Moored structures are suitable for operations in icecovered regions owing to their security and efficiency. This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during icestructure interaction with a spherical Discrete Element Method (DEM). In this method, the level ice and mooring lines consist of bonded sphere elements arranged in different patterns. The level ice model has been widely validated in simulation of the ice load of fixed structures. In the mooring line simulation, a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure. The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results. The motion of the structure was calculated in the quaternion method, considering the ice load, mooring force, and hydrodynamic force. The hydrodynamic force comprised wavemaking damping, current drag, and buoyancy force. Based on the proposed model, the interaction of a semisubmersible structure with level ice was simulated, and the effect of ice thickness on the ice load was analyzed. The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.
Floating structures are prospective engineering equipment used for oil exploration and exploitation in the Arctic and subArctic regions. They are costeffective in deep waters and maneuverable in harsh environments. The mooring system is still the preferred choice for the stationkeeping of floating structures, particularly under heavy ice conditions, although many researchers are exploring the feasibility of dynamic positions in iceinfested sea. Among the various types of ice features in the Arctic, level ice is the most common challenge for stationkeeping capacity of floating structures and controls the design load levels in many cases. Therefore, it is necessary to develop an effective numerical method for predicting the ice load and mooring system response of moored structures in level ice.
As the most direct research method, a monitoring project on the ice load has been conducted for more than 10 years on the floating offshore structure,
Numerical methods, especially the meshfree methods, are suitable to simulate the whole process of the icestructure interaction at a full scale. Song et al. [
Previous numerical studies on moored structures in icy regions focused on ice actions, and the mooring system was often simplified as a linear or nonlinear spring [
In this study, we applied the spherical discrete element method with the parallel bond model to construct the level ice and mooring lines of floating structures. We validated the accuracy of the mooring line by comparing the DEM numerical results with the nonlinear FEM solutions and experimental results. The effects of ice thickness on the ice load and dynamic response of a semisubmersible structure was studied based on the DEM results.
The DEM models of level ice and mooring lines are based on spherical discrete elements with the parallel bond model. The different mechanical properties of the two structures are defined with different element configurations and computational parameters.
In the parallel bond model, two adjacent elements are bonded by a virtual disk lying on the contact plane and centered at the contact point, as shown in
The level ice model was established by the bonded spherical elements arranged in Hexagonal Closest Packed (HCP) type, as shown in
The shear strength follows the MohrCoulomb criterion and is in proportion to the maximum normal stresses
In
The DEM parameters should be calibrated using relevant numerical mechanical tests to simulate the mechanical behaviors of level ice precisely. Based on the uniaxial compression and threepoint bending tests of sea ice, the relationship between the DEM parameters and macroscopic mechanical parameters of level ice was established, considering the size effect [
In
The model has been used to simulate the interaction between level ice and fixed structures such as the conical structure [
The DEM model of the mooring line is composed of a string of spherical elements, as shown in
In the catenary test, the two ends of a stretchable mooring line are fixed in the direction of a slope angle of
Definition  Unit  Value 

Distance between fixed points  1000  
Mooring line length  1026  
Weight per unit length  kN/m  2 
Axial stiffness (AE)  2052  
Slope angle  45 
The DEM model was employed to calculate the dynamic response of the mooring line in the towed test [
Definition  Unit  Value 

Length  7.305  
Dry weight  0.162  
Equivalent diameter  0.0052  
Elastic modulus  77.2  
Initial vertical projection  1.2  
Initial vertical projection  6.97 
The energy dissipation caused by hydrodynamic force has significant effect on dynamic behavior of the mooring line. The modified Morison formula [
The calculation results were plotted compared with experimental results, as shown in
Based on the established DEM models of level ice and mooring lines, we adopted a moored semisubmersible structure to simulate its interaction with level ice. The platform with iceresistant slope in the bow and stern mainly consisted of a hull and braces as
The dynamic equation of a semisubmersible structure in the time domain is established according to the Cummins’ method [
To simulate the rotation of the structure, a quaternion
Buoyancy is the main component of restoring force and has significant effects on the stiffness of the dynamic system. Thus, the buoyancy of a structure was calculated based on the instantaneous submerged volume of the structure in every time step. For the hull composed of triangular elements (
A numerical method was developed for simulating the buoyancy acting on the bracings. Each bracing is uniformly discretized into
A free pitch oscillation test of the semisubmersible structure was simulated based on the proposed method for buoyancy calculations. The zeroupcrossing frequencies for different amplitudes of oscillation are as shown in
Based on the methods, we calculated the interaction between the semisubmersible structure and the level ice. The ice load and dynamic response of the structure were analyzed to validate reliability of the DEM method. Further, a series of simulations were performed to study the effect of ice thickness on the ice load and positioning ability of the semisubmersible structure.
The moored semisubmersible platform concept was designed for drilling operations in the Barents sea. Considering that the maximum depth of the water is 600 m in the region, the depth was set to 400 m in the simulation. The interaction between mooring lines and the seafloor is calculated directly based on the contact law between spherical elements and the boundary of an arbitrary shape [
Definition  Unit  Value 

Length × Width × Draft  m × m × m  86.2 × 64.6 × 14.0 
Mass  35000.5  
Vertical position of center of gravity (above baseline)  m  8.9 
Rotational inertia of roll  3.0 × 10^{10}  
Rotational inertia of pitch 
5.0 × 10^{10} 

Vertical position of center of buoyancy (above baseline)  m  5.4 
Antiice cone angle  10 
The level ice was assumed to be dragged by a current of 1 m/s with an ice area of 200 m × 400 m. The boundary of the level ice was set as a spring boundary, and the ice thickness is 1.0 m. The main DEM parameters are listed in
Definition  Unit  Value 

Sea ice density  920  
Sea water density  1035  
Element diameter  m  1.0 
Normal stiffness  1.72 × 10^{7}  
Shear stiffness  1.72 × 10^{6}  
Bonding friction coefficient    0.3 
Normal bonding strength  MPa  1.5 
Number of elements  92000 
The spread mooring system comprises 12 catenary mooring lines. The 12 mooring lines are grouped into four bundles stretching out in four directions symmetrically. Each bundle consisted of three mooring lines, and the angle between the adjacent lines is 5°, as shown in
The simulating time duration was set as 200 s to ensure the stability of the result and meanwhile, avoid the influence of the boundary of the level ice. According the wave propagation theory and related parameters of the DEM elements, the time step was set to be
The cone angle and dynamic friction angle of the iceresistant structure were
The amplitudes of surge, sway and heave are respectively 17.3, 3.6 and 0.2 m, respectively, and the maximum horizontal offset were less than 5% of the water depth (
The load on the semisubmersible structure without the conical iceresistant structure can be estimated with the ISO formula [
In
The maximum tension of the mooring lines is a important critical design parameter for moored structures, according to API 2SK [
Ice thickness is a key parameter in ocean engineering design for icecovered regions. A series of numerical calculations were conducted to analysis the effect of ice thickness on the ice load of the moored semisubmerged structure. The ice thickness ranged from 1 to 1.6 m in intervals of 0.2 m in the simulation. The other parameters of the semisubmerged structure, level ice and mooring system are listed in
Segments  Length (m)  Wet mass (kN/m)  

Platform chain  190  700.8  0.075  0.52 
Steel cable  250  900.2  0.101  0.23 
Anchor chain  20  675.0  0.061  0.43 
A DEM method was established in the study to accomplish coupled calculations of the ice load and mooring force of moored structures in level ice. The DEM models of the level ice and mooring lines were based on spherical elements with different parallel bonding models. A catenary test and a towed test were simulated to validate the accuracy of the mooring line model. The dynamic response of a semisubmersible structure was simulated using the proposed DEM model. In the simulations, the buoyancy was calculated based on the instantaneous submerged volume of the semisubmersible structure to model the nonlinear dynamic characteristics of the structure. The comparison between the DEM result and the ISO result validated the reasonability of the DEM method to simulate the ice load and mooring force of a moored structure in level ice.
The DEM results demonstrated the dynamic behavior of the semisubmersible structure significantly influenced the failure mode of level ice. The surge and yaw motion were the most critical among the motions of the semisubmersible structure in level ice with six degrees of freedom. The tension of the mooring lines mainly depended on the surge motion of the structure.
The influences of the ice thickness on the ice load and the mooring force were also analyzed. The results shown the maxim values of the ice load and mooring force were all in a linear positive correlation with the ice thickness. The mean and maximum offset also increased evidently as the ice thickness increased. For the mooring system analyzed in this paper, the mean offset exceeded the design criteria for the level ice thicker than 1.2 m. The mooring system should be optimized for the thick level ice in future studies.