APPLICATION OF A NUMERICAL-BASED DESIGN METHOD FOR LATERALLY LOADED MONOPILES IN LAYERED SOILS

Transcription

1 APPLICATION OF A NUMERICAL-BASED DESIGN METHOD FOR LATERALLY LOADED MONOPILES IN LAYERED SOILS Y He AECOM, Birmingham, UK; formerly Department of Engineering Science, University of Oxford, Oxford, UK; yiling.he@yahoo.com BW Byrne and HJ Burd Department of Engineering Science, University of Oxford, Oxford, UK Abstract The Pile Soil Analysis (PISA) project, established to improve design methods for laterally loaded monopiles for offshore wind turbines (OWTs), proposes two new one-dimensional (D) design methods: (a) a rule-based method similar to existing design standard approaches, and (b) a numerical-based method drawing on the results of three dimensional (3D) finite element (FE) computations. This paper examines the applicability of the numerical-based method for analysing monopile response in layered soil conditions. Soil reaction components were extracted from 3D FE through a calibration exercise on homogeneous soils, parameterised to develop soil reaction curves, with these curves then incorporated into a D beam model for predicting pile responses in layered soils. Good agreement in the ultimate capacity and initial stiffness between the results obtained using the calibrated D model and the 3D FE simulations provided evidence that the numericalbased method is applicable for layered soil analyses. Further insights into layering were obtained by comparing soil reaction components extracted from layered soil analyses to those from homogeneous soil analyses.. Introduction Monopile foundations are the major foundation type for OWTs, being used for over 7% share of the UK market (Doherty and Gavin, ). They typically comprise large diameter ( to m) steel tubes with relatively low slenderness ratios (L/D < ). Because OWT operation is sensitive to tilting and rotation of the foundation, the design of monopiles must satisfy strict pile head deflection and rotation tolerances (e.g. as described in design standards). The recommended approach for lateral pile design (e.g. in the API and DNV standards) is the p-y method, originally developed for long and slender piles used in the oil and gas industry (Matlock, 97; Reese et al., 97). It is now recognised that extrapolating these methods to monopile geometries appropriate to wind turbines may not be entirely appropriate (e.g. Roesen et al., ; Doherty and Gavin, ; Byrne et al., a). For example, evidence from full-scale field measurements (Hald et al., 9) demonstrates that current p-y methods underestimate the stiffness of measured pile lateral response, identifying that current design methods are (excessively) conservative. A joint-industry project PISA was established to develop improved design methods for large diameter monopiles (Byrne et al., a, b; Zdravković et al., ). Two design procedures, the rule-based method (equation based) and the numerical-based method (calibration through finite element calculations), are proposed. Figure : Soil reaction components and the D beam model proposed by the PISA project (Byrne et al., a)

2 The PISA methodology decomposes the pile-soil interaction into four components. In addition to the distributed lateral soil reaction acting on the pile shaft (i.e. corresponding to the conventional p-y response) there is a distributed moment acting along the pile due to shear tractions developed at the pilesoil interface. A horizontal force and a moment is developed across the pile annulus and soil plug at the pile base. The four soil reaction components are incorporated into a D beam model as illustrated in Figure (Byrne et al., a). Most design guidelines for laterally loaded piles do not explicitly account for soil layering. In practice, it is common for monopiles to be embedded in layered soils, for example at Kentish Flats and Barrow offshore wind farms in the UK, and Lely and Irene offshore wind farms in Netherlands (Arany et al., ). The potential effects of soil layering on pile capacity and deflection are not well documented in the literature. Pile responses in a two-layer system under small working loads was first investigated by Davisson and Gill (93) using a linear p-y method. This approach is not appropriate for cases where ultimate limit states need to be considered. Reese et al. (9) conducted small-scale model tests and a field test on slender piles in layered soils, and found that there was relatively good agreement between experimental results and predictions using the nonlinear p-y curves derived from homogeneous soil analyses at the same depth. Georgiadis (93) proposed an equivalent depth concept for developing p-y curves for layered soils. The p-y curves for the lower soil layer are determined using expressions derived from homogeneous soil analyses that account for the equivalent depths of the overlying layers. This method has been incorporated in the commercial pile design software LPILE (LPILE User s Manual, 3). Ashour et al. (99) proposed a semi-empirical strain wedge approach to develop p-y curves for layered soils, and the predictions indicated a good match with full-scale test results. Yang and Jeremić () extracted p-y curves from 3D FE analyses on a single pile in clay-sand interbedded deposits, and suggested that the soil layering has an effect in both the lower and the upper layers. The study reported in this paper provides a preliminary study on the application of the PISA numerical-based method to analysis of laterally loaded monopiles in layered soils. Two sets of homogeneous soil reaction curves, for clay and for sand, were required as input for the layered soil analyses. The development and calibration of these soil reaction curves followed the procedure described in Byrne et al. (a). The overall methodology adopted for the study is given in Figure. The first step in the process was to conduct the calibration finite element calculations, to determine the soil reaction curves, completed for the two homogeneous soil cases, across a small set of representative geometries. These were then combined for the layered soil case, and compared against a finite element calculation specific to the layered case. The study adopted simplified forms of the parameterised expressions, consistent with the limited scope and focus of the study. Figure : Flowchart of the methodology adopted in this study. 3D finite element models. General description The 3D FE models were developed using the commercial software Abaqus (Abaqus/Standard, Version.3). A circular pile with cross-sectional diameter D and embedded length L within the soil deposit was considered. Half-symmetry was adopted to reduce the computational effort. The pile was discretised with -noded doubly curved shell elements with hourglass control and finite membrane strains. The soil was discretised with - noded linear reduced integration solid elements, with hourglass control. An example of the model geometry and mesh is shown in Figure 3. The adopted mesh ensured a good balance between computational cost and result quality. The pile thickness, t, was found to have a minor effect on the pile response, hence its variation was not considered in the calibration process. The bottom of the soil domain was fixed in all coordinate directions (x, y and z). The displacement

3 Stickup height ratio h/d Aspect ratio L/D in the y-direction and the x- and z- axis rotational degrees of freedom at the symmetric plane (y=) and along the edge of pile shell elements were set to zero. The pile-soil interaction was modelled using small displacement, surface-to-surface master/slave contact pair formulation. The tangential contact behaviour at the interface was modelled using the Coulomb friction law with a friction coefficient, μ. Table Pile geometries adopted in the analyses Pile reference (unit) D L h t L/D (m) (m) (m) (mm) Calibration analysis (homogeneous soils) P 9 P 9 P3 3 P 3 soil analysis PA 9 PB Figure 3: Geometry and mesh for a typical 3D model The analysis consisted of three steps. An initial geostatic stress field was computed in the first step. The contact condition between the pile and the soil was then activated. Next, the pile was either displaced or loaded incrementally along the x-axis until failure. In the layered soil analyses, instead of applying loads directly, an incremental displacement along the x-axis was applied around the pile top perimeter to achieve better convergence. The total horizontal load acting on the pile was obtained as the reaction to the imposed displacement.. Pile model and parameters The pile was modelled as a linear elastic material, with a Young s modulus of GPa and a Poisson s ratio of.3. The pile parameters for the layered soil analyses were selected within the parameter range from the calibration analyses (see Figure and Table ). For simplicity, the pile was wished in place and assumed weightless (though attributing weight to the pile is not anticipated to affect the results). PB PA Calibration soils Pile diameter D Pile diameter D Figure : Pile parameters employed in the calibration and layered soil analyses (PA and PB please refer to Table ) PB PA.3 Soil models and parameters The layered soil profiles consisted of a layer of clay and a layer of sand. The clay layer was modelled as an elastic perfectly plastic material with a Von Mises failure criterion, and a Poisson s ratio close to.. The sand layer was modelled as an elastic perfectly plastic material with Mohr-Coulomb failure criterion. For simplicity, each layer is assumed uniform. The soil models employed in this study are relatively rudimentary and may not, therefore, provide a close representation of the performance of actual installed monopiles. This is justified on the basis that the study is concerned with exploring differences in behaviour between piles embedded in homogeneous soils and layered soils, rather than predicting pile behaviour for a sitespecific soil profile. Further investigations are needed to confirm the applicability of the current study to more advanced soil models. The soil parameters for the homogeneous clay and sand layers are given in Table and Table 3, respectively. The friction coefficient of the clay layer was estimated based on an empirical relationship between the plasticity index and friction coefficient used by Lehane et al.,, assuming an average plasticity index PI = and the adhesion parameter as unity. The sand layer parameters were based on the profile used by Abdel-Rahman & Achmus () and a friction coefficient of. was adopted to maintain consistency. The derivation of the soil parameters and details of the calibration 3D FE analyses are further discussed in He (). Gapping at the pile-soil interface was allowed in the clay layer, but not in the sand layer. A small cohesion was adopted for the sand layer to avoid numerical singularity issues.

4 H ult computed by D analyses k.d computed by D analyses Table Material parameters for clay layer Parameter Value Shear modulus, G (MPa) 37. Undrained shear strength, s u (kpa) Poisson s ratio, υ.9 Saturated bulk unit weight, γ (kn/m 3 ). Earth pressure coefficient at rest, K. Friction coefficient at pile-soil interface, μ. Table 3 Material parameters for sand layer Parameter Value Shear modulus, G (MPa) Effective internal friction angle, φ' ( ) 3 Dilation angle, ψ ( ) Poisson s ratio, υ. Submerged unit weight, γ' (kn/m 3 ) Earth pressure coefficient at rest, K. Friction coefficient at pile-soil interface, μ. Cohesion (kpa).. Extraction of soil reaction curves After the 3D FE calibration analyses were completed, the nodal force of the soil elements immediately surrounding the pile, and the nodal displacements of the pile elements, were processed to obtain the soil reaction components. As mention previously, this process follows the procedures outlined in Byrne et al. (a). The distributed soil reaction curves along the pile length were derived at the reference nodes, which were defined at the centre of each quadrilateral shell element used to model the pile. The distributed lateral soil reaction, p, was calculated by dividing the sum of the horizontal nodal forces of a ring of elements at the same depth, by the shared length of the ring of elements along the pile length direction. The pile lateral displacement, v, at the reference location was interpolated from the average nodal displacement of the shell element at the same depth. The distributed moment (denoted by m) was calculated by multiplying the distributed vertical shear forces at the pile-soil interface with their distance along the x-axis from the neutral axis of the pile. The distributed vertical shear forces were calculated by dividing the sum of the vertical nodal forces of an element, by the length of the element along the pile length direction. The rotation of the pile cross-section, θ, was determined by regression of the vertical nodal displacement against the distance of the reference node from the central axis of the pile cross-section, to obtain the best linear fit slope. The base horizontal force, S, and base moment, M were derived by summing the nodal forces and the moments due to the nodal forces of the soil elements located immediately below the pile base and the soil plug.. Parameterisation The extracted soil reaction components from the calibration analyses were normalised and parameterised to produce dimensionless soil reaction curves (described further in He, ). The parameterised soil reaction curves were then provided as input to the D beam model to predict pile lateral responses in layered soil cases. The effectiveness of the soil reaction extraction and parameterisation was determined by comparing the results from the D beam model using the parameterised soil reaction curves and those from 3D FE analyses for (a) the ultimate lateral load defined at.d ground level displacement and (b) the initial stiffness defined at.d ground level displacement. This is presented in Figure. The maximum difference in the ultimate lateral load is within %, while the differences in the initial stiffness are largely within %. Overall, the calibrated D model was considered acceptable for exploring application to layered soil cases, particularly considering the small number of analyses from which the reaction curves are drawn and the range of geometries to which they apply. Improved agreement could be obtained by increasing the number of calibration analyses and by introducing more complex parameterisation expressions. overpredicted underpredicted L/D = L/D = % band H ult computed by 3D analyses 3 overpredicted underpredicted L/D = L/D = % band 3 k.d computed by 3D analyses (a) H ult (MN) (b) k.d (MN/m) Figure : Comparison of the ultimate lateral load (H ult ) and initial stiffness (k.d ) predicted by the D model (with parameterised curves) and 3D models for the calibration analyses (solid symbols:sand, open symbols: clay) 3. soil analyses 3. Problem definition Two simple layered soil profiles were analysed in this study: a uniform sand layer over a uniform clay layer (denoted S/C ), and a uniform clay layer over a uniform sand layer (denoted C/S ), as illustrated in Figure. The input soil reaction curves for the

5 Lateral load at pile top (MN) Lateral load at pile top (MN) H ult computed by D analyses k.d computed by D analyses Lateral load at pile top (MN) Lateral load at pile top (MN) sand or clay layer were produced from the 3D homogeneous sand or clay analyses accordingly. In the following, a unique code is given to each analysis, formatting as AA-BB. AA corresponds to pile references (PA or PB, see Table ), and BB refers to soil profiles (S/C or C/S). 3D D Parameterised D Numerical Displacement at ground level (m) (c) PB-S/C analysis (a) S/C (b) C/S Figure : Soil profiles for the layered soil analyses 3. Load-displacement results The load-displacement results predicted by the D model, using the parameterised curves (D Parameterised) are compared to the 3D FE analysis results, as shown in Figure 7. Additional analyses (D Numerical) were completed to determine whether the differences between the D results predicted using the parameterised curves (D Parameterised) and the 3D FE results were due to the parameterisation of soil reaction components or soil layering effects. This involved conducting 3D FE for the piles PA and PB in homogeneous soil profiles, extracting the soil reaction components, and then incorporated these as numerical data into the D model at the corresponding depth for the layered soil analyses. 9 3D 3 D Parameterised D Numerical Displacement at ground level (m) 9 (a) PA-S/C analysis 3D 3 D Parameterised D Numerical..... Displacement at ground level (m) (b) PA-C/S analysis (d) PB-C/S analysis Figure 7: Comparison of the load-displacement responses for D and 3D analyses overpredicted 3D D Parameterised D Numerical Displacement at ground level (m) underpredicted L/D = L/D = % band H ult computed by 3D analyses overpredicted underpredicted L/D = L/D = % band k.d computed by 3D analyses (a) H ult (MN) (b) k.d (MN/m) Figure : Comparison of the ultimate lateral load (H ult ) and initial stiffness (k.d ) of pile response predicted by the D model (with parameterised curves) and 3D models for the layered soil analyses (solid symbols: S/C, open symbols: C/S) Figure 7 and Figure indicate satisfactory agreement between the 3D results and the D prediction using the parameterised curves. The maximum difference in the ultimate capacity of approximately % is for the PB-S/C analysis of a short pile embedded in sand over clay. The differences in the initial stiffness of pile response are within %. Note that the maximum displacement achieved in the short pile analysis was limited due to convergence issues in the FE analysis; the maximum load was thus taken as the ultimate lateral load. The difference between predictions using numerical and parameterised curves indicates that employing parametric soil reaction curves has an influence on the load-displacement predictions, with the influence more pronounced for the short pile (PB) than for the long pile (PA). This is due to the parameterisation process averaging the response across a number of different calibration analyses. However, the overall difference due to parameterisation of soil reaction components is less than % compared with the 3D

6 analysis results. It is therefore likely that parameterised curves, extracted from 3D analyses of homogeneous soil profiles, can be satisfactorily applied to layered soil profiles. 3.3 Comparison of soil reaction curves The soil reaction components developed from the 3D FE analyses for homogeneous soil profiles (sand or clay) and layered soil profiles (S/C, or C/S) were compared to investigate the effects of layering. The soil reaction curves were compared at four depths (.L,.L,.L and.9l), where L is pile embedded length, with the soil reaction components extracted from the layered soil analyses compared to those obtained from the homogeneous soil analyses at the same depth. Normalisation of the soil reactions was adopted to facilitate comparison between the sand and clay layers. The distributed load was normalised by the undrained shear strength (s u ) times diameter (D) for the clay layer (i.e. p/s u D), and by the local effective stresses (σ vi ) times the diameter for the sand layer (i.e. p/σ vi D). The horizontal pile displacement was normalised by s u D divided by the shear modulus (G) for clay (i.e. vg/s u D), and by σ vi D/G for sand (i.e. vg/σ vi D). The distributed moment for clay was normalised by s u D, and by σ vi D for sand. The pile rotation was normalised by s u /G for clay, and by σ vi /G for sand Distributed lateral load curves The normalised distributed lateral load against normalised ground level displacement at different depths is presented in Figure 9 (denoted by normalised p and v respectively). The initial stiffness of the distributed lateral load curves extracted from the layered and homogeneous soil analyses is generally in good agreement. However, differences are observed for large lateral displacements in both the upper and lower layers; this may be due to effects of soil layering. For the cases considered, the ultimate lateral responses in the layered soils tended to be higher than those in the homogeneous soils for sand, while they tended to be lower for clay. In addition, the differences in the ultimate lateral response are not constant within the same layer, as can be seen in both the upper and lower layers of PA-C/S analysis. at depth =.L 3 3 at depth =.L 3 at depth =.L depth =.L 3... at depth =.L at depth =.L 3 3 at depth =.L 3 3 at depth =.L 3... (a) PA-S/C analysis (b) PA-C/S analysis at depth =.9L at depth =.L 3 at depth =.9L (c) PB-S/C analysis at depth =.L at depth =.L 3 at depth =.9L at depth =.L at depth =.9L.... (d) PB-C/S analysis Figure 9: Comparison of the distributed lateral load curves from the homogeneous and layered soil analyses

7 3.3. Distributed moment curves The normalised distributed moment against normalised pile rotation at different depths is shown in Figure (denoted by normalised m and θ respectively). The comparison indicates that initial stiffness determined from the homogeneous and layered soil analyses matches well. Differences are again observed for the ultimate response.... at depth =.L at depth =.L at depth =.L at depth =.L at depth =.L at depth =.L at depth =.L (a) PA-S/C analysis at depth =.9L at depth =.L...3. (b) PA-C/S analysis at depth =.9L at depth =.L... (c) PB-S/C analysis. at depth =.9L.... at depth =.L at depth =.L at depth =.L..... at depth =.9L.. 3 (d) PB-C/S analysis Figure : Comparison of the numerical distributed moment curves extracted from homogeneous and layered soils The above detailed comparison of the distributed lateral load and moment determined from the homogeneous soil and layered soil analyses illustrates the complexity of the soil layering effects. However these differences appear to balance out when integrated into the overall load-displacement response. Further studies are required to investigate soil layering effects on the individual soil reaction components, particularly more complex layering profiles, and therefore the overall pile behaviour. Also, care should be employed when applying base shear and base moment in layered soils, as soil layers above and below the actual pile tip may have influence on the soil resistance. However, due to limited scope of this study, the potential effect of variation of base soil layer has not been examined, and further analysis will be needed to address this matter.. Conclusions 3D FE and D pile analyses have been performed to examine the application of the PISA numericalbased method to monopile analyses in layered soils. The comparison of results using a D model incorporating homogeneous soil reaction curves and 3D finite element calculations for layered profiles show excellent agreement in both the ultimate capacity and initial stiffness, considering the relative simplicity of the input data and the methodology adopted. This demonstrates that soil reaction curves extracted and parameterised from 3D homogeneous soil analyses can be feasibly applied to analyse layered soil conditions. Inspection of the distributed soil reaction components (normalised p and m), show differences in the ultimate response, for both the upper and lower layers, but this appeared to even out when integrated along the D model. The soil reaction component comparisons show the complex nature of the soil laying effects. Further work is needed to explore the application of this method to more complex layering conditions.

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