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# Numerical Modelling of Multidirectional Loading on Piles in Soft Clay

Cristian Soriano-Camelo, Luc Thorel, Matthieu Blanc

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Cristian Soriano-Camelo, Luc Thorel, Matthieu Blanc. Numerical Modelling of Multidirectional Loading on Piles in Soft Clay. 2024. hal-05037741

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# Numerical modeling of multidirectional loading on piles in soft clay

Cristian Soriano-Camelo (✉), Luc Thorel, Matthieu Blanc

Geotechnical Centrifuge Laboratory

Université Gustave Eiffel

cristian.soriano-camelo@univ-eiffel.fr

**Abstract.** In the search for approaches to reduce costs in the deployment of offshore wind farms utilizing floating systems, multiline anchors represent a viable alternative by reducing the number of anchors and installations needed. As part of the research objectives of the ShareWind project, this study introduces a workflow for conducting numerical simulations that apply multidirectional loads, simulating the convergence of three mooring lines onto a single pile anchor installed in soft clay. Utilizing OpenSees, the numerical model is first calibrated against centrifuge test data for piles under monotonic and cyclic loads. Subsequently, a series of numerical analyses were performed by applying variable amplitude load sequences and considering seabed inclination conditions. The research concludes with a suite of numerical simulations that impose loads characteristic of a floating wind turbine, thereby simulating the convergence of three mooring lines onto the pile anchor. The findings present a modeling framework for this specific load condition, which could be instrumental for other researchers and practitioners in the field.

> "This is a preprint of the following chapter: Foundation Engineering and Subsea Technologies, published in, Lecture Notes in Civil Engineering, vol 590, edited by Huynh, D.V.K., Doan, H., Cao, T.M., Watson, P. (eds), 2025, Springer, Singapore reproduced with permission of Springer. The final authenticated version is available online at: https://doi.org/10.1007/978-981-96-3912-0_40"

## 1 Introduction

In the context of renewable energy, research efforts are underway to develop anchoring systems for floating wind turbines (Aubeny 2017; Knappet et al. 2015; Randolph 2020). Among the various anchor types (gravity, piles, and plates), new approaches are being explored to optimize the costs and environmental impacts associated with the development of offshore wind farms. One such alternative involves sharing anchors, where multiple mooring lines are connected to a single anchor (Fontana et al. 2018).

The ShareWind project aims to leverage the expertise accumulated in the offshore wind industry regarding anchor design considerations and the concept of shared anchors. This paper presents a set of numerical simulations of the response of a pile anchor subjected to cyclic and multidirectional loads. The numerical models were developed using OpenSees software (McKenna et al., 2000) and employed the pressure independent multiyield (PIMY) soil constitutive model, which considers the degradation of stiffness under cyclic loading and is suitable for cohesive materials. The model was initially developed based on centrifuge tests conducted at the Université Gustave Eiffel (Khemaken, 2012) to obtain a calibrated model of a pile subjected to monotonic and cyclic loading.

Following the calibration of the numerical model, a series of numerical models were constructed to evaluate the response of piles installed in soft clay under variable amplitude load
scenarios. Subsequently, the numerical models simulated multidirectional load scenarios employing loads representative of floating wind turbines and were adapted to the problem studied in this paper. The findings of this research aim to present a methodology to simulate the application of a multidirectional load on a single pile anchor. Although this study does not focus on the anchor load capacity, it provides several insights into the response of this type of anchoring system in terms of cyclic and permanent displacements.

# 2 Numerical model

## 2.1 Reference model: SOLCYP centrifuge tests

For the calibration of the numerical model, centrifuge tests conducted at the Université Gustave Eiffel by Khemakhem (2012) were employed. These experiments, which are part of the SOLCYP project (Puech and Garnier 2017), consisted of monotonic and cyclic loading tests on piles installed in Speswhite kaolin clay. The experiments were conducted at a centrifuge acceleration of 50 g. The model pile was installed at 1 g by jacking it through a prebored hole with a smaller diameter than that of the pile. Given this installation method, the pile can be considered wished-in-place. The pile was instrumented with 21 levels of strain gauges to measure the bending moments throughout the length of the pile. Figure 1 depicts the geometry of the pile with the dimensions presented at the prototype scale. Further details about the model preparation methodology are provided by Khemakhem (2012).

<figure><img src="image_3.png" /><figcaption>Fig. 1. Pile geometry parameters</figcaption></figure>

The type of soil used in the centrifuge experiments was Speswhite kaolin clay. The model preparation methodology involved reconstitution, which consisted of mixing kaolin powder with water to achieve a water content of approximately 90%, creating a slurry that could be poured into the centrifuge model container. The clay was then consolidated at 1 g by applying a sequence of pressures using a hydraulic pump. Figure 2 presents a view of the setup for consolidating clay samples at the centrifuge laboratory of the Université Gustave Eiffel.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Setup for consolidation of the clay samples</figcaption></figure>
Based on the experimental results of T-bar tests conducted during centrifuge tests, Khemakhem (2012) proposed an undrained shear strength ($s_u$) profile that increases with depth, as shown in Equation 1:

$$s_u = 1.27 + 1.17 z \qquad (1)$$

where z is the clay depth in meters and $s_u$ is in kPa.

## 2.2 Model calibration

A series of numerical simulations were performed using OpenSeesPL (Elgamal and Yang, 2011), employing a three-dimensional mesh. For the soil domain, 8-node brick elements were employed, and for the pile, ‘elasticBeamColumn’ elements were utilized.

To simulate the response of piles installed in clay and subjected to monotonic and cyclic loads, an appropriate constitutive model was needed. The pressure independent multiyield (PIMY) constitutive model (Mazzoni et al. 2005) was employed for simulating the clay. The PIMY model simulates elastoplastic behavior where plasticity occurs in the deviatoric stress-strain response and is not sensitive to confinement, making it suitable for simulating the undrained response of clays. The PIMY material model uses nested yield surfaces to control the plastic modulus and can be further adjusted by specifying a backbone curve. Figure 2 shows a view of the half mesh and a summary of the model calibration parameters.

<figure><img src="image_5.png" /><figcaption>Fig. 2. A view of the finite element mesh (half view) and model parameters</figcaption></figure>

The finite element mesh shown in Figure 2 was set with a boundary distance from the edge of the pile at 20 times the pile diameter (20 meters) and a vertical extent of twice the pile embedment length (32 meters). Boundary conditions were defined to fix all displacement components at the bottom boundary, and normal displacements were fixed at the vertical boundaries. To account for the variation in the undrained shear strength with depth, the profile defined in Equation 1 was divided into sublayers of 1 m, following a similar approach to that used by Soriano et al. (2024) in models of clay slopes subjected to earthquake loads.
## 2.3 Model calibration results

To evaluate the performance of the numerical model, the SOLCYPC05S1ins centrifuge experiment was used for the monotonic load case, and the SOLCYPC01S1ins experiment was used for the cyclic load scenario (Khemakhem 2012). For both cases, the load was applied at the pile head, 2 m above the ground surface, as shown in Figure 1. Figure 3 shows the results of the monotonic load response of the numerical model in terms of the pile head displacements and bending moment distribution at two load levels (200 kN and 305 kN). The experimental results indicate an ultimate load of approximately 350 kN, which was mobilized until the displacements reached approximately 20 cm, or approximately 20% of the pile diameter. Overall, the numerical model follows the load-displacement response and the bending moment distribution recorded during the centrifuge experiment.

<figure><img src="image_6.png" /><figcaption>Fig. 3. Monotonic load test: experimental and numerical model response</figcaption></figure>

Figure 4 presents the load sequence applied in the cyclic load test SOLCYPC01S1ins, where a set of 1000 loading cycles were applied at a frequency of 0.25 Hz. The numerical model follows the peak displacement trend from the centrifuge tests for this relatively large number of cycle load conditions.

<figure><img src="image_7.png" /><figcaption>Fig. 4. Cyclic load test: experimental and numerical model response</figcaption></figure>
## 3 Cyclic load numerical models

To assess the response of the numerical model, a set of load scenarios was defined to observe the accumulation of the pile head displacements. For the numerical models, the same geometry defined in the model calibration was employed. Table 1 presents a list of the numerical models used. Given the nature of the simulations, load multipliers were applied to a defined peak load ($H_{max}=233$ kN). For this purpose, a safety factor (FS) of 1.5 was applied to the ultimate load ($H_{ult}=350$ kN) achieved in the monotonic load test (Figure 3).

<table><caption>**Table 1.** List of numerical models used</caption><thead><tr><th>Model</th><th>H<sub>ult</sub><br>(kN)</th><th>FS</th><th>H<sub>peak</sub><br>(kN)</th><th>Description</th><th>N(cycles)</th></tr></thead><tbody><tr><td>M1</td><td rowspan="4">350.0</td><td rowspan="4">1.5</td><td rowspan="4">233.3</td><td>Variable amplitude storm - increasing</td><td>1228.0</td></tr><tr><td>M2</td><td>Variable amplitude storm -decreasing</td><td>1228.0</td></tr><tr><td>M3</td><td>Variable amplitude storm - increasing - 2.5 degrees slope</td><td>1228.0</td></tr><tr><td>M4</td><td>Variable amplitude storm - increasing - 5 degrees slope</td><td>1228.0</td></tr><tr><td>M5</td><td rowspan="3">M6</td><td rowspan="3">M7</td><td rowspan="3"></td><td>Multidirectional load WWC 0 deg</td><td>-</td></tr><tr><td>M6</td><td>Multidirectional load WWC 30 deg</td><td>-</td></tr><tr><td>M7</td><td>Multidirectional load WWC 60 deg</td><td>-</td></tr></tbody></table>

### 3.1 Unidirectional cyclic loading

Models M1 to M4 presented in Table 1 correspond to a series of unidirectional loads applied at the pile head. The load composition based on load packages from Andersen (2015) was selected for the analyses. Figure 5 illustrates an adaptation of the load composition presented in the form of load multipliers.

<figure><img src="image_8.png" /><figcaption>**Fig 5.** Load multipliers applied to models M1 to M4</figcaption></figure>

Figure 6 compares the load-displacement curves obtained from the application of the increasing and decreasing loading sequences to models M1 and M2. One aim was to observe the performance of the model under a relatively high number of cycles (>1000 cycles) while applying a well-established load history used in offshore foundation applications. The results show a distinct response depending on the order of the load packages applied.

The increasing load sequence results in an accumulation of permanent displacements of approximately 11 cm and cyclic displacements reaching values of 20 cm. In contrast, the decreasing loading sequence presented an initial generation of
relatively large cyclic displacements (approximately 16 cm) and a relatively stable trend in terms of permanent displacement, reaching values of approximately 7 cm at the end of the load sequence. This difference can be attributed to a progressive accumulation of plastic deformations during the increasing amplitude load sequence, with a sharp increase during the application of the last two loading packages. Similar observations have been reported by other researchers in numerical models of suction caissons subjected to this type of loading sequence (Al-Ramthan and Aubeny 2020; Al-Janabi and Aubeny 2022).

<figure><img src="image_9.png" /><figcaption>Fig 6. Variable amplitude load: increasing amplitude loading sequence (M1) and decreasing amplitude loading sequence (M2)</figcaption></figure>

With the baseline model and load sequence of increasing amplitude, additional analyses were conducted to account for the inclination of the ground surface, simulating gently sloping ground conditions. Models M3 and M4 incorporated ground-level inclinations of 2.5 degrees and 5 degrees, respectively. These angles align with the ranges of slope angles for shallow seafloors reported by Canals et al. (2019) in a study related to submarine landslides. The results of models M1, M3, and M4 underscore the influence of the sloping ground level on the accumulation of permanent displacements at the pile head. A slightly larger accumulation of permanent displacements was observed, ranging between 11 cm and 15 cm, as the slope angle increased from 0 to 5 degrees. This suggests that seabed inclination should be included in the evaluation of pile anchor performance under cyclic loading.

<figure><img src="image_10.png" /><figcaption>Fig 7. Variable amplitude load response and ground inclination: M1 0 deg, M3 2.5 deg and M4 5.0 deg</figcaption></figure>
## 3.2 Multidirectional loading

A set of numerical models was constructed to assess the performance of the piles under multidirectional loading. The motivation behind these models is based on the observation that offshore structures such as wind turbines and offshore platforms are subjected to wind, wave, and current (WWC) loads with variable directions. The numerical model was subjected to a set of loads designed to represent multidirectional loading conditions. The configuration involved the convergence of three mooring lines at the pile head. This approach aims to apply the shared anchors concept, as utilized in projects such as Hywind Tampen, WindFloat, and Hybrid Spar (Fontana et al., 2018). Figure 8 presents a schematic representation of three floating wind turbines, with their mooring lines converging to a single anchor.

<figure><img src="image_11.png" /><figcaption>**Fig 8.** Schematic representation of the configuration of shared anchors for floating wind turbines</figcaption></figure>

The loads for the shared anchors configuration were derived from the calculations presented by Balakrishnan et al., 2020. The configuration involved three spar buoy-supported wind turbines (NREL 5 MW with OC3) sharing anchors, as depicted in Figure 8. Figure 9 shows the tensile forces for two loading cases representing two wind, wave, and current (WWC) component orientations: 0°WWC and 30°WWC. The components T1, T2, and T3 represent the forces for each mooring line, with an angular separation of 120°. Additionally, the Tmulti component represents the resultant force obtained by vector addition.

<figure><img src="image_12.png" /><figcaption>**Fig 9.** Time histories of forces from three mooring lines arriving at a single anchor (Adapted from Balakrishnan et al., 2020)</figcaption></figure>

The multidirectional loads were normalized by the peak value of the H1 component time history to obtain a set of multipliers that were subsequently scaled to the peak force used
in the previous models, Hpeak=233 kN. Figure 10 summarizes the scaled load applied to the model and the orientation of the resultant force component (Hmulti). The orientation of the resultant forces exhibits a relatively complex pattern that oscillates around the orientation of the WWC components.

<figure><img src="image_13.png" /><figcaption>**Fig 10.** Time histories of multidirectional forces scaled to Hmax=233 kN and orientation of the multidirectional forces.</figcaption></figure>

The resultant displacements for each load case are depicted in Figure 11. The responses exhibit patterns that correspond to the orientations of the multidirectional force components. In the WWC0 load case, the peak displacement reached approximately 9 cm, which closely approximates the value obtained for the WWC30 load case, where the displacement was approximately 10 cm. Both patients showed similar mean displacements of approximately 8 cm. The similarity in displacement highlights the importance of using an axisymmetric anchor able to provide a balanced distribution of multidirectional forces.

<figure><img src="image_14.png" /><figcaption>**Fig 11.** Multidirectional load: resultant pile head displacements for load cases WWC0° and WWC 30°</figcaption></figure>
# 4 Conclusions

This study investigated the behavior of pile anchors under multidirectional and cyclic loading conditions representative of offshore wind turbine installations in soft clay. Through numerical simulations calibrated against centrifuge test data, several findings were observed:

* The response of the pile under monotonic and cyclic loading demonstrated a good correlation with the experimental results, validating the accuracy of the numerical model. The pile exhibited significant plastic deformations, particularly under increasing amplitude load sequences, highlighting the importance of considering the order and nature of cyclic loads in design calculations.

* The introduction of seabed inclinations, which simulate gently sloping ground conditions, revealed an increase in permanent displacements at the pile head as the slope angle increased. This suggests that seabed topography should be incorporated into the assessment of pile performance under cyclic loading conditions.

* The multidirectional loading scenarios, simulating the convergence of three mooring lines onto a single pile, resulted in complex displacement patterns that aligned with the orientation of the applied loads. The results indicated that an axisymmetric anchor design could effectively balance multidirectional forces, thereby enhancing the stability and performance.

Overall, this study provides a modeling framework for evaluating pile anchors under realistic offshore loading conditions. Future research should continue to refine these models and explore additional variables, such as varying soil properties and more complex loading sequences, to further enhance the understanding of pile anchor behavior in offshore environments.

## Acknowledgments

This research received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement 101106921 - Project ShareWind.

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