Cyclic Bearing Mechanism of Suction Caissons Supporting Offshore Wind Turbines in Clay

The bearing behavior of suction caissons supporting offshore wind turbines under two-way cyclic lateral loading and dead load in clay was investigated with consideration of soil strength degradation and adhesive interface friction between caisson walls and heterogeneous clay using the finite-element package ABAQUS. An ABAQUS built-in user subroutine was programmed to calculate the adhesive interface friction between clay and caisson walls. The results of parametric studies showed that the degradation of bearing capacity could be aggravated by the decrease of the aspect ratio. The offset between the rotation point of the soil inside the caisson and the central axis of the caisson increased with the increasing vertical load and number of cycles. The linearly increasing strength profile and adhesive interface led to the formation of an inverted spoon failure zone inside the caisson. The settlement-rotation curves in each cycle moved downwards with increasing number of cycles due to the soil strength degradation.


Introduction
The suction caisson is a bucket structure inverted into the seabed, which is also called bucket foundation or suction bucket foundation. Suction caisson is closed at the top, open at the bottom and its top is equipped with drainage and air pumping port. Its self-weight is firstly used to penetrate into a certain depth creating a seal between skirt and soil. The caisson is then further installed through suction by pumping water from caisson interior to create a differential water pressure across the caisson lid. The suction caisson has great advantages over traditional gravity and monopile foundations in many aspects, such as shortening the installation period, enhancing the overturning stability, lowering the construction cost and recycling for reutilization. The suction caisson has been widely used in supporting or anchoring ocean structures, such as wind turbines and platforms. Offshore wind turbines founded on suction caissons often suffer from monotonic or cyclic lateral environmental loads, such as wind and wave loads acting on turbine tower and rotor blades. In particular, the consideration of cyclic loading has been a research trend for the design of suction caissons in recent years.
In recent studies, model tests (Villalobos et al., 2010;Chen,2013;Zhu et al., 2013;Foglia et al., 2015;Wang et al., 2017), or field tests (Houlsby et al., 2005) were used to explore the response of the suction caisson under cyclic loading in sand or clay. Results from these tests showed that bucket geometry, soil conditions, cyclic displacement amplitude and cyclic number have significant influence on the bearing capacity and settlement of suction caissons. Jara (2006) suggested that the increasing vertical load is favorable to the response of suction caisson. The results of Zhu et al. (2013) showed larger accumulation of rotation for larger cyclic magnitude and two-way cyclic loading for fully drained conditions in sand. However, these model tests and field tests cannot provide an insight into failure mechanisms of the soil inside and outside the caisson due to the technical difficulties in observing soil movement and evolution of plastic zone. In addition, the number of the experiments was limited due to high cost of time and funding. In contrast, finite element (FE) simulation has been considered as a powerful tool to solve the above problems. Some finite element simulations have been carried out on the response of bucket foundation under different loads. Achmus et al. (2013) developed a numerical simulation scheme combined with stiffness attenuation method by per-forming three-dimensional finite element numerical simulation on suction bucket foundation under monotonic and cyclic horizontal loads. Wu (2007) studied the influence of load eccentricity and lateral anisotropy of soil on the failure envelope under composite load, based on ABAQUS and its secondary development. There are two tough problems for FE simulation to analyze the bearing mechanism of the suction caissons in clay under the cyclic loading. One major concern is the degradation of soil strength. But it was ignored in previous FE simulations (Kourkoulis et al., 2014;Cheng et al., 2016;Liu et al., 2014). In the present study, strain-softening of soil strength under cyclic loading is considered. Compared with the previous finite element simulations, it can simulate the bearing mechanism of caisson and failure mode of soil more accurately. A strength degradation model proposed by Einav and Randolph (2005) was incorporated into the commercial FE software ABAQUS by programming its user subroutine USDFLD. Another crucial problem is the modelling of the interface between the suction caisson and the clay. In previous numerical simulations (Gerolymos et al., 2015;Ansari et al., 2014;Haiderali et al., 2015), the ABAQUS built-in Coulomb's law of friction was often used by default to model the frictional behavior between the clay and structures. The ultimate friction acting on the contact interface is always proportional to the normal stress in the Coulomb's law of friction. However, for numerical simulations of suction caissons under undrained conditions, it is more appropriate and convenient to adopt the total stress method, in which the ultimate friction between the clay and caisson walls is defined by the undrained shear strength multiplied by an adhesion coefficient for considering soil strength degradation, irrespective of the normal stress, which has been used by several previous numerical studies (Kourkoulis et al., 2014;Zhou and Randolph, 2006). In the present study, the ABAQUS built-in user subroutine FRIC_COEF was programmed to calculate the adhesive interface friction between the clay and caisson walls.
The objective of the present study is to investigate the cyclic bearing mechanism of suction caisson supporting offshore wind turbines founded in clay. A three-dimensional finite element model of a suction caisson foundation system was built through ABAQUS. Parametric studies were conducted by a series of FE simulations. The influence of dead weight of the suction caisson and superstructures, number of load cycles, and aspect ratio on the cyclic bearing capacity, failure mechanism of the soil and settlement of the suction caisson was discussed.

Modelling of adhesive interface and validation τ crit
For cohesive soil, the interface shear stress calculation is crucial to the FE simulation. The ultimate friction α between the caisson and clay can be estimated by multiplying the initial undrained shear strength s u by a dimensionless adhesion coefficient (Kourkoulis et al., 2014;Cheng et al., 2016;Randolph and House, 2002;Chen and Randolph, 2007): (1) The value of the adhesion coefficient can not only be related to the soil softening during installation and operation of suction caisson, but also be connected with the soil strength recovery when the wind turbines are under no or little environmental loading. The value of adhesion coefficient ranged from 0.3 to 0.85 according to the previous experimental studies (House and Randolph, 2001;Andersen and Jostad, 2002;Jeanjean et al., 2006;Gourvenec et al., 2009). τ crit However, the linear-elastic perfectly plastic Coulomb's law of friction is used by default in ABAQUS, and the ultimate friction is described by: μ where is the coefficient of friction, and p is the contact pressure acting normal to the interface. Frictional constraints are enforced with a finite stiffness (penalty method) by default in ABAQUS/Standard. As shown in Fig. 1, when the frictional state is "sticking", ABAQUS allows an elastic slip to occur, and when the friction increases to the ultimate friction, the frictional state turns into "slipping". τ crit τ crit For heterogeneous clay, a series of values of varying with depths cannot be specified in ABAQUS/CAE, which was often ignored by previous papers (Cheng et al., 2016;Chatterjee et al., 2012). In this study, the user subroutine FRIC_COEF was used to calculate the values of of adhesive interface. The coefficient of friction needs to be prescribed in the user subroutine as the following equation: μ = αs u /p. (3) As shown in Fig. 2, a two-dimensional axis-symmetric finite element model that models a displacement pile penetrated into a clay layer was built to validate the programmed user subroutine FRIC_COEF. In ABAQUS, the pile model can be constrained as a rigid body moving with a reference point (RP). Soil elements were simulated using a 4-node bilinear axisymmetric quadrilateral element with reduced in- α μ tegration (CAX4R). The upper and lower boundaries of the soil model were not allowed to move along the vertical direction. A distributed pressure of 20 kPa that keeps the pile and soil in contact was applied at the right boundary. The undrained response of the soil was modelled as a linear elastic-perfectly plastic model, governed by the Tresca failure criterion, and defined by the Young's modulus of 5 MPa, Poisson's ratio of 0.49 and initial undrained shear strength s u increasing linearly with depth according to s u = 10 + 60z (kPa), where z is the depth. The soil-pile interaction was modelled using the "surface-to-surface" contact. The normal contact behavior was defined by the "hard" contact, and the tangential contact behavior was defined by FRIC_COEF or Coulomb's law of friction. The adhesion coefficient was 0.3 when FRIC_COEF was used to calculate the friction. For comparison, the coefficient of friction was also 0.3 in ABAQUS with built-in Coulomb's law of friction for the purpose of revealing the unreasonable simulation made by some previous studies (Gerolymos et al., 2015;Ansari et al., 2014;Haiderali et al., 2015). Fig. 3 shows cyclic friction-displacement response of two nodes at the soil-pile adhesive interface. The shear strength s u1 at Node 1 and s u2 at Node 2 are 10.5 kPa and 15.5 kPa, respectively. The adhesive ultimate friction calculated by the user subroutine FRIC_COEF was quite precise and varied with the undrained shear strength, s u1 and s u2 , while the ultimate friction calculated by the Coulomb's law of friction varied with the normal pressure at the interface.

Strength degradation model
ξ Einav and Randolph (2005) proposed a strength degradation model that is a simple extension of the ideal rigidplastic model. The current shear strength s uc was assumed to depend on the accumulated absolute plastic shear strain , using the following expression: where s u is the initial undrained shear strength, is the fully remolded strength ratio calculated by inverting the sensitivity of the soil, and represents the cumulative shear strain required for 95% remolding. Typical values of and can been estimated in the range of 0.2 to 0.5 (Randolph, 2004) and 10 to 50 (Einav and Randolph, 2005), respectively. ξ t This study incorporated the strength degradation model into ABAQUS by writing the user subroutine USDFLD. The current accumulated absolute plastic shear strain is updated by: where is the previous accumulated absolute plastic shear strain, and are the maximum and minimum principle plastic strain increments respectively, which can be calculated from the six plastic strain increments.

Geometry and modelling of suction caissons
The finite element model of a suction caisson in a clay layer is shown in Fig. 4. By considering the symmetry of both geometrical and loading conditions, only half of the suction caisson and half of the soil were constructed in order to reduce computational cost. The suction caisson was considered as wished-in-place. If the thickness of the caisson walls is considered, the horizontal size of soil elements under the skirt tip will be very small, which can be easy to cause convergence problems. Therefore, the suction caisson was modelled as a shell shape without thickness. It has been confirmed that by comparing the ultimate bearing capacity of suction caissons with and without thickness, the influence of the thickness can be ignored. Moreover, the hori-  zontal bearing capacity of caisson has nothing to do with the caisson wall thickness (Randolph and House, 2002). A soil model diameter of eight times the caisson diameter and a soil depth of four times the skirt length were chosen. The soil model consists of two parts including the soil inside the caisson and the soil outside, which are bonded with a tie constraint.
The clay was modelled as the modified Tresca material. All displacements were fixed at the bottom of the soil, both horizontal displacements were prevented on the cylindrical surface of the soil, and a symmetrical constraint was applied on the symmetry plane. The suction caisson is constrained as a rigid body moving with a reference point (RP). In the first analysis step, the geostress field was built by applying the body force to the soil. In the second analysis step, the "surface-to-surface" contact pairs were built between the soil and caisson walls, including interior, exterior skirt walls and the underside wall of caisson lid. The normal contact behavior was defined by "hard" contact, and the tangential contact behavior was defined by FRIC_COEF. Then, the dead weight of the suction caisson and superstructures was applied at RP in the form of a concentrated force. Lastly, a displacement-controlled cyclic lateral loading was applied at RP. Both the dead weight and the lateral loading were assumed to act on RP of the suction caisson because the center of gravity of the suction caisson and superstructures is usually located in the lower part of the turbine tower. A three-dimensional 8-node linear brick element with reduced integration was used (C3D8R) for the soil model.

Validation of FE model
In order to validate the aforementioned FE model, a case study was performed by making a comparison between FE results and experimental data reported by Chen (2013). Chen (2013) conducted 1-g model tests of suction caissons under lateral loading and finite element analysis using ABAQUS under an undrained static loading condition. Model parameters of the suction caisson and clay are listed in Table 1. The load eccentricity h is the distance from RP to the center of caisson lid. A set of preliminary calculations for monotonic lateral loading of suction caisson were carried out to study the dependency of the solution on the mesh density. The mesh shown in Fig. 4 is regarded as the medium dense mesh, where the soil surrounding the skirt is discretized into 20 elements in the vertical direction. If the soil surrounding the skirt in the vertical direction is discretized into 40 and 10 elements, the meshes will be defined as the dense and coarse mesh, respectively. Fig. 5 compares the lateral load-displacement curves from FE simulations and experimental data. Results indicate that the simulated results using the dense mesh and medium dense mesh correlate well with the experimental data. In consideration of the computational efficiency and accuracy, the medium dense mesh was selected in the subsequent calculation. Table 2 displays the parameters of FE model. The diameter of suction caisson is 20 m, which is a typical size of the single large caisson called "monopod" (Houlsby et al., 2005). The aspect ratio L/D is 0.5 and 1. With the operating water depths of offshore wind turbines ranging from 0 m to 25 m, the load eccentricity h of cyclic wave loads was taken as 20 m. The realistic dead weight of superstructures ranges from 5 MN to 12 MN (Achmus et al., 2013). In this study, the vertical load of the half model was assumed with V =   (Lekkakis, 2012). Consequently, the lateral displacement of the caisson lid should be limited to 0.02D. The ratio of displacement amplitude and diameter x a /D = 0.004 and 0.02 were adopted to correspond to the normal and extreme working conditions, respectively. In this study, the relation between the lateral displacement of RP, x rp , and time, t, is expressed by the sine function: x rp = x rpa •sin( ), where x rpa is the cyclic displacement amplitude of RP. When a cyclic displacement with a fixed displacement amplitude was applied at RP, the cyclic displacement amplitude x a was found to remain approximately constant. In order to meet the condition of x a /D = 0.004 and 0.02, the cyclic displacement amplitude of RP can be determined by a tentative calculation, in which a larger displacement was applied at RP. The time points when x a /D = 0.004 and 0.02 can be obtained from the results of the tentative calculation, and then the corresponding cyclic displacement amplitude of RP can also be obtained at the same time points. For cyclic motion of suction caisson under larger displacement amplitudes, the sharp fall of bearing capacity of suction caisson mainly occurs in the first 10 cycles, then the lateral loads gradually stabilized to lower lateral loads in the 10 to 200 cycles (Chen, 2013). In order to focus on the effects of strength degradation on bearing mechanism and save computing time, the specified number of cycles N = 10 was used in the present study. The initial undrained shear strength s u increased linearly with a depth with the gradient k = 2 kPa/m. The Young's modulus E was 500 s u,av , and s u,av is the average undrained shear strength of the soil in the depth range of the soil surface to the caisson tip. In order to consider the effects of soil softening on the interface friction, the adhesion coefficient at the soil-wall interface was set as 0.3. Einav and Randolph (2005) mentioned that can take a value equal to the adhesion coefficient which can be taken as the inverse of the sensitivity of the soil. Therefore, = 0.3 is taken.

Cyclic bearing capacity
The horizontal load at RP can be directly obtained by the output results files of ABAQUS. In order to evaluate the moment bearing capacity, a load reference point (LRP) was taken at the skirt tip level along the midline of suction caisson. As illustrated in Fig. 6, the moment at LRP is calculated as follows:  Table 3 shows the calculated horizontal and moment bearing capacity, H ult and M ult , in the first and tenth right loading. The moment bearing capacity was calculated when H = H ult1 or H ult10 . Compared with the L/D, the vertical load V had less influence on the horizontal and moment bearing capacity in the present study. The last two columns in Table 3 represent the degradation of bearing capacity. The degradation of the horizontal and moment bearing capacity was aggravated with the decreasing aspect ratio L/D. This is because the maximum angle of rotation of the suction caisson increases with the decreasing aspect ratio, as shown in Fig. 7. Thus, the extra rotation of the caisson with a small aspect ratio makes the soil inside and outside the caisson experience more plastic strain, resulting in the aggravated degradation of soil strength and bearing capacity.

Soil failure mechanisms
The failure mechanisms of the soil can be explained by the distribution of displacement vectors and equivalent plastic strain of the soil inside and outside the caisson at extreme conditions. Figs. 8 and 9 show the distribution of displacement vectors of the soil for different aspect ratios, number of cycles and vertical loads. Black circles in Figs. 8 and 9 were illustrated to present locations of points of rotation of the soil inside the caisson, where the velocities of the soil particles are approximately zero. It can be observed from Figs. 8 and 9 that rotation of the points of rotation was the dominating failure mechanism, and there was an offset between the points of rotation and the central axis of the caisson, which can be attributed to the relative sliding at the soil-wall interface inside the caisson and the effects of the vertical loads. On the side of loading, a passive soil wedge, similar to that suggested by Murff and Hamilton (1993), was pushed upward. In addition, the offset increased with the increasing vertical load, which also indicated that the offset of the points of rotation of the soil in caisson from the central axis of caisson is related to vertical load. As the number of cycles increased, the points of rotation of the soil moved upwards. The reason is that the softening degree of soil in the lower part of the caisson was larger than that in the upper part of the caisson with the increasing number of cycles, and it was easier to be moved by caisson movement, leading to the rise of points of rotation. By comparing Fig. 8 with Fig. 9, it can be seen that with the decrease of aspect ratio, the offset of the points of rotation increased. ξ Figs. 10 and 11 show the distribution of equivalent plastic strain of the soil for different aspect ratios, number of cycles and vertical loads. Note that in the platform of ABAQUS, the equivalent plastic strain PEEQ is the sum of direct plastic strain components, which can indicate the amount of the accumulated absolute plastic shear strain . In the first cycle, it can be obviously observed that an inverted spoon-shaped failure zone was formed inside the caisson and a wedge-shaped failure zone was formed in front of the caisson along the direction of motion. However, in previous studies (Kourkoulis et al., 2014;Bransby and Yun, 2009), the external scoop failure zone below the caisson was formed below the caisson when the homogeneous soil profile and fully bonded interface were used. Therefore, the in-verted spoon zone mechanism can be resulted from the linearly increasing strength profile and adhesive interface with a low adhesion coefficient. The damage of the inverted scoop was accumulated with the increasing number of cycles, therefore, with the increasing number of cycles, the soil softened in the inverted spoon failure zone in the caisson more seriously, and the strength of soil in the caisson was less than that of the soil on both sides of the caisson, thus remolded ahead of time. The values of PEEQ were hardly affected by the vertical load V, which thus had limited effect on the degradation of the bearing capacity. In addition, the values of PEEQ in the inverted scoop zone were larger for smaller aspect ratio, thereby aggravating the degradation of bearing capacity, as described in Section 3.2.

Settlement
θ In this paper, the settlement w is the vertical displacement at the center of the caisson lid. As shown in Fig. 12(a), the decrease of w indicates the settlement of suction caisson while the increase of w indicates the uplift of suction caisson. The settlement-rotation responses of the suction caissons with L/D = 1 and 0.5 are respectively shown in Figs. 13 and 14. In this study, the relation between the rotation angle of suction caisson, , and time, t, can be expressed by the  θ θ a ωt θ a ω sine function: = •sin( ), where is the amplitude of the rotation angle. Thus, the first cycle means the cyclic movement during the period from 0 to 2π/ . The shapes of the settlement-rotation curves in the first cycle were different from those with regular butterfly shapes in the latter cycles because the gaps had not been formed in the first cycle. The butterfly-shaped settlement-rotation curve for each cycle moved downwards with the number of cycles because the strength degradation of the soil inside the caisson led to the decrease of the vertical bearing capacity. However, the moving rate of the butterfly trajectories de-creased with the number change of cycles. This is because the degrading rate of the soil strength decreases gradually with the number of cycles (Einav and Randolph, 2005). The settlement increased naturally with increasing vertical load.
The settlement or uplift of suction caisson varied regularly with the loading or unloading. As shown in Fig. 12b, the loading stages were defined as the time when the moment reduced from zero to the negative peak value or increased from zero to the positive peak value in each cycle. The unloading stages were defined as the time when the moment reduced from the positive peak value to zero or in-  WANG Teng et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 135-144 141 creased from the negative peak value to zero in each cycle. For L/D = 1 and x a /D = 0.02, the settlement of the suction caisson increased sharply during unloading stages of each cycle. Then, the suction caisson was uplifted during the following loading stages of each cycle except the first cycle. The reason is that the caisson settles down due to the decrease of the total friction with an upward direction acting on the caisson wall during loading; during the following loading, the total friction with an upward direction keeps increasing with rotation, leading to the uplift of the suction caisson.

Conclusions
Three-dimensional FE analyses were performed to investigate the bearing mechanism of the suction caisson supporting offshore wind turbines under cyclic loading and dead load in clay. The cohesive contact was used to consider interaction between the caisson walls and clay, and the practical ultimate friction defined by the partially mobilized undrained shear strength was calculated by the programmed  user subroutine FRIC_COEF. The soil strength degradation under cyclic loading were considered by the programmed user subroutine USDFLD. The following conclusions can be drawn from this study: (1) The horizontal load-displacement curves showed that the horizontal load could decrease with increasing displacement during the right and left loading of the first cycle due to the effect of the vertical load. The degradation of the bearing capacity could be aggravated by the decrease of the aspect ratio.
(2) The offset between the rotation point of the soil inside the caisson and the central axis of the caisson increased with increasing vertical load and number of cycles.
The linearly increasing strength profile and low adhesive interface friction result in the formation of the inverted spoonshaped failure zone inside the caisson, and cancel the formation of an external scoop below the caisson. In addition, the vertical load had little influence on the soil strength degradation, and thus it also hardly affected the degradation of bearing capacity.
(3) The settlement-rotation curves in each cycle moved downwards with increasing number of cycles due to the soil strength degradation. The settlement increased sharply during the unloading stages of each cycle, but the uplift during the loading stages of each cycle was related to the aspect ratio and displacement amplitude.