To study interaction loads between ice and sloping structures, numerical models are required that can predict failure of the ice based on physical ice properties, deformations and structural shape and size. An important component of these models consists of the failure criteria that are employed, as failure limits the loading of the ice on the structure. Failure in interaction with a sloping structure can occur in multi-directional tension, compression, bending, splitting or a combination of these, making it important to capture and combine all failure conditions in a single model. In this paper, these failure criteria are derived for a lattice model, linked to field measurements and failure envelopes are presented. For the first time, a complete set of failure criteria that is required to simulate ice-sloping-structure interaction scenarios, is derived in this paper. It is shown that the criteria have minimal dependence on cell-size and -orientation and are applicable for multi-directional loading conditions.@en

Lattice models are successfully used in modelling of fracture of brittle materials. To date, most of the lattice multi-dimensional (2D and 3D) models known to the authors describe either in-plane or three-dimensional mechanics of the materials. Only a few lattice models are available in the literature for the description of the out-of-plane mechanics of plates. However, the parameters of those lattice models have not been linked to those of the classical plate models, such as Mindlin-Reissner plate theory, based on the classical continuum theory. Nor has the dynamic behaviour of the out-of-plane lattice models been compared to that of the classical plates. This gap is closed in this paper by means of developing a lattice model that reproduces the out-of-plane dynamics of a shear-deformable plate in the low frequency band. The developed model can be applied in various fields of engineering. In this paper, however, it is discussed taking example of an ice sheet. The linear dynamics of the model is focused upon in this paper in order to show its consistency with a continuum plate theory in the low frequency band and underline the differences emerging at higher frequencies. The developed model is composed of masses and springs whose morphology and properties were derived to match the out-of-plane deformations of thick plates as described by the Mindlin-Reissner theory. Bending, shear and torsion are taken into account. The eigenfrequencies and the steady-state response of the model to a sinusoidal in time point load are computed and compared to those of a corresponding continuum plate. It is proven that the developed lattice predicts the same dynamic behaviour as the corresponding continuum plate at relatively low frequencies. At higher frequencies deviations occur. These are discussed in this paper in terms of the dispersion, anisotropy and specific boundary effects of the lattice model.

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Structures with a downward sloping waterline shape in Arctic or sub-Arctic regions experience reduced loading from ice on the structure and its foundation compared to vertical structures as the slope causes the ice to fail in bending. For the design of these structures, a numerical model is desired that can predict the loading from the ice on the structure by simulating the physical processes that occur when the ice fails. A numerical 2D lattice model has been developed to simulate level ice behavior. The model is composed of masses and interconnecting springs, taking into account deformation in tension, compression, bending, shear and torsion in the ice sheet. Deformation and failure criteria in the model are based on first principles, enabling a physically sound simulation of breaking processes. In addition, the discrete lattice model avoids stress singularities in fracture modeling since the model only describes displacements and forces in the connections and no stresses are present. In this paper interaction between ice and a downward sloping conical structure is simulated with the lattice model and compared with data from scale model tests. From the model test results it was observed that level ice and larger ice floes fail in sequential bending during interaction with a structure, giving a repetitive load pattern. Smaller ice floes split and break in bending into smaller parts and a sequential breaking pattern does not develop. The lattice model is capable of simulating failure in bending, splitting and combinations of these. In contrast, predictions of the model presented herein suffer from limitations of the contact model between the ice and the structure, the lack of a clearing mechanism and the use of a regular lattice mesh.@en

To study interaction between ice and sloping structures, numerical models are required that can predict failure of the ice based on physical ice properties, deformations and structural shape and size. An important element of these models is the set of failure criteria that is applied, as failure limits the loading of the ice on the structure. Failure in interaction with a sloping structure can occur in multi-directional tension, compression, bending, splitting or a combination of these, making it important to capture and combine all failure conditions in a single model. In this thesis, a lattice model is developed to simulate an ice plate and failure criteria are derived for the model, linked to field measurements and failure envelopes. Fracture patterns generated with the lattice model compare well with those observed in basin tests. Lattice models are successfully used in modelling of fracture of brittle materials. To date, most of the lattice multi-dimensional (2D and 3D) models describe either in-plane or three dimensional mechanics of the materials. Only a few lattice models are available in the literature for the description of the out-of-plane mechanics of plates. However, the parameters of those lattice models have not been linked to those of the classical plate models, such as Mindlin-Reissner plate theory, which is based on the classical continuum theory. To be able to simulate out-of-plane deformations of a plate, thereby enabling physically correct simulation of ice-structure interaction, a 2-dimensional lattice model is developed that reproduces the out-of-plane dynamics of a shear-deformable plate in the low frequency band. The developed model is composed of masses and springs whose morphology and properties were derived to match the out-of-plane deformations of thick plates as described by the Mindlin-Reissner theory. Bending, shear and torsion are taken into account. The eigen frequencies and the steady-state response of the model to a sinusoidal-in-time point load are computed and compared to those of a corresponding continuum plate. It is proven that the developed lattice predicts the same dynamic behaviour as the corresponding continuum plate at relatively low frequencies, which are dominant in ice-structure interaction processes. At higher frequencies deviations occur. These are discussed in terms of the dispersion, anisotropy and specific boundary effects of the lattice model. A lattice model for in-plane vibrations of a plate in plane strain conditions is described in literature and is adjusted in the current work to plane stress conditions and to reproduce the Poisson effect. Combined with the lattice model for out-of-plane deformations a single model is formed, which captures in- and out-of-plane deformation of a shear deformable plate under the assumption of small deformations. Failure criteria were developed for the lattice model which are linked to field measurement data of ice. The deformation and failure criteria in the lattice model are based on first principles, enabling physically sound simulation of deformation and fracture processes of the ice plate material. Failure in compression, tension, bending and splitting are simulated with the lattice model, providing a complete set of failure scenarios relevant to study interaction between ice and sloping structures. It is shown that the criteria have minimal dependence on cell size and orientation and are applicable for multi-directional loading conditions. By means of numerical assessment, a multitude of structures and loading conditions can be analysed and structural shapes can be optimized for interaction with ice at reasonable costs. Validation of the model against field measurements for ice in complex loading conditions of combined bending, shear and torsion as well as basin tests show that fracture location and fracture patterns can be predicted well with the lattice model. A 3-dimensional model, which would reduce computational efficiency, is required to accurately simulate out-of plane shear and spalling failure of the ice, however in engineering applications these are often not governing over bending and tensile failure. Inclusion of ice rubbling and clearance processes as well as improving the simulation of the contact with a structure would further improve the model and ice load predictions. @en