense sand. A steelpipe pile with a wall thickness of 46mm was considered. Ahorizontal load was applied with a moment arm of 37.9m.The load magnitude was chosen to 40% of the ultimateload. The deflection lines depicted in Fig. 7 top show thatthe monopile with an embedded length of 15m behavesalmost rigid, whereas the pile with an embedded length of21m behaves more flexible.X (1) X (0)(10)1 X (0)Here the index (1) means the cyclic stress ratio at loadingphase and the index (0) means at unloading phase (cf Fig.6). At the initial (and unloading) phase, only the verticalload V due to the tower weight is considered, and the lateralload H is applied subsequently in the loading phase. Thecharacteristic cyclic stress ratio is derived from thedifference between the stress ratios in the loading and theunloading phase. Due to the denominator in Equation (10)this value varies from 0 to 1. The accumulation of plasticstrain and the degradation of stiffness of the soil elementcan be obtained from Eq. (8) by replacing X by Xc.In the last step of the simulation (model C in Fig. 6),the deformation response of the system is analyzed usingthe degradation stiffnesses obtained from evaluation ofFig. 7: Deflection Lines of Monopiles D 4m in DenseSand (Top) and Results of the Stiffness DegradationMethod (Bottom)
98M. AchmusThe stiffness degradation method was applied, usingthe typical parameters b1 and b2 for dense sand stated above.In Fig. 7 bottom the relative increases (with regard to thestatic deflection) of pile head displacement are shown.These curves can be interpreted as a measure of the cyclicperformance of a pile. The longer flexible pile (L 21m)performs better than the shorter and almost rigid pile(L 15m). Thus, the funct
A maximum rotation of the pile head of 0.5 is usually demanded. Regarding axially loaded piles an important question is how the axial ultimate pile capacity can be predicted with sufficient accuracy. The ß-method commonly used in offshore design (e.g. API, 2000) is known to either over-or underestimate pile capacities, dependent on the boundary
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Chapter 2 Axially Loaded Members . Structural components subjected only to . tension. or . compression: solid bars with straight longitudinal axes, cables and coil springs – can be seen in truss members, connecting rods, spokes in bicycle wheels, columns in buildings, and struts in aircraft engine mounts. 2.2 Changes in Lengths of Axially .
soil resistance but treat the pile as a linear, elastic beam. The assumption of pile linearity may not be valid in many cases. This paper considers the effect of this assumption on the behavior of laterally loaded piles and introduces a method for representing nonlinear pile bending behavior in the analysis of laterally loaded piles.
DESIGN OF AXIALLY LOADED COLUMNS σc (Mpa) fy λ Euler curve Design curve with α 0.003 200 00 1 50 100 150 Fig.2 Robertson’s Design Curve Robertson evaluated the mean values of α for many sections as given in Table 1: Table1: α values Calculated by Robertson Column
The static and free vibration analyses of axially functionally graded . materials with a continuously varying function in desired directions. The grading of material properties increases the strength of functionally graded materials under sudden varying loads or temperature changes [12,13]. Functionally graded materials are produced with low .
CIVL 4135 Chapter 3. AXIALLY LOADED MEMBERS 45 3.3.1. Example 1 Given: 4 # 8 bars Assume: fc′ 4000 psi fy 40 ksi area of steel 4(area of # 8 bars) 4(0.79) 3.16in2 (see ACI 318 - ba
ABB/ BU Machines / HV Induction motors IEC catalogue / Standard motors EN 12-2007 15 1 Bearings The motors are normally fi tted with single-row deep groove ball bearings as listed in the table below. Axially-locked bearings All motors are equipped as standard with an axially-locked bearing at the D-end.
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