Three-dimensional discrete element simulations on pressure ridge formation

This study presents the first three-dimensional discrete element method simulations on pressure ridge formation. Pressure ridges are an important feature of the sea-ice cover, as they contribute to the mechanical thickening of ice and likely limit the strength of sea ice in large scale. We validate the simulations against laboratory-scale experiments, confirming their accuracy in predicting ridging forces and ridge geometries. Then we demonstrate that Cauchy-Froude scaling applies for translating laboratory-scale results on ridging to full-scale scenarios. We show that non-simultaneous failure, where an ice sheet fails at distinct locations across the ridge length, is required for an accurate representation of the ridging process. This process cannot be described by two-dimensional simulations. We also find a linear relationship between the ridging forces and the ice thickness, contrasting with earlier results in the literature obtained by two-dimensional simulations

Limit mechanisms for ice loads: FEM-DEM and simplified load models

This work summarizes our recent findings on mechanisms and limits for the ice loads on wide inclined Arctic marine structures, like drilling platforms or harbour structures. The fresults presented are based on hundreds of two-dimensional combined finite-discrete element method (FEM-DEM) simulations on ice-structure interaction pro- cess. In such processes, a floating sea ice cover, driven by winds and currents, fails against a structure and fragments into a myriad of ice blocks which interact with each other and the structure. The ice load is the end result of this interaction process. Using the simu- lation data, we have studied the loading process, analysed the statistic of ice loads, and recently introduced a buckling model [1] and extended it to a simple probabilistic limit load model and algorithm [2], which predict the peak ice load values with good accuracy. These models capture and quantify the effect of two factors that limit the values of peak ice loads in FEM-DEM simulations: The buckling of force chains and local ice crush- ing in ice-to-ice contacts. The work here describes the models and demonstrates their applicability in the analysis of ice-structure interaction

Ahtojäävallin kölin lujuus: mallikokeita ja simulointeja diskreetti- sekä yhdistetyllä diskreetti- ja elementtimenetelmällä

Simulations and laboratory-scale experiments were performed to study sea ice ridge keel punch through experiments and ice rubble behavior in them. The punch through experiments are an important method for deriving ice rubble properties, yet the interpretation of the experiment results is far from straightforward. Anyhow, accurate interpretation is important for the material modeling of ice rubble, and further for an accurate modeling of the ice rubble related problems needed when designing marine structures in ice covered waters.The experimental work was performed using rubble consisting of plastic blocks. Plastic blocks made it possible to study of experimental method itself, because the interpretation of the experiment results was simplified from that of the experiments with ice rubble. The effect of indentor velocity was experimentally studied, as earlier laboratory-scale punch through experiments have suggested that the ice rubble sheer strength depends on the loading rate. The loading rate dependency of the rubble shear strength was found to be likely related to the experimental set-up rather than to the rubble material. Simulations of punch through experiments were performed using a three dimensional discrete element method and a two dimensional combined finite discrete element method. In both of these methods, rubble is modelled as a discontinuum. The methods were developed during this work for the research on ice mechanics. Simulations of punch through experiments on non-cohesive rubble were performed using the three dimensional discrete numerical model. A technique for modeling freeze bonds was developed within the framework of two dimensional combined finite discrete element method simulations. The simulations helped to provide insight on the analysis of the punch through experiment results. The simulation results clearly showed that the evolution of the deformation patterns was related to the load records in the experiments. In the case of partly consolidated rubble, the initial failure patterns of the rubble were observed to be related to the measured maximum force values. Furthermore, the behavior that has been earlier understood to be the result of rubble material softening was in fact shown to be due to changes in the rubble geometry during the experiment. The discontinuous modeling of rubble showed that physical phenomena could potentially be rendered out from the more traditional continuum models. These phenomena included, for example, the importance of tensile freeze failures in the failure process of partly consolidated rubble.Ahtojäävallin kölin materiaaliominaisuuksia mitataan tavallisimmin kokeilla, joissa levymäinen työntyri painetaan vallimassaan samalla kun työntyriin kohdistuva voima mitataan. Vaikka koemenetelmä on tärkeä ja paljon käytetty, kokeiden tulosten tulkitseminen on hyvin vaikeaa. Toisaalta tulosten tarkka tulkitseminen on välttämätöntä kölin materiaalin tarkassa mallinnuksessa, jota puolestaan tarvitaan Arktisten merirakenteiden suunnittelussa. Tässä työssä kyseisiä kokeita on tutkittu sekä simuloimalla että kokeellisesti. Työn kokeellisessa osassa tehtiin laboratoriossa kokeita kölimassalla, joka koostui muovikappaleista jääkappaleiden sijaan. Tavoitteena kokeissa oli tutkia itse koejärjestelyä ja sen vaikutuksia tuloksiin ja muovikappaleita käytettiin tuloksiin vaikuttavien ilmiöiden lukumäärän vähentämiseksi. Erityisesti tarkasteltiin kuormitusnopeuden vaikutusta, koska aikaisempien laboratoriokokeiden perusteella on epäilty vallin leikkauslujuuden kasvavan kuormitusnopeuden kasvaessa. Tässä työssä näytettin, että tämä leikkauslujuuden kasvuksi tulkittu ilmiö johtuu todennäköisesti koejärjestelystä vallin materiaalin sijaan. Työssä kokeita mallinnettin käyttäen sekä kolmiulotteista diskreettielementtimenetelmää, että kaksiulotteista yhdistettyä elementti- ja diskreettielementtimenetelmää. Molemmissa mallinnustekniikoissa valli mallinnetaan epäjatkuvana materiaalina. Tekniikoita kehitettiin työn aikana erityisesti jäämekaniikan ongelmiin sopiviksi. Vallia, jossa jääkappaleet eivät olleet yhteenjäätyneet, mallinnettiin kolmiulotteisella diskreettielementtimenetelmällä, kun taas osittain jäätyneen vallin mallinnuksessa käytettiin kaksiulotteista yhdistettyä elementti- ja diskreettielementtimenetelmää. Jälkimmäisen mallinnustekniikan yhteyteen kehitettiin menetelmä jääkappaleita yhteensitovien sidosten mallintamiseksi. Simulaatioiden avulla voitiin tarkastella ja analysoida kokeita yksityiskohtaisesti. Mallinnuksen perusteella löydettiin selkeä yhteys vallin deformaatiokentän kehittymisen ja mitattujen kuormien välille. Toisaalta osittain jäätyneen vallin tapauksessa löydettiin yhteys maksimikuorman ja vallin ensimmäisen vaurion geometrian välille. Lisäksi mallin perusteella voitiin näyttää, että aikaisemmin vallin materiaalin pehmenemiseksi tulkittu ilmiö selittyykin vallin deformaatiokentän ja vallin geometrian muutoksilla kokeen aikana. Käyteyt epäjatkuvat mallinnusmenetelmät paljastivat ilmiöitä, joita ei esiinny vallimassan kontinuumimallinnuksessa. Esimerkkinä näistä ilmiöistä voidaan mainita kappaleiden välisten sidosten vedosta johtuvien vaurioiden suhteellisen suuri merkitys

Numerical model for a failure process of an ice sheet

Funding Information: The author is grateful for the financial support from the Academy of Finland research project (309830) Ice Block Breakage: Experiments and Simulations (ICEBES). Dr. Janne Ranta and Dr. Devin O’Connor are thanked for the insightful discussions on the contact force model, its parameterization, and estimates on added mass. The research leading to this article was partly performed while visiting Thayer School of Engineering at Dartmouth College (Hanover, NH, USA) during spring 2020. Thanks are extended to Prof. Erland Schulson for hosting and the Finnish Maritime Foundation for partial funding of the visit. CSC–IT Center for Science (Finland) is acknowledged for computational resources under the project (2000971) Mechanics and Fracture of Ice. Author also wishes to thank the five anonymous reviewers whose comments helped to improve the manuscript. Funding Information: The author is grateful for the financial support from the Academy of Finland research project (309830) Ice Block Breakage: Experiments and Simulations (ICEBES). Dr. Janne Ranta and Dr. Devin O'Connor are thanked for the insightful discussions on the contact force model, its parameterization, and estimates on added mass. The research leading to this article was partly performed while visiting Thayer School of Engineering at Dartmouth College (Hanover, NH, USA) during spring 2020. Thanks are extended to Prof. Erland Schulson for hosting and the Finnish Maritime Foundation for partial funding of the visit. CSC–IT Center for Science (Finland) is acknowledged for computational resources under the project (2000971) Mechanics and Fracture of Ice. Author also wishes to thank the five anonymous reviewers whose comments helped to improve the manuscript. Publisher Copyright: © 2022 The Author(s)Model for describing a three-dimensional continuous failure process of an ice sheet is introduced. The presented model is based on the combined finite-discrete element method. The ice sheet consists of polyhedral rigid discrete elements joined by a lattice of Timoshenko beam elements, which go through cohesive softening upon sheet failure. The contact model accounts for inter-particle friction and local failure of ice in contacts. The model is carefully validated against a laboratory experiment, where an ice sheet is pushed against an inclined plane. Convincing agreement between the modelled and experimental failure process is found. The effect of ice sheet tessellation and element size is tested and found to be only moderate. The model compares favorably to earlier ones: The modelling and the experimental results agree, the domain sizes used can be large, and the modelled failure processes are long in duration. Requirements for numerical modelling of ice failure processes are discussed. (C) 2022 The Author(s). Published by Elsevier Ltd.Peer reviewe

Yhdistetty elementti- ja diskreettielementtimenetelmä ahtojäävallin kölin muodonmuutoksen analysoimiseen kolmessa ulottuvuudessa

In this thesis, the applicability of the combined finite-discrete element method in calculation of ridge keel loads is studied. The aim of this thesis is to implement a combined finite-discrete element method application for studying the mechanics of ridge keels and to use example cases to demonstrate the usability of the application. In this thesis, an introduction to the discrete element method is presented. This is done in order to discuss the differences in the modelling of discontinuum with the discrete element method and the combined finite-discrete element method. In the theory part of the work, first the determination of the contact force and frictional force in the combined finite-discrete element method is presented. After this, the determination of the effect of buoyancy and fluid drag in the combined finite-discrete element method is described. In the en of the theory part, the use of the energetics of a system of discrete elements to measure the accuracy of a combined finite-discrete element method simulation is presented. The examples given in this thesis demonstrate the applicability of the combined finite-discrete element method in the study of the ridge keel loads. The example cases include discussion on the penalty function method and its effect on the ridge keel deformation studies using combined finite-discrete element method. Also in the example cases, three dimensional modelling of ridge keels is discussed

A review of discrete element simulation of ice–structure interaction

Sea ice loads on marine structures are caused by the failure process of ice against the structure. The failure process is affected by both the structure and the ice, thus is called ice–structure interaction. Many ice failure processes, including ice failure against inclined or vertical offshore structures, are composed of large numbers of discrete failure events which lead to the formation of piles of ice blocks. Such failure processes have been successfully studied by using the discrete element method (DEM). In addition, ice appears in nature often as discrete floes; either as single floes, ice floe fields or as parts of ridges. DEM has also been successfully applied to study the formation and deformation of these ice features, and the interactions of ships and structures with them. This paper gives a review of the use of DEM in studying ice–structure interaction, with emphasis on the lessons learned about the behaviour of sea ice as a discontinuous medium.Peer reviewe

Limit mechanisms for ice loads on inclined structures: Local crushing

This paper focuses on mechanisms that limit the sea ice loads on offshore structures. It introduces a probabilistic limit load model, which can be used to analyze peak ice load events and to estimate the maximum peak ice load values on a wide, inclined, offshore structure. The model is based on simple mechanical principles, and it accounts for a mixed-mode ice failure process that includes buckling and local crushing of ice. The model development is based on observations on two-dimensional combined finite-discrete element method simulations on the ice-structure interaction process. The paper also presents a numerical limit load algorithm, which is an extension of the probabilistic limit load model and capable of yielding a large number of stochastic peak ice load values. The algorithm is compared to simulation-based and full-scale observations. Analyzing peak ice load events is challenging as sea ice goes through a complex mixed-mode failure process during such events. The algorithm is an effective tool for this analysis, and it shows that distinguishing between the buckling and local crushing failure is virtually impossible if the only data available from a peak load event is the value of the peak ice load. The algorithm shows potential in improving estimates of maximum peak ice load values on offshore structures.Peer reviewe

Variation of stress in virtual biaxial compression test of ice rubble

Ice rubble constitutes ice ridges and rubble fields, which can exert high loads on offshore structures. To characterize the ice rubble, its average properties are often desired. The properties, such as, the critical state friction angle, rely on the continuum notion of stress. This study uses discrete element model for the ice rubble. We use an average stress tensor from the contact forces between the ice blocks and compare it to the macroscopic stress tensor yielded by the boundary contact forces. These stress definitions are used to evaluate the uncertainty in defining the stress tensor for the ice rubble, and the related uncertainty in defining the critical state friction angle for the rubble.Peer reviewe

Breakage in quasi-static discrete element simulations of ice rubble

Funding Information: The authors are grateful for financial support from the Academy of Finland through the projects ( 309830 ) Ice Block Breakage: Experiments and Simulations (ICEBES), and ( 348586 ) WindySea: Modelling Engine to Design, Assess Environmental Impacts, and Operate Wind Farms for Ice-covered Waters. MP gratefully acknowledges the Jenny and Antti Wihuri foundation, Finland , the Finnish Maritime Foundation and the Doctoral Program of the Aalto University School of Engineering, Finland for financial support. The authors wish to acknowledge CSC – IT Center for Science, Finland, for computational resources under the project (2000971) Mechanics and Fracture of Ice. The authors also wish to thank Prof. Knut Høyland for providing direct shear box experiment data, Dr. David M. Cole for valuable discussions on the topic, the anonymous reviewers for their insightful suggestions on improving the paper, and Cody C. Owen for proofreading the manuscript. Publisher Copyright: © 2023 The Author(s)Breakage of particles plays a key role in force transmission in granular materials. Discrete element method (DEM) simulations are often used to model granular materials, but modeling particle breakage in them remains a challenge. Models for breakage of non-spherical particles are scarce and often the existing models are computationally heavy to be used in simulations with large numbers of particles. To address this, the present study develops a particle breakage model for quasi-static DEM simulations of non-spherical particles that fail due to shear. The model is novel, since it is based on experimental observations and high resolution modeling. Breakage models based on experimental evidence are rare as it is often virtually impossible to gain detailed data on the mechanisms related to breakage. The developed particle breakage model was integrated into a DEM code and direct shear box experiments on ice rubble, a granular material consisting of ice particles, were then simulated. Accounting for particle breakage in DEM simulations improved their accuracy: simulations were compared to experiments and the results were found to be in better agreement when particle breakage was taken into account. The effect of particle breakage on the shear strength of a granular material was found to be independent of particle size, decreasing fast with increasing particle strength. The combined effect of shear box length and breakage was also studied. The results showed that the strength of a granular material may be determined reasonably well with a shear box that has a box to particle length ratio greater than 60.Peer reviewe