Title of paper

PREDICTING LONG TERM PERFORMANCE OF OWT FOUNDATION USING CYCLIC SIMPLE SHEAR APPARATUS AND DEM SIMULATIONS

L Cui, S Bhattacharya and G Nikitas

Department of Civil and Environmental Engineering, University of Surrey, Guildford, UK

JN Vimalan

VJ Tech Ltd, Reading, UK

AbstractUnder cyclic loading, most soils change their characteristics. Cyclic behaviour (change of shear modulus and accumulated strain) of the RedHill 110 sand was investigated by a series of cyclic simple shear tests. The effects of application of 50,000 cycles of shear loading with different shear strain amplitudes and vertical stresses were investigated. The results correlated quite well with the observations from scaled model tests of different types of offshore wind turbine foundations and limited field observations. Specifically, the test results showed that shear modulus increases rapidly in the initial loading cycles and then the rate of increase diminishes; the rate of increase depends on strain amplitude, initial relative density and vertical pressure. Complementary DEM simulations were performed using PFC2D to analyse the micromechanics underlying the cyclic behaviour of soils. It shows that the change of soil behaviour strongly related to the rotation of principle axes of fabric and degree of fabric anisotropy.

1. Introduction

1.2 Background

Offshore wind turbine foundations are subjected to a combination of cyclic and dynamic loading arising from wind, wave, 1P (rotor frequency) and 2P/3P (blade passing frequency). Designing foundations for offshore wind turbines (OWTs) are challenging as these are dynamically sensitive structures in the sense that natural frequencies of these structures are very close to the forcing frequencies (Bhattacharya and Adhikari, 2011). Typically for the widely used soft-stiff design (target frequency of the overall wind turbine is between 1P and 2P/3P), the ratio of forcing frequency (ff) to natural frequency (fn) is very close to 1 and as a result is prone to dynamic amplification of responses such as deflection/rotation. This effect may enhance the fatigue damage, thereby reducing the intended design life. Therefore, a designer apart from predicting the natural frequency of the structure, must also ensure that the overall natural frequency due to dynamic-soil-structure-interaction does not shift towards the forcing frequencies making the value of ff/fn even closer to 1 (Cui and Bhattacharya, 2016; Bhattacharya et al, 2012; Lombardi et al, 2013). Therefore foundations are one of the critical components of OWTS not only because of the overall stability of the structure but also due to financial viability of the project.

The global natural frequency is dependent on the soil-structure stiffness, thus an investigation of soil stiffness under cyclic loading is desired. Majority of current OWTs are supported by monopile foundation, which is a large steel tube typically 30-40m in length and 3-7m in diameter. Unlike the slender piles for offshore structure, monopile tends to rotate rather than bend under lateral load or overturning moment. Therefore, the interactions between the monopile and the surrounding soil could be represented by cyclic simple shear tests. Cyclic responses of soil stiffness have been studied intensively (Vucetica and Mortezaie, 2015; Liu et al, 2014), but few of them were focused on the micro-mechanism underlying these responses.

1.2 Aim and scope of the paper

The aim of this paper is to study the soil stiffness responses under cyclic simple shear loading with a focus on the micromechanics. Experimental cyclic simple shear tests on typical silica sand (RedHill 100) were first presented. DEM simulations were then performed using PFC2D, and the macroscopic soil stiffness and volumetric responses were validated against experiments. The micromechanical parameters were then analysed to find the relationships between the micromechanical parameters and macroscopic responses.

2. Experimental tests

2.1 Test apparatus

Dynamic/cyclic simple shear apparatus, as shown in Figure 1, is used for testing cylindrical samples of 50mm in diameter and 20mm in height, as suggested in ASTM D6528. The apparatus is capable of applying vertical and horizontal loads using two electro-mechanical dynamic actuators and the vertical and horizontal displacements can be measured using encoders within the servo motors. External LVDTs were also used to record displacements and to verify the effectiveness of feedback control. Loads up to +/-5kN can be applied in two directions with horizontal travel up to 25mm and vertical travel of 15mm. These are sufficient to study the effects of large strain levels applied to the soil. This also allows to study effects of cyclic shear stress under drained and undrained conditions. The loads can be applied at frequencies of up to 5Hz. This apparatus was used to investigate the cyclic behaviour of a silica sand (typical of North Sea) by maintaining the constant vertical consolidation stress while cycling the shear strain in horizontal direction, see Figure 1. More details can be found in Nikitas (2016).

Figure 1: Dynamic/cyclic simple shear apparatus with details of the sample

2.2 Test material

RedHill 110 Sand, a poorly graded fine grained silica sand with d50=0.18mm (PSD curve shown in Figure 2), was tested in this study as this soil has been used to carry out scaled model tests on different types of foundations. The sand has a specific gravity, Gs of 2.65 and minimum and maximum void ratio of 0.608 and 1.035 respectively.

Figure 2: Particle size distribution (PSD) of test sand in experiments and DEM simulations

2.3 Test procedure and test programme

Specimens of 50 mm diameter and 20 mm height were prepared for testing. A membrane was first rolled over the base pedestal and was sealed using an O-ring. Sand was poured into the mould together with gentle tamping on the top layers to obtain the required relative density. Once the sample is poured to the desired height, the top-cap is placed and membrane is pulled over and secured using double O-rings. The top plate assembly, vertical load cell and external displacement transducer were then attached and the specimen was ready for testing.

Strain controlled cyclic simple shear tests on medium dense sand with different relative densities (Dr = 50%, 75%) were performed. Tests were carried out with various vertical stresses (σ = 50kPa, 100kPa, 200kPa) and shear strain amplitudes (γmax = 0.1%, 0.2%, 0.5%).

2.4 Test results and discussion

The variations of shear modulus are illustrated in Figures 3. The shear modulus increases rapidly in the initial loading cycles and then the rate of increase diminishes and the shear modulus remains below an asymptote. The shear modulus increases with increasing vertical stress and relative density, but decreases with increasing strain amplitude as expected.

The accumulated vertical strains are illustrated in Figures 4. The increase of shear modulus is underlain by the consistent contractive responses of all samples. It can also be observed that vertical accumulated strain is proportional to the shear strain amplitude but inversely proportional and relative density of soil.

Figure 3: Variation of shear modulus in experiments (Legend: σ, Dr, γmax)

The results correlated quite well with the observations from scaled model tests with different types of offshore wind turbine foundations (Cuéllar et al 2012; Bhattacharya et al, 2012; Lombardi et al, 2013). The only abnormal trend observed is that the accumulated vertical strain decreases with increasing vertical stress. This is mainly due to the fact that more soil contraction was resulted by the application of higher vertical consolidation stress and the initial relative density has increased to a value higher than 50%. It could be deduced that the initial relative density has more significant impact on the vertical strain than the vertical stress. It also shows the difficulties of controlling the relative density for various vertical stresses in sample preparation. More tests with cautious control and accurate measurements of initial volumetric strain prior to shearing will be performed in the future to explore this effect.

Figure 4: Accumulated vertical strain in experiments (Legend: σ, Dr, γmax)

3. DEM simulations

3.1 Description of DEM setup

To explore the micro-mechanism which underlying the change of soil stiffness under cyclic loading, numerical simulations were performed. The discrete element method (DEM) was adopted because it is found to be more appropriate than other numerical methods (e.g. Finite Element Method) as it allows direct monitoring of change in soil stiffness during cyclic loading, rather than specify the stiffness change in the soil constitutive model.

Originally proposed by Cundall and Strack (1979), DEM simulates granular materials as assemblies of individual particles which respond to given load conditions. The interactions between particles are simulated by contact laws, where the normal and tangential contact forces are dependent on the overlap and relative displacement between two contact particles. In this study, the linear elastic contact model (Itasca, 2008) is adopted. The contact forces, accelerations, velocities and displacements of all particles are updated in each small time step using the central difference time integration method. Stresses and strains are then calculated from the contact forces within a representative volume element or along a boundary. A commercial DEM code PFC2D (Itasca, 2008) was used to perform the presented simulations.

The sample initially generated for testing is about 20mm in height and 50mm in width, containing 8000 disks with size ranging from 0.1mm to 0.3mm and d50=0.18mm, matching the value in experiments. The PSD curve is also given in Figure 2. Particle density is 2650 kg/m3. Inter-particle and particle-boundary frictional coefficient, μ, is 0.5. Normal stiffness of particle is 8.0×107 N/m and shear stiffness of particle is 4.0×107 N/m. Normal and shear stiffness of boundary are 4.0×109 N/m. Two sets of samples were generated with radius expansion approach followed by K0 consolidation with μ =0 and 1.0 to generate dense and loose samples, respectively. The void ratios (e) of dense samples at consolidation pressure of 50kPa and 100kPa are 0.185 and 0.181, respectively. The void ratios (e) of loose samples at consolidation pressure of 50kPa and 100kPa are 0.215 and 0.227, respectively. Note that due to different boundary velocity in consolidation stage, the loose sample reached slightly lower e at 50kPa than that at 100kPa. 6000 cycles of shear strain in the range of (-0.5%, 0.5%) were applied to each sample. The dense sample at consolidation pressure of 100kPa was also sheared with the shear strain amplitudes of (-0.1%, 0.1%), (-1.0%, 1.0%), and (-5.0%, 5.0%) to 6000 cycles. 12 measurement circles were defined within the sample to measure the average stress, void ratio and coordination number.

3.2 Macro-scale responses

The shear modulus (G) was calculated as

(1)

where τmax = shear stress at maximum shear strain γmax and τmin = shear stress at minimum shear strain γmin. The variations of shear modulus and vertical strain of the four samples under cyclic loading are illustrated in Figure 5. The magnitudes of shear moduli in the DEM simulations are in the same range as the values in the experimental tests. For both loose samples, there is a clear increase in the shear modulus under cyclic load; while for both dense samples, shear modulus decreases slightly. After 6000 cycles, the shear moduli of the loose sample and the dense sample approach a same constant at a same vertical stress. As shown in Figure 5(b), the initial shear modulus increases dramatically with reducing strain amplitude, and in all cases the shear modulus reduces slightly during cyclic shearing.

(a) Comparing packing density and σ with γmax =0.5%

(b) Comparing γmax with dense sample and σ=100kPa

Figure 5: Evolution of shear modulus in simulations

The evolutions of void ratios of the four samples under cyclic loading are illustrated in Figure 6. The increasing shear modulus of both loose samples could be explained by the densification (reduction in void ratio) as observed in Figure 6. The shear moduli for two dense samples reduce obviously, but they only dilated slightly. Moreover, the void ratios of the two loose samples were still higher than the corresponding dense samples at the end of 6000 loading cycles, but their shear moduli have approached the value for the dense sample. These observations should be explored in more details by considering their particle-scale parameters. As shown in Figure 6(b), with higher strain amplitude, dense sample dilated more. And with strain amplitude at 1.0% and 5.0%, sample dilates first and then contracts remarkably.

(a) Comparing packing density and σ with γmax =0.5%

(b) Comparing γmax with dense sample and σ=100kPa

Figure 6: Evolution of void ratio in simulations

3.3 Particle-scale responses

3.3.1 Coordination number (Nc)

The coordination number (Nc) is the average number of contacts surrounding each particle. It has a strong relation with the stress level within the sample (Cui et al, 2007). The evolutions of Nc under cyclic loading for the four samples are shown in Figure 7. It is clear in Figure 7(a) that the initial low Nc corresponds to initial low shear stress (thus low shear modulus). The increase in shear modulus for the two loose samples is related to the increase in Nc and the decrease in shear modulus for the dense samples agrees with the reduction in Nc. With higher strain amplitude, Nc reduces more and quicker with loading cycles (Figure 7(b)).

(a) Comparing packing density and σ with γmax =0.5%

(b) Comparing γmax with dense sample and σ=100kPa

Figure 7: Evolution of coordination number (Nc)

3.3.1 Fabric

There are many evidences of the impact of fabric anisotropy on characteristics of granular materials (e.g. Cui and O’Sullivan, 2006; Li and Yu, 2014). It is worth to analyse the evolution of soil fabric in the current cyclic loading conditions. The spatial distribution of directions of particle contact normals can be quantified using the Fourier approximation (Rothenburg and Bathurst, 1989) as:

(2)

where a = a parameter defining the magnitude of anisotropy and θa = the direction of the principal fabric. For an isotropic sample, a=0 and E(θ)=1/2π, which is a circle with a distribution of 1/2π per radian.

The histogram of spatial distribution of directions of particle contact normals for the dense sample at σ=100kPa is illustrated in Figure 8. The Fourier approximation function is indicated by the red ellipse with the long axis (θa) indicating the major principle direction of fabric. The major principle fabric of the initial sample is θa=56°. When sheared to the maximum strain (0.5%), the major principle fabric direction rotated to the diagonal direction (θa≈130.0°); when it is sheared to minimum strain (-0.5%), the major principle fabric direction rotated to the perpendicular diagonal direction (θa≈40.0°). Note that the sample boundary only rotated up to ±0.5°; however, the major principle fabric direction rotated about 90°.

Figure 8: Spatial distribution of contact normal

The evolution of θa at the maximum strain and minimum strain for all four specimens are plotted in Figure 9. Note that the initial θa for the four samples are 83° (loose, σ=50kPa), 165° (loose, σ=100kPa), 80° (dense, σ=50kPa) and 56° (dense, σ=100kPa). It can be observed that the rotation of θa occurs slowly in loose samples. For the loose sample with σ=50kPa, θa at γmax starts from about 110° and increases slowly to 130° at large cycle number; while for the loose sample with σ=100kPa, θa at γmax starts from about 140° and decreases slowly to 130°. However, for both dense samples θa at γmax reaches 130° in the first loading cycle and remains at 130°. Rotation of θa at γmin shows similar trend: rotation of θa occurs slowly in loose samples until it reaches 40°; θa in dense samples arrives at 40° in the first cycle.

For the dense sample with σ=100kPa, rotation of θa does not show obvious difference with various strain amplitude (Figure 9(b)).

(a) Comparing packing density and σ with γmax =0.5%

(b) Comparing γmax with dense sample and σ=100kPa

Figure 9: Evolution of major fabric direction at maximum strain and minimum strain

The magnitude of fabric anisotropy is quantified by a in Equation (2). It has been demonstrated previously (Cui and O’Sullivan, 2006; Li and Yu, 2014) that larger magnitude of anisotropy can result in higher shear stress. As illustrated in Figure 8, a relates to the aspect ratio of the red ellipse. At τmax, the long axis is along 130°; at τmin, the long axis is along 40°. Considering the shear modulus is determined by τmax - τmin, the sum of a at corresponding strain values, i.e. amax + amin could be an indicator of τmax - τmin. The evolutions of amax + a0 for the seven simulations are shown in Figure 10. It is clear that amax + amin for the dense samples drop significantly, which agrees with the fact that the τmax - τmin for this sample also drop obviously. And amax + amin for the loose samples increase clearly, which agrees with the increase in τmax - τmin. With higher strain amplitude, degree of anisotropy increases dramatically, which reflects that the shear stress level increases.

(a) Comparing packing density and σ with γmax =0.5%

(b) Comparing γmax with dense sample and σ=100kPa

Figure 10. Difference of magnitude of fabric anisotropy between maximum strain and zero strain

4. Discussions

The experimental cyclic simple shear test is a three-dimensional problem; however it is simulated in plane-strain conditions in the current study. It is obvious that a two-dimensional simulation cannot accurately represent a three-dimensional granular soil. However, there is no intention in this paper to reproduce the physical test quantitatively, but analyse the similar underlying micro-mechanism. One big difference between the 2D disk assembly and 3D soils is the typical range of void ratios. The void ratios of the RedHill 110 sand are in the range of (0.608, 1.035). There is no well-established minimum void ratio and maximum void ratio for disk packings with arbitrary particle size distributions. However, considering that the minimum void ratio for random packing of identical disks is about 0.205 (Quickenden and Tan, 1974) and the maximum void ratio of stable packing of identical disks is the square packing (Williams 1979) with void ratio at 0.273, the samples with void ratio at 0.185 and 0.181 are equivalent to dense soil samples and the samples with void ratio at 0.215 and 0.227 are equivalent to loose soil samples.

5. Conclusions

Both experimental tests and DEM simulations of cyclic simple shear tests were performed to explore the variations of soil characteristics under cyclic loading and its underlying micro-mechanism. It has been found that:

· Shear modulus for loose soil increases rapidly in the initial loading cycles as a result of soil densification, and then the rate of increase diminishes when void ratio approaches constant.

· Shear modulus increases with increasing vertical stress and relative density, but decreases with increasing strain amplitude as expected.

· Vertical accumulated strain is proportional to the shear strain amplitude but inversely proportional to the relative density of soil.

· Initial relative density has more significant impact on the volumetric response than vertical stress does.

· Higher shear stress level and shear modulus is correlated to higher coordination number.

· Rotation of principle direction of fabric occurs slowly in loose sample, but reaches the final value in the first cycle in dense sample.

· Higher shear stress level and shear modulus is directly correlated to higher magnitude of fabric anisotropy.

This study verifies the capability of DEM in analysing the micro-mechanism underling the soil stiffness variation during cyclic loading. More parametric studies will be carried out in the future work, including cyclic loadings with various ratio of maximum strain to minimum strain. Non-circular disks will be considered as well. An empirical model for evolution of shear modulus will be established to include the impact of all macroscopic and microscopic parameters

References:

ASTM D6528 – 07, (2007). Standard Test Method for Consolidated Undrained Direct Simple Shear Testing of Cohesive Soils.

Bhattacharya S and Adhikari S, (2011). Experimental validation of soil–structure interaction of offshore wind turbines. Soil Dynamics and Earthquake Engineering, 31 (5–6), 805-816.

Bhattacharya S, Cox JA, Lombardi D and Muir Wood D (2012): Dynamics of offshore wind turbines on two types of foundations. Proceedings of the Institution of Civil Engineers: Geotechnical Engineering, 166, 159 –169.

Cuéllar P, Georgi S, Baeßler M and Rücker W (2012) On the quasi-static granular convective flow and sand densification around pile foundations under cyclic lateral loading. Granular Matter 14(1), 11-25.

Cundall P and Strack O (1979) A discrete numerical model for granular assemblies. Geotechnique. 29(1): 47-65.

Cui L and Bhattacharya S (2016) Soil–monopile interactions for offshore wind turbines. Proceedings of the ICE - Engineering and Computational Mechanics, 169(4), 171–182.

Cui, L. and C. O’Sullivan (2006) “Exploring the macro- and micro-scale response characteristics of an idealized granular material in the direct shear apparatus” Geotechnique Vol 56(7), pp 455-468.

Cui, L., C. O’Sullivan and S. O’Neil (2007) “An analysis of the triaxial apparatus using a mixed boundary three-dimensional discrete element model” Geotechnique Vol 57(10), pp 831-844.

Itasca, (2008) PFC2D manual 4.0.

Li X., H.S. Yu (2014), Fabric, force and strength anisotropies in granular materials: a micromechanical insight Acta Mechanica 225 (8), 2345-2362.

Liu H., D. Zou, J. Liu, (2014) Constitutive modeling of dense gravelly soils subjected to cyclic loading. International Journal for Numerical and Analytical Methods in Geomechanics, 38(14), 1503-1518.

Lombardi, D., Bhattacharya, S. and Muir Wood, D (2013) Dynamic soil–structure interaction of monopile supported wind turbines in cohesive soil. Soil Dynamics and Earthquake Engineering 49, 165-180

Nikitas G, L Arany, S Aingaran, JN Vimalan and S. Bhattacharya (2016) Predicting long term performance of Offshore Wind Turbines using Cyclic Simple Shear apparatus. Journal of Soil Dynamics and Earthquake Engineering, 92, 678-683.

Quickenden, T. J. and G. K. Tan (1974). Random packing in two dimensions and the structure of monolayers. Journal of Colloid and Interface Science, 48(3), 382-393,

Rothenburg L., R.J. Bathurst (1989), Analytical study of induced anisotropy in idealized granular materials Geotechnique, 39, 601-614.

Vucetica M., A. Mortezaie (2015) Cyclic secant shear modulus versus pore water pressure in sands at small cyclic strains. Soil Dynamics and Earthquake Engineering, 70, 60-72.

Williams, R. (1979) Circle Packings, Plane Tessellations, and Networks. §2.3 in Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, pp. 34-47.

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Loose σ=50kPaLoose σ=100kPaDense σ=50kPaDense σ=100kPa

02468101214110100100010000Shear Modulus (MPa)Number of Cycles

γ (-0.1%,0.1%)γ (-0.5%,0.5%)γ (-1.0%,1.0%)γ (-5.0%,5.0%)

0.150.160.170.180.190.20.210.220.230.24110100100010000Void RatioNumber of Cycles

Loose σ=50kPaLoose σ=100kPaDense σ=50kPaDense σ=100kPa

0.170.1750.180.1850.19110100100010000Void RatioNumber of Cycles

γ (-0.1%,0.1%)γ (-0.5%,0.5%)γ (-1.0%,1.0%)γ (-5.0%,5.0%)

2.62.833.23.43.63.844.2110100100010000Coordination NumberNumber of Cycles

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2.62.833.23.43.63.844.2110100100010000Coordination NumberNumber of Cycles

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0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%100.0%0.0100.1001.000Percentage passingSeive size (mm)PSD in experimentsPSD in DEM simulations