This thesis is composed of theoretical, experimental, and numerical studies. In Part I, it discusses fundamental challenges of the discrete element method, provides a set of algorithms for addressing them, and presents performance gains of an improved algorithm on a target computer platform. A new contact detection and force resolution algorithm based upon (i) the fast common-plane (FCP) algorithm, (ii) using axisaligned bounding boxes (AABBs) to perform a proximity search, (iii) estimating the time of collision, and (iv) accurate resolution of contact points is presented. Benchmark simulations indicate an order of magnitude increase in performance is achievable for a relatively small number of elements. A new parallel discrete element algorithm is presented which combines the domain decomposition, object-oriented, and perfectly parallel strategies of parallelism to eliminate the drawbacks of parallel discrete element algorithms put forth by past studies. A significant speed-up is observed in comparison to past studies in trials conducted on a NUMA-based SMP computer. In Part II, various applications of the discrete element method are reviewed, with an emphasis on ice-structure interaction. The conical design of the Kulluk drillship is of particular interest due to its success in operating in the Beaufort Sea from 1975- 1993 and its subsequent purchase and recommission by Shell in 2006. Three previous experimental studies and a unique set of full-scale data measurements form the basis for comparison of a concurrent experimental and numerical investigation. The results of a model scale experiment at the NRC-IOT are analyzed and presented, followed by results of the numerical simulations. A 1:40 scale replica of the Kulluk platform in level ice produces results which are consistent with past experiments and confirm expected trends as well as different regimes of results dependent on the ductile/brittle behavior of ice. The numerical setup models the full-scale platform in three dimensions with a 24-sided rigid conical structure, ice as an elastic brittle material with plate-bending elements, and platform mooring through the implementation of a spread mooring algorithm. Numerical results are in agreement with past results for ice thickness of less than 1.2m, confirming that the initial design goal of the Kulluk was achieved while still overestimating the loads in comparison to the full-scale data set. Two explanations are presented for the non-conformity of the experimental and numerical predictions to the full-scale data results.

This thesis is composed of theoretical, experimental, and numerical studies. In Part I, it discusses fundamental challenges of the discrete element method, provides a set of algorithms for addressing them, and presents performance gains of an improved algorithm on a target computer platform. A new contact detection and force resolution algorithm based upon (i) the fast common-plane (FCP) algorithm, (ii) using axisaligned bounding boxes (AABBs) to perform a proximity search, (iii) estimating the time of collision, and (iv) accurate resolution of contact points is presented. Benchmark simulations indicate an order of magnitude increase in performance is achievable for a relatively small number of elements. A new parallel discrete element algorithm is presented which combines the domain decomposition, object-oriented, and perfectly parallel strategies of parallelism to eliminate the drawbacks of parallel discrete element algorithms put forth by past studies. A significant speed-up is observed in comparison to past studies in trials conducted on a NUMA-based SMP computer. In Part II, various applications of the discrete element method are reviewed, with an emphasis on ice-structure interaction. The conical design of the Kulluk drillship is of particular interest due to its success in operating in the Beaufort Sea from 1975- 1993 and its subsequent purchase and recommission by Shell in 2006. Three previous experimental studies and a unique set of full-scale data measurements form the basis for comparison of a concurrent experimental and numerical investigation. The results of a model scale experiment at the NRC-IOT are analyzed and presented, followed by results of the numerical simulations. A 1:40 scale replica of the Kulluk platform in level ice produces results which are consistent with past experiments and confirm expected trends as well as different regimes of results dependent on the ductile/brittle behavior of ice. The numerical setup models the full-scale platform in three dimensions with a 24-sided rigid conical structure, ice as an elastic brittle material with plate-bending elements, and platform mooring through the implementation of a spread mooring algorithm. Numerical results are in agreement with past results for ice thickness of less than 1.2m, confirming that the initial design goal of the Kulluk was achieved while still overestimating the loads in comparison to the full-scale data set. Two explanations are presented for the non-conformity of the experimental and numerical predictions to the full-scale data results.

This thesis is a summary of studies that were carried out as part of candidacy for aPhD degree. The purpose of these studies was to evaluate some factors in shipdesign that are intended for navigating in ice using numerical simulations. A semiempiricalnumerical procedure was developed by combining mathematical modelsthat describe the various elements of the continuous-mode icebreaking process inlevel ice. The numerical procedure was calibrated and validated using full- andmodel-scale measurements. The validated numerical model was in turn used toinvestigate and clarify issues that have not been previously considered.An icebreaker typically breaks ice by its power, its weight and a strengthened bowwith low stem angle. The continuous icebreaking process involves heave and pitchmotions that may not be negligible. The numerical procedure was formulated toaccount for all of the possible combinations of motions for six degrees of freedom(DOFs). The effects of the motion(s) for certain DOF(s) were investigated bycomparing simulations in which the relevant motion(s) were first constrained andthen relieved.In the continuous-mode icebreaking process, a ship interacts with an icebreakingpattern consisting of a sequence of individual icebreaking events. The interactionsamong the key characteristics of the icebreaking process, i.e., the icebreakingpattern, ship motions, and ice resistance, were studied using the numericalprocedure in which the ship motions and excitation forces were solved for in thetime domain and the ice edge geometry was simultaneously updated.Observations at various test scales have shown that the crushing pressure arisingfrom the ice–hull interaction depends on the contact area involved. A parametricstudy was carried out on the numerical procedure to investigate the effect of thecontact pressure on icebreaking.The loading rates associated with the ship’s forward speed have been anticipatedto play an important role in determining the bending failure loads, in view of thedynamic water flow underneath the ship and the inertia of the ice. The dynamicbending behavior of ice could also explain the speed dependence of the icebreakingresistance component. A dynamic bending failure criterion for ice was derived,incorporated into the numerical procedure and then validated using full-scale data.The results obtained using the dynamic and static bending failure criteria werecompared to each other.In addition, the effect of the propeller flow on the hull resistance for ships runningpropeller first in level ice was investigated by applying the information obtainedfrom model tests to the numerical procedure. The thrust deduction in ice wasdiscussed.