Evaluation of p-y Approaches for Large Diameter Monopiles in Sand Klaus Thieken , Martin Achmus, Katrin Lemke, Mauricio Terceros Institute for Geotechnical Engineering, Leibniz University Hannover Hannover, Lower Saxony, Germany
ABSTRACT For the design of monopile foundations, the soil resistance is usually modeled by the subgrade reaction method. The commonly used p-y approach described in the offshore guidelines is generally assumed to be sufficiently accurate for slender piles with diameters D ≤ 2 m. However, several investigations indicate that the pile deflections of large diameter monopiles are underestimated for extreme loads but overestimated overestimated for small operational loads. A three dimensional finite element model is presented to evaluate the currently used p-y approach for piles in sand under static loading conditions in dependence on the pile dimensions and soil’s relative density. In addition, modified p-y formulations of Wiemann et al. (2004) and Kirsch et al. (2014) to account for the effect of the pile diameter are compared to the FE results .
KEY WORDS: wind energy converter, monopile, p-y curve, sand, foundation stiffness, small strain stiffness
INTRODUCTION Monopiles are currently the preferred support structure for offshore wind energy converters (OWEC) in water depths less than thirty meters. The cost-effective and relative simple manufacturing and installation process is a great advantage in comparison to lattice structures like jackets or tripods. A monopile foundation (cf. Fig. 1) consists of a single steel pipe pile driven into the seabed. These large diameter monopiles have to withstand large and discontinuous horizontal forces H and bending moments M caused by wind and wave actions. Large water depths and sizable wind turbines necessitate large pile dimensions. Pile diameters more than D = 6 m have already been realized and diameters up to D = 8 m are currently planned. The relative pile length, i.e. the ratio of embedded pile length L to diameter D, lies usually around L/D = 5. In the design of the wind turbine, the ultimate limit state (ULS) and the serviceability limit limit state (SLS) design pro of have to be fulfilled. In the ULS proof, a sufficient soil resistance has to be guaranteed to ensure the structural safety of the wind turbine. Thereby, effects of cyclic loading have to be considered, i.e. degradation in soil resistance has to be accounted for. For the SLS proof, the deflections and rotations under the characteristic extreme load cases (hereinafter: extreme loads) have to stay below certain serviceability limits. In that, also the accumulation of deflection due to cyclic loading has to be considered (cf. Achmus et al., 2008). Beside these geotechnical design
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proofs, the stiffness of the monopile foundation system under operational loads has to be determined. Considering this stiffness in a dynamic analysis of the whole OWEC structure, it has to be ensured that the eigenfrequencies of the wind turbine have a sufficient distance to the main excitation frequencies of the dynamic loading. In that, neither an overestimation nor an underestimation of foundation stiffness is in general conservative. An incorrect estimation of foundation stiffness results in an increase of uncertainties and leads to additional but unnecessary costs. Moreover, in the worst case it could have a negative influence on the structural lifetime of the structure (Kallehave et al., 2012).
Fig. 1: Schematic sketch of an OWEC with monopile foundation
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In all design proofs it is common practice to use the subgrade reaction method to simulate the occurring soil resistance p in dependence on the horizontal displacement y. The soil is herein replaced by a number of spring elements along the pile shaft (cf. Fig. 1). In most cases the so-called p-y method, recommended in the offshore guidelines (OGL) of the American Petroleum Institute (API, 2007) and Det Norske Veritas (DNV, 2013), is used. Based on experience in the oil and gas industry, the p-y method seems to be sufficiently accurate for slender piles with diameters up to two meters. For larger pile diameters, several investigations showed that the horizontal deflections of monopiles are underestimated for extreme loads (cf. Achmus, 2011). In contrast, experience from operating offshore wind farms with monopiles indicate that the foundation stiffnesses for small operational loads are significantly underestimated (Hald et al., 2009), (Kallehave et al., 2012). Investigations on the accuracy of predicting the ultimate resistance in dependence on the pile diameter are not known by the authors. However, Thieken et al. (2014) showed that the ultimate bedding resistance of the p-y method is, independent of the pile diameter, conservative in conjunction with the German standard for earth pressure (DIN 4085, 2007). The determination of structural loads in a dynamic analysis of the whole OWEC system is usually carried out by considering a linear elastic system. Therefore it is necessary to derive constant spring stiffness values from the non-linear system which characterizes the system behavior under usual dynamic operational loads. The spring stiffness can be determined with a typical operational load by calculating the secant stiffness in the considered depth from the resulting p and y values of the “static” p-y curves (E py = p/y). However, assuming that the deflections under such operational loads remain small, the initial bedding stiffness of the p-y curves is used in most cases. A degradation of initial bedding stiffness due to a repeated (cyclic/ dynamic) loading is in general not taken into account. This assumption is supported by model tests of LeBlanc et al. (2010), which indicated that the un- and reloading system stiffness do not decrease, but even slightly increase with the number of load cycles. In contrast, the effects of cyclic loading have to be considered in the ULS and the SLS design proof. Therefore, p-y curves which account for these effects have to be used. However, these “cyclic” p -y curves as given by the OGL or the EAP recommendations (EAP, 2012) are based on the “static” p -y curves, i.e. consider the cyclic load case by modifying the static curves. A deficient formulation of the static p-y curves will therefore not only influence the foundation stiffness for the dynamic analysis but also the estimated horizontal deflections and the ultimate resistance of the monopile.
k OGL z y A p u
p A p u tanh
(1)
Here, A ∙ pu is the maximum bedding resistance which depends on the internal friction angle φ’, the overburden pressure γ’ and the pile diameter D. A is a calibration factor which is specified to A = 3.0 - 0.8 ∙ (z/D) ≥ 0.9 for static loading and A = 0.9 for cyclic loading. z is the depth below ground surface and k OGL is an initial stiffness coefficient, which depends on the angle of internal friction φ’ or the relative density of the sand, respectively. A goo d approximation of k OGL for depths below the water table (cf. Eq. 2) is introduced by Augustesen et al. (2009). Analyzing Eq. 1, it can be easily derived that k OGL∙z is the initial slope of the p -y curve, which is also termed the initial bedding stiffness E py. k OGL MN / m³ 0.008085 2.45 26.09
for 29 ' 45
(2)
The mentioned p-y approach was derived based on several model and field tests (Murchison & O’Neill, 1984). The most famous field test and also the largest one with a pile diameter of D = 0.61 m was conducted at Mustang Island near to the Gulf of Mexico in 1974 (Reese et al., 1974; Cox et al., 1974; see also section “Back -calculation”). It is a prevalent misunderstanding that the p-y curves which Reese et al. developed based on this test are identical to the approach presented in the OGL. Actually, the two p-y approaches differ significantly, even if the initial stiffness E py and the ultimate resistance p u are almost identical. Altogether, the comparative study of Murchison & O’Neill included ten static and five cyclic field tests of different kinds. Steel pipe piles and I-profiles as well as square precast concrete piles and tapered timber piles, all of various dimensions, were included in the study. The test results were compared to a total of five different p-y approaches. For the evaluation of the approaches, the differences in the horizontal resistances and the corresponding bending moments were analyzed for a horizontal displacement y = 0.01∙D. The respective deviations were summed for every p-y approach and compared. Concluding, it was found that the current p-y approach is suited best for the design. It has to be noted, that no explicit consideration of the influence of the diameter was performed. It is remarkable that the foundation stiffness of the largest and best instrumented pile tests at “Mustang Island” is overest imated significantly by the OGL method (cf. Fig. 5 and 6). As the p-y approach of Reese et al. was calibrated only on the “Mustang Island” field tests, it is understood that this approach results in a much softer behavior.
To evaluate the currently used static p-y approach according to the offshore guidelines for the design of horizontal loaded piles of various dimensions, three dimensional numerical simulations of a monopile foundation in homogenous sand are presented. A comprehensive study on the discrepancy between the numerical results and the results of the p-y approach of the OGL is depicted. Furthermore, also modified p-y approaches proposed in literature which shall account for the effects of a large pile diameter are compared to the numerical results.
EVALUATED P-Y APPROACHES All suggested p-y curves have nonlinear, soil- and depth-dependent load-displacement characteristics. The p-y approach for non-cohesive soil according to the offshore guidelines (OGL) is given as follows: Fig. 2: Comparison of p-y curves for a small and a large diameter pile
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Fig. 3: Quotient of initial stiffness coefficients k modified / k OGL; very dense sand (top); medium dense sand (bottom) An exemplary comparison of the p-y curves for a small and a large diameter pile in a single depth is presented in Fig. 2. The p-y approach by Reese et al. divides the p-y curve into four sections. In the first section, the p-y curve is identical to the OGL formulation, as the identical initial bedding stiffness is assumed. In the second section, a parabolic curve is proposed crossing over to a linear course. The linear increase is limited by the ultimate bedding resistance, which is again almost identical to the OGL formulation. For more details with regard to the construction of the p-y curves see Reese et al. (1974). A modification of the OGL method to account for an overestimation of bedding stiffness under extreme loads is proposed by Wiemann et al. (2004). Wiemann recommends reducing the initial stiffness of the OGL p-y curves while considering the same basic approach (cf. Eq. 1). The initial stiffness coefficient k Wiemann depends on the initial stiffness coefficient according to the offshore guidelines k OGL, the pile diameter D and the soil stiffness exponent “a” as follows:
D k Wiemann k OGL ref D
41a 4a
(3)
The reference pile diameter is set identical to the diameter of the “Mustang Island” test D ref = 0.61 m. Hence, the p-y curve in Fig. 2 (top) is identical to the curve of the OGL. The exponent is recommended to a = 0.5 for very dense sand and a = 0.6 for medium dense sand. In Fig. 3 (left), the resulting k Wiemann are compared to the corresponding values of the offshore guidelines k OGL. It becomes obvious, that the stiffness coefficient from the Wiemann et al. formulation becomes considerably smaller with increasing diameter D. A further modified initial stiffness formulation to counteract the overestimation of bedding stiffness for extreme loads is introduced by Sørensen (2012). Here, the initial stiffness coefficient k Sørensen depends on the depth z, the soil stiffness Es and the pile diameter D (cf. Eq. 4 ).
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k Sørensen
b
z D a z z ref Dref 1
c
d
E s E s,ref
(4)
For the dimensionless constants b, c and d the values b = 0.3, c = 0.5 and d = 0.8 are recommended. The reference stiffness a = 1 MPa is valid for a reference depth zref = 1 m, a reference pile diameter Dref = 1 m and a reference soil stiffness E s,ref = 1 MPa. The soil stiffness Es is considered likewise to the numerical simulations by using Eq. 14. It is understood, that differing soil stiffnesses would cause differing reductions in the initial stiffness coefficient k. However, the chosen soil stiffness formulation is assumed to give reasonable results at least for locations of OWECs in the North Sea. An overview of the quotient k Sørensen / k OGL is given in Fig. 3. Evidently, the reduction of the initial stiffness coefficient is even larger than it results from the Wiemann et al. formulation. Therefore, also the Sørensen’s formulation leads to significantly “softer” p-y curves than it results from the p-y approach of the OGL. Please note that Sørensen proposed a comparable formulation already two years before (Sørensen et al., 2010) which yields, however, differing results (cf. Achmus et al., 2014). Kallehave et al. (2012) suggested a modified initial stiffness formulation (Eq. 5) to avoid an underestimation of stiffness under small operational loads and should therefore also be valid for a primary initial loading in general (cf. Thieken & Achmus, 2013).
k Kallehave
1 z
m
k OGL
z D z 0 z 0 D 0
0.5
(5)
The recommended initial stiffness coefficient depends on the initial bedding stiffness according to the offshore guidelines (k OGL∙z0) in a reference depth z0 = 2.5 m. The dimensionless parameter m, which
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rules the course with depth z, is suggested to be 0.6. The reference diameter is given to the diameter of the “Mustang Island” test D0 = 0.61 m. Overall, the p roposed formulation results in a considerably “stiffer” behavior than the formulation of the offshore guidelines. The resulting initial stiffness coefficients are also compared to the values of the offshore guidelines (cf. Fig. 3). In comparison to the OGL method, a strong increase can be found especially in small depths below the surface z.
In the following, the modified formulations of Wiemann et al. (2004) and Kirsch et al. (2014) shall be evaluated with the results of numerical simulations. The approaches of Sørensen (2012) and Kallehave et al. (2012) were already compared to these numerical results in Achmus et al. (2014). Concluding, both modified initial stiffness formulations were found to be not generally suitable for the design of large d iameter monopiles.
Kirsch et al. (2014) proposed a p-y approach to account for an underestimation of foundation stiffness under small operational loads and an underestimation of pile deflection for extreme loads simultaneously. In contrast to the p-y formulations presented before, the Kirsch et al. formulation shall also include the effects of a cyclic loading. Therefore, the results of this approach are not completely comparable to the considered “static” approach of the OGL and the conducted numerical simulations. However, based on the assumption that the foundation stiffness due to small dynamic loading does not degrade with the number of load cycles, the approach should be able to catch the foundation stiffness for small load levels. Regarding the load bearing behavior for larger load levels, the predicted pile deflections should be larger than it results from the “static” calculations as the Kirsch et al. formulation purports to account for an accumulation of pile deflection due to cyclic loading.
NUMERICAL MODEL
Because of the consideration of cyclic loading, the approach is based on the “cyclic” p-y curves of the OGL (identical k OGL, A = 0.9, cf. Eq. 1). Furthermore, the ultimate bedding resistance p u and the basic value of the initial bedding stiffness coefficient k red (using Eq. 2) are determined based on a reduced friction angle φ’ red (cf. Eq. 6). Here, the diameter D must be set in meter and the internal friction angle φ’ in degree to obtain φ’ red also in degree.
'red '0.50 D 2
A three-dimensional numerical model of a monopile foundation system is developed using the finite element program PLAXIS 3D (Brinkgreve et al., 2013). With regard to the symmetry of both geometrical and loading conditions, only one half of the monopile foundation is modeled in order to reduce computational effort. Preliminary analyses focused on the mesh fineness and model dimensions to reach sufficiently accurate results and avoid an impact of the boundary conditions. The reference system is discretized with 73407 elements. The mesh is refined in a volume which is defined by surfaces located at a distance of 1.5∙D around the pile. As PLAXIS simulates the cylindrical pile with triangular elements, a large number of elements in one row is necessary to avoid a peak out at the corners. Through the refinement close to the pile, 24 elements per row could be reached. An exemplary mesh of the finite element model with is presented in Fig. 4.
(6)
Beside k red, the initial stiffness coefficient of the Kirsch et al. formulation k Kirsch depends on the ratio of dynamic to static soil stiffness modulus Esd / Es and the ratio of bedding resistance to ultimate bedding resistance p / p u : k Kirsch
p E k red 1 1 sd 1 p u E s
(7)
The dependency of the initial stiffness coefficient on the bedding resistance utilization ratio results indirectly in a complete new shape of the p-y curve (cf. Fig. 2). A quite large initial stiffness becomes obvious (cf. also Fig. 3) which degrades with increasing bedding resistance and finally crosses over to a reduced ultimate bedding resistance. Please note that likewise to the Sørensen formulation the change in bedding stiffness is dependent on the considered soil stiffness. Here, the static soil stiffness modulus E s is scheduled according to Eq. 14 and the dynamic soil stiffness modulus Esd is converted from the dynamic shear modulus G 0 given in Eq. 8. Additionally to the p-y approaches, a three dimensional numerical study on the foundation stiffness of monopiles under small operational loads by Thieken & Achmus (2013) is to be pointed out. In a comprehensive study it is shown that the foundation stiffness depends strongly on the considered horizontal head displacement. For very small loads the foundation stiffness was found to be underestimated by the approach of the OGL. In con trast, the stiffness for larger loads was smaller in comparison to the OGL approach. However, in this study a quite time-consuming iterative calculation procedure was used to account for the strain-dependency of soil stiffness.
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Fig. 4: Finite element mesh used in the simulations (D = 5m, L = 25m) The monopile is modeled as an open tubular steel pile with a wall thickness t. The steel material properties E = 210 GPa, ν = 0.27 were applied, where E and ν represent the modulus of elasticity and Poisson’s ratio of steel material, respectively. The monopile is extended above the soil surface with a rigid pile to enable the application of the horizontal and moment loading by a single horizontal load H with a load eccentricity h. An elasto-plastic contact is implemented between the inside and the outside of the steel pile and the adjacent soil. The maximum shear stress in the contact surface τmax results from the product of the horizontal stress σH and the contact friction angle δ = 2/3 ∙ϕ’. The calculation is done in several steps. In the first step the initial stress state is generated by consideration of soil elements only. The horizontal stress σH is defined by a coefficient of horizontal earth pressure at rest k 0 = 1 - sin ϕ’. Subsequently, the predefined elements defining the monopile geometry are replaced by steel elements representing the structure. In the same step, the contact between the pile and the surrounding soil is activated. In a third step, the load is applied by assigning the point load to the center of a rigid top plate.
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Constitutive model For the modeling of the soil, the HSsmall model according to Benz (Benz, 2006) was used. This soil model is an upgrade of the sophisticated Hardening Soil Model according to Schanz (Schanz, 1998) which enables for instances the consideration of the stressdependency of soil stiffness. The HSsmall model is additionally able to account for the strain dependency of soil stiffness, being crucial for the description of the bearing behavior under small loads. For very small shear strains (γ < 10 -6), the soil stiffness is described by the dynamic shear modulus G0. For determination of G0, an approach presented by the German Geotechnical Society (DGGT, 2002) was used (Eq. 8). This formulation is valid for poorly grained sandy soils with rounded grain shapes, which are mostly found in German offshore wind farm areas. The dynamic shear modulus G 0 depends on void ratio e and a mean principal stress σm defined by the effective stress components σ1’, σ2’, σ3’. Here stresses must be set in kPa to obtain G0 in kPa. For constant void ratio, the dynamic shear modulus is increased stress-dependent by the power of λ G0. G0
3
(8)
For the description of the stiffness degradation with shear strain, Santos & Correia (2001) suggested to use the following formulation, which is also implemented in P LAXIS3D. G G0
1
(9)
1 0.385 / ref
Therefore, the ratio between the actual shear modulus G and the dynamic shear modulus G0 depends on the value of shear strain γ. The reference shear strain γ ref corresponds to a secant shear modulus which is reduced to 72.2 % of its initial value and is chosen to γ ref = 10-4 as it is common practice. For large shear strains, the degradation is limited by the “static” soil stiffness. The Hardening Soil Model distinguishes three moduli which are the secant stiffness in a drained triaxial test E50, the tangent stiffness for primary oedometric loading E oed and the un- and reloading stiffness at engineering strains E ur . All moduli are based on a stress-dependent power law with an exponent m and a reference stress p ref . Note that the oedometric stiffness E oed depends on the major principal stress σ1 instead of the minor principal stress σ 3. m E ref oed '1 / p ref
E oed E50
ref E50 '3 / p ref
(11)
'3 / p ref m
(12)
G 0ref '3 / p ref m
(13)
ref
G0
(10)
m
E ur E ur
Whereas the dynamic shear modulus G 0 is fitted according to Eq. 8, the modulus Eoed is adapted to the stress-dependent oedometric stiffness formulation presented in Eq. 14. Thereby, the parameter κ defines the soil stiffness at the reference pressure σat = 100 kPa and λ Eoed rules the stress dependency with regard to the mean principal stress σm. The parameters κ and λ are selected in dependence of the relative density (cf. Table 1). These combinations are assumed to give reasonable results at least in many German wind farm areas. E oed
at m / at Eoed
(14)
In PLAXIS the power m and the reference stress p ref are likewise valid for all four moduli. To reach a best possible fit between the input parameters in PLAXIS 3D and the assumptions in Eq. 8 and Eq. 14, the (homogenous) soil has to be divided into layers if different exponents of stress dependency (λ G0 ≠ λ Eoed) shall be considered.
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(15)
E ur 3 E 50
(16)
The soil parameters used in the simulations are presented in Table 1 in dependence of the relative density. Table 1: Soil parameters used in the simulations Description
Parameter
Medium dense
Very dense
Buoyant unit weight
γ' [kN/m³]
9.76
10.31
Friction angle
ϕ' [°]
35.0
40.0
Dilatancy
ψ [°]
5.0
10.0
Cohesion
c' [kN/m²]
0.1
0.1
Stiffness parameter
κ [-]
400
700
Stiffness parameter
λ Eoed [-]
0.6
0.5
e [1]
0.69
0.60
Stiffness parameter
λ G0 [-]
0.5
0.5
Poisson’s ratio
ν [-]
0.25
0.20
Void ratio
2.17 e2 1 ' 2 '3 G0 6900 1 e
The incorporated moduli E50 and Eur are calculated based on the oedometric modulus Eoed using Eq. 15 and 16.
Extraction of bedding resistance in PLAXIS3D The extraction of bedding resistance(4)along the pile shaft in PLAXIS3D is quite labor-intensive. The main problem is that PLAXIS offers the bedding resistance only in terms of contact stresses in normal and orthogonal direction at the stress points (weight factors of the stress points can be found in: Dunavant, 1985). In consequence, the stresses have to be transformed in a global coordinate system and integrated for the considered pile section. This is a challenging task as the elements are usually of different size and the values are given in tabular form more or less randomly. If p-y curves shall be created, several loading steps have to be analyzed. Besides, also the deflection lines and the bending moments of the pile have to be extracted from stress point data in tabular form. It is desirable that PLAXIS3D in future offers the possibility to output the soil resistance force or the deflection line of a conn ected structure directly.
BACK-CALCULATION OF “MUSTANG ISLAND” TEST As stated before, the “Mustang Island” test is the largest and best instrumented pile test considered for the p-y approach of the offshore guidelines. In consequence, the mentioned test described by Cox et al. (1974) was also used for the validation of the numerical model. The test pile had an embedded length L = 21 m, a diameter D = 0.61 m and a wall thickness t = 9.52 mm. The soil conditions were specified as dense, poorly graded sand with a friction angle φ’ = 39.3° and a buoyant unit weight γ’ = 10.37 kN/m3. The soil conditions are therefore quite similar to the very dense sand assumed. This enables the usage of the identical stiffness parameters for the back-calculation. Reese et al. (1974) presented a load deflection curve (cf. Fig. 5) as well as a course of bending moments along the pile shaft (cf. Fig. 6) which were determined by strain measurements on the pile. A good agreement between the numerical back-calculations and the field test is obtained. Besides, a quite well agreement between the results of Thieken & Achmus (2013) and the numerical simulations performed here can be found. Concluding, the numerical model seems to be suitable for the determination of the monopile’s load bearing behavior.
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from FEM is smaller than from the OGL approach. For head displacements y > 20 mm, the resistance is even smaller than it results from the p-y approach of Wiemann et al. The resistance predicted by the approach of Kirsch et al. is significantly larger than from the numerical simulations. Due to the smaller ultimate bedding resistances and the degradation (cf. Eq. 7) of the initial stiffness coefficient, the difference to the FEM results is decreasing with increasing head displacement y.
Fig. 5: Load-displacement curves for the “Mustang Island” test Furthermore, the field tests are back-calculated with the considered p-y approaches. For the calculations, the program IGtHPile (Terceros, 2014) was used. As expected, the approach of Reese et al. coincides very well with the field tests. In contrast, the current p-y approach of the offshore guidelines predicts a significantly stiffer behavior for large horizontal displacements (reasons are described before in section “Evaluated p-y approaches”). The overestimation in soil resistance of the OGL approach results additionally in a smaller reduction of the bending moment with increasing depth (Fig. 6). The approach of Wiemann et al. is identical to the approach of the OGL due to the pile diameter D = Dref = 0.61m. The Kirsch et al. approach predicts a much stiffer load bearing behavior, especially for small load levels. Please remember that the Kirsch et al. approach is expected to predict smaller resistances due to the consideration of cyclic loading.
Fig. 6: Corresponding bending moment for the “Mustang Island” test
Fig. 7: Horizontal resistances for the reference system In Fig. 8, the correspondig secant bedding stiffnesses (E py = p / y) for two pile head displacements are presented. Please note that E py values resulting from the Kirsch et al. approach are depicted by using a secondary axis to reach a meaningful presentation. For a head displacement y = 2.5 mm (at mudline) the bedding stiffness is overall comparable to the stiffness resulting from the approach of the OGL. The extreme values in the numerical simulations are due to the point of rotation and the pile tip which strongly influences the load transfer into the soil. Due to the very small deflection occurring near to the point of rotation, this effect is only of marginal meaning to the bearing behavior. By contrast, the effect of the pile toe shearing will contribute significantly to the foundation resistance. The results of the OGL and the Reese et al. approach for the small head displacement are identical due to identical initial stiffness formulation underlying. The approach of Wiemann et al. underestimates the bedding stiffness whereas the approach of Kirsch et al. significantly overestimates E py. For larger head displacements, the stiffness resulting from the numerical simulation is strongly decreased and even smaller than it results from the Wiemann et al. approach. It is understood that the bedding stiffness resulting from the p-y methods depend on the respective deflections, i.e. the bedding stiffness decreases with increasing deflection as specified by the p-y formulation.
RESULTS FOR A REFERENCE SYSTEM First, the results for a reference system shall be presented and discussed in detail. The reference system consists of a monopile with a diameter D = 5 m, an embedded length L = 25 m and a wall thickness t = 68.9 mm embedded in medium dense sand. The eccentricity of the horizontal load H is chosen to h = 25 m. The horizontal resistances at mudline are depicted in terms of load-displacement curves and secant stiffness (K sec = H / y) displacement curves in Fig. 7. Please note the different range of horizontal displacements in both figures. Evidently, the numerical simulations predict a strong dependency of the foundation stiffness on the horizontal head displacement y. For small head displacements, the numerical simulation gives larger resistances than the p-y approach according to the offshore gu idelines. In contrast, for larger head displacements, the resistance resulting
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Fig.8: Comparison of secant bedding stiffness for the reference system
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PARAMETRIC STUDY
Comparison to the approach of Wiemann et al. (2004)
In the following a comprehensive parametric study on the validity of the mentioned p-y approaches in dependency on the pile dimension and the relative density of the soil is presented. For this purpose, the numerical model was extrapolated to a total of 224 pile-soil systems. Horizontal loaded piles with diameters in a range of D = 0.5 - 8 m and relative lengths L/D = 4 - 10 are considered. To enable a meaningful evaluation of the p-y approaches in dependence on the pile dimensions, the load eccentricity h and the wall thickness are normalized with the pile diameter D. Here, the wall thickness is set to t [mm] = 0.0125∙D [mm] + 6.35 [mm] and the load eccentricity is arranged to five times the pile diameter.
For small head displacements, the approach of Wiemann et al. results especially for small relative lengths in significantly smaller foundation stiffnesses than the FEM (Fig. 11). For head displacements y = 0.01∙D, a relative constant overestimation of foundation resistance below 30 % can be found for pile diameters larger than D = 3 m. For smaller pile diameters the discrepancies increase till they exceed the values resulting from the OGL approach for D = 0.5 m. For larger head displacements, the overestimation of pile head deflection is increasing especially for relative pile lengths in a range about 5 - 6.
The results of the parametric study are given in terms of contour plots in Figs. 9 - 12. Black dots in the figures indicate the supporting points of the contour plots, representing each a calculation result. Here, the quotients of the horizontal load resulting from the p-y approaches and the numerical simulations (H p-y / HFEM) are presented. In consequence, a value larger than one means that the p-y approach results in a stiffer behavior than the FEM. Normalized head displacements y = 0.0005∙D, 0.01∙D and 0.03∙D are considered to give the best possible view of the occurring discrepancy with regard to the horizontal resistance. Based on the presentation in Fig. 7 it is understood that, especially for small horizontal head displacements, the determined discrepancy will strongly vary with the considered head displacement. However, this presentation enables the characterization of the considered p-y approaches with regard to the validity for piles of arbitrary dimension.
The approach of Kirsch et al. results in a quite large overestimation of foundation resistance for small head displacements in a range of 40-100%. Also for larger head displacements, a considerable overestimation of resistance is found which becomes maximum for piles with diameters smaller than D = 4 m. However, the overestimation for typical monopiles lies in a range between 40 -100%. It must be remembered that Kirsch et al. purport to consider an accumulation of pile deflection due to cyclic loading. In fact, the overestimation of resistance for typical monopiles is comparable to the results of the static approaches of Reese et al. (2004) and Wiemann et al. (2004). For smaller pile diameters, the overestimation is even larger than it results from these “static” approaches.
The approach by Wiemann et al. applies to large diameter monopiles and extreme loads as considered in the SLS design proof. As the authors give no explicit limitations with regard to pile dimensions or load levels, the approach is compared to all systems analyzed.
It can be concluded, that none of the current p-y formulations is generally suitable for the design of large diameter monopiles without additional calibration on the considered pile-soil system and load level. It is to be expected that a simple modification of the initial stiffness coefficient of the OGL approach is not the way to success. A complete new p-y curve formulation is needed, which is able to account for the stiffer behavior under small head displacements and the softer behavior under large head displacements. A schematic course of such a realistic p-y curve in comparison to the current p-y curves is presented in Fig. 13.
Comparison to the approach of the offshore guidelines For the smallest normalized head displacement y = 0.0005∙D (Fig. 9, left) an almost constant overestimation of foundation stiffness can be found for pile diameters larger than three meters, if very dense sand is assumed. For medium dense sand, almost identical stiffnesses based on the two methods occur. Independent of the relative density, the stiffness is underestimated for small diameter piles. For larger head displacements, an overestimation of foundation stiffness occurs for all systems considered. Thereby, the pile dimensions have much more influence than the relative density of the soil. The overestimation becomes maximal for a large pile diameter and a small relative length, which coincides to the dimensions of typical monopiles. Here, a maximum value of 2.2 becomes obvious, which means that the resistance from the numerical simulations is not even half of the resistance predicted by the approach of the offshore guidelines.
Comparison to the approach of Reese et al . (1974) As the initial stiffness formulation is identical to the OGL approach, it is clear that the same results occur for small head displacements. For larger head displacements, the qualitative distribution of discrepancies remains identical. However, the predicted resistances for piles with diameters D ≥ 1.5m are up to 50 % larger than it results from the numerical simulation. In contrast, very similar results are achieved for small pile diameters (cf. Fig. 10).
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Comparison to the approach of Kirsch et al . (2014)
Evaluation of current p-y formulations
Fig. 13: Schematic distribution of a realistic p-y curve In general, the approach of Kirsch et al. could be able to fulfill this requirement due to a load level dependent initial stiffness formulation. However, the current formulation behaves much too stiff which is caused by the consideration of the d ynamic soil stiffness for the whole range of horizontal displacements (cf. Eq. 7). This is in strong contrast to experience after which the dynamic soil stiffness has only influence under small loads or shear strains in the soil, respectively. Furthermore it could be more meaningful to develop a formulation which leads directly to the shape of the p-y curve instead of obscure it in the tanhformulation of the OGL.
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Fig. 9: Quotient of horizontal resistance based on the p-y app roach by the OGL and FEM; very dense sand (top); medium dense sand (bottom)
Fig. 10: Quotient of horizontal resistance based on p-y approach by Reese et al. and FEM; very dense sand (top); medium dense sand (bottom)
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Fig. 11: Quotient of horizontal resistance based on p-y approach by Wiemann et al. and FEM; very dense sand (top); medium dense sand (bottom)
Fig. 12: Quotient of horizontal resistance based on p-y approach by Kirsch et al. and FEM; very dense sand (top); medium dense sand (bottom)
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CONCLUSIONS The p-y method is usually applied for the determination of soil resistance in the design of monopile foundations. The considered p-y curves affect both the magnitude of the monopile deformation under extreme loads (SLS proof) and the foundation stiffness - which influences the structural loading in a dynamic analysis - under small operational loads. Beside the p-y approach of the offshore guidelines, several modified p-y approaches which shall account for the effect of a large pile diameter are recommended in the literature. For the evaluation of the mentioned p-y approaches, three dimensional numerical simulations of a monopile foundation in homogenous sand were executed. The model included a strain-dependent stiffness formulation which enables a realistic determination of the pile-soil system stiffness under small loads. The numerical model is validated successfully on the “Mustang Island” field test , which was previously also included in the calibration of the OGL approach. A comprehensive parametric study on the discrepancy between the results based on the p-y approaches and the FEM results is depicted. The following main conclusions can be drawn.
The foundation stiffness is strongly dependent on the pile head displacements occurring under the considered load, reflecting the non-linearity in the load-bearing behavior of the pile-soil system. This is in particular valid for small loads. For small head displacements, the numerical derived foundation stiffness is larger than it results from the approach by the offshore guidelines. However, the stiffness is much smaller than predicted by the approach of Kirsch et al. (2014). For large head displacements, the foundation stiffness is smaller than it results from the approach of the offshore guidelines and even falls below the results of the approach by Wiemann et al. (2004). Even if the approach of Kirsch et al. (2014) purports to account for an accumulation of pile deflection due to cyclic loads, the resistance is significant larger than p redicted by FEM.
Concluding, none of the current p-y approaches fit suitable with the results of the numerical simulations under arbitrary pile dimensions, soil conditions and load levels. Even if the numerical simulations have their own uncertainties and the relation between the relative density and the assumed soil stiffnesses is not generally valid, the results, however, clearly indicate that the current approaches are not generally suitable for the design of large diameter monopiles. A new p-y formulation is needed which does not exhibit underestimation of foundation stiffness for small operational loads and overestimation for extreme loads.
ACKNOWLEDGEMENTS This study was partly carried out in the scope of the research project “GIGAWINDlife” funded by the Federal Ministry for Economic Affairs and Energy (BMWI). The authors sincerely acknowledge BMWI support.
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sand”. Proceedings of the 7th European Conference on Numerical Methods in Geotechnical Engineering, pp. 907-912. Sørensen, S.P.H. (2012). “Soil-structure interaction for non-slender, large-diameter offshore monopiles”. PhD Thesis, Aalborg University Denmark, Department of Civil Engineering. Schanz, T. (1998). “Zur Modellierung des Mechanischen Verhaltens von Reibungsmaterialien”, Habilitation, University of Stuttgart (in German). Thieken, K., Achmus, M. (2013). “Small strain effect s on the stiffness of monopile foundations in sand”, International Symposium on Computational Geomechanics (ComGeoIII), Poland.
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Thieken, K., Achmus, M., Schmoor, K. (2014). “On the ultimate limit state design proof for laterally loaded piles“, Geotechnik 3 7 (1). Terceros, M. (2014). IGtHPile Software & Calculation Examples. http://www.igth.uni-hannover.de/downloads Wiemann, J., Lesny, K., Richwien, W. (2004). “Evaluation of the Pile Diameter Effects on Soil-Pile Stiffness”. Proceedings of the 7th German Wind Energy Conference (DEWEK), Wilhelmshaven.
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