A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load (original) (raw)

A method of calculating ice loads when ice piles up on a fixed wall

Journal of Applied Mathematics and Mechanics, 2006

A model for calculating ice loads on a shelf ice-resistant platform is developed which corresponds to a cyclic scenario of the interaction of ice with the wall of a platform observed in laboratory experiments. Using relations which follow from the laws of conservation of mass, momentum and energy written for ice which fills a ridge formed at the wall of the platform, an explicit formula is obtained for the ice load on the wall. The generalized forces characterizing the dependence of the energy dissipation accompanying ridging on the dimensions of the sail and keel of the ridge and on the shape of the wall are parametrized. It is shown that the calculated loads obtained using the assumption of hydrostatic equilibrium of the sail and the keel of the ridge correspond to the lower boundary of the experimentally measured loads. The calculated loads obtained using the assumption that the keel of a ridge is of constant size yield an upper estimate of the ice loads. In order to estimate the limit loads at which collapse of the ice into the water occurs, a problem on the formation of a flexural crack in an ice floe which is thrust onto the wall is considered. The average and maximum ice loads on the wall of a platform are calculated on a real scale.

The Uniform Motion of an External Load along the Edge of the Ice Cover

2018

The problem about uniform motion of a load has been thoroughly studied for the homogeneous ice sheet that covers the water surface completely. To our knowledge, this problem was first solved by Dotsenko (1976). This solution is also presented in Cherkesov’s book (1980). Many studies on this topic were summarized by Squire et al. (1996). In the case of inhomogeneous ice cover, there are only some solutions of particular problems. The examples of solutions for a moving load in the case of bounded ice cover can be found in the book by Zhestkaya and Kozin (2003). The basic equations of motion of ice plate and fluid were numerically solved using the finite-element method. The behavior of a very large rectangular elastic plate, which simulates a floating airport during the takeoff and landing of the aircraft, was studied by Kashiwagi (2014). The problem of ice deflection due to a moving load was solved by Brocklehurst (2012) in linear and nonlinear formulations for a semi-infinite ice pla...

The dynamic ice loads on conical structures

Ocean Engineering, 2013

Two series of model tests were performed to observe the dynamic ice loads on conical structures. The variable testing parameters include the water line diameter of the model cone and ice parameters. During small water line diameter tests, two-time breaking is found to be the typical failure of ice on steep conical structure, and also be controlled by other factors, such as ice speed and the cone angle. During big water line diameter tests, the ice sheet failed nonsimultaneously around the cone. Several independent zones of bending were found in the nonsimultaneous failure process of ice. With the increase of the ratio of D/h and the number of independent zones, the total ice force was found being gradually reduced. c

Comparison of Ice Load Development on Non-Planar Surface

International Journal of Offshore and Polar Engineering

It is important to understand the sequential ice load development on ships during ice-structure interaction when the ship structure may not be a planar surface. Laboratory tests were performed based on the assumption that the shape of the structure is perfectly flat or slightly convex/surfaces in general. This study plans to consider the cases where the shape of the structure is a wedge or conical. Obtained results were compared with flat surface test conditions. Trends of forcedisplacement, pressure-area curve, contact area and changes of pressure within the contact region were evaluated. Pressure distribution on nonplanar surface showed a significant difference and induced a higher ice load compared to a flat surface.

Model-scale ice — Part A: Experiments

Cold Regions Science and Technology, 2013

This paper is presenting novel model-scale ice property measurements for grain size, elastic strain-modulus, compressive and tensile specimen tests. The testing and analyzing procedure is targeted to define the basic material behavior accurately to understand the material behavior for the future development of a numerical material model. Additionally, the model-scale ice thickness and the bending strength (following ITTC) are determined to classify the ice properties. The experiments consist of systematic in-situ tests to identify the model-scale ice properties in a format suitable for numerical simulations. The elastic strain-modulus is determined on the intact level ice sheet based on the load displacement relationship of the infinite plate deflection. All specimens are cut with a template to minimize dimensional variations. The specimens are loaded with a linear drive at constant speed while displacement and force are recorded. The resulting load-displacement curves indicate good repeatability. The experiments are conducted over a time of 4 h-5 h in the keeping phase, where the cooling system is adjusted to maintain the mechanical ice properties, and the obtained results do not show a dependency on the time of testing. A linear-elastic finite element model is used to reproduce the plate bending measurements for the elastic strain-modulus determination. Therewith, it is found that the actual elastic strain-modulus is 27% larger than in plain stress theory due to stresses in thickness direction. Additionally, the approximate yield strength of the model-scale ice is investigated and is found to be significantly lower than the determined maximum stresses in compression, tension and bending. Consequently, this paper contributes to a deeper understanding of the mechanics of model-scale ice, and a procedure is shown how the mechanical parameters can be determined by systematic experiments and analyses.

The Influence of External Boundary Conditions on Ice Loads in Ice-Structure Interactions

Volume 8: Polar and Arctic Sciences and Technology; Petroleum Technology, 2016

Design ice loads are generally derived from field measurements or laboratory experiments. The latter commonly neglect the circumstance that most ice-structure interactions occur underwater, despite the fact that studies report higher ice loads if water is present. Other than a few studies on ice extrusion processes, most investigations on ice loads also do not specifically consider the presence of snow or granular ice at the ice-structure interface. To elucidate the influence of water, snow and crushed ice, as external boundary conditions, on ice load magnitude, 71 small-scale laboratory tests were carried out. Testing involved a hydraulic material testing system (MTS machine) located in a cold room at −7°C. Ice specimens were conical shaped with 25 cm in diameter and with 20° and 30° cone angles. Those were impacted with a flat indentation plate at 1 mm/s, 10mm/s and 100 mm/s indentation rates. Time-penetration and time-force histories from the MTS machine, as well as qualitative c...

Bearing Capacity of Floating Ice Covers: Theory versus Fact

Various criteria have been advanced to describe and predict the conditions under which a load will break through a floating ice cover. As a rule, the experimental basis for each of these criteria has been limited, and a comprehensive performance evaluation has yet to be carried out. Criteria based on stress, strain, deflection, and strain energy are discussed first, in conjunction with the viscoelastic nature of ice and the mode of failure of an ice sheet. Five data sets are then described and utilized to test and compare the performance of failure criteria that have been proposed in the literature. Stress-based criteria, though simple to use, are only useful for very brief loading because they do not account for loading time and history. Strain- and deflection- based criteria are also subject to time and history effects. On the other hand, strain-energy criteria are found to apply equally well to short- and long-term loads of different histories. This feature is attributed to consi...

Nonlinear effects in the response of a floating ice plate to a moving load

Journal of Fluid Mechanics, 2002

The steady response of an infinite unbroken floating ice sheet to a moving load is considered. It is assumed that the ice sheet is supported below by water of finite uniform depth. For a concentrated line load, earlier studies based on the linearization of the problem have shown that there are two 'critical' load speeds near which the steady deflection is unbounded. These two speeds are the speed c 0 of gravity waves on shallow water and the minimum phase speed c min . Since deflections cannot become infinite as the load speed approaches a critical speed, Nevel (1970) suggested nonlinear effects, dissipation or inhomogeneity of the ice, as possible explanations. The present study is restricted to the effects of nonlinearity when the load speed is close to c min . A weakly nonlinear analysis, based on dynamical systems theory and on normal forms, is performed. The difference between the critical speed c min and the load speed U is taken as the bifurcation parameter. The resulting normal form reduces at leading order to a forced nonlinear Schrödinger equation, which can be integrated exactly. It is shown that the water depth plays a role in the effects of nonlinearity. For large enough water depths, ice deflections in the form of solitary waves exist for all speeds up to (and including) c min . For small enough water depths, steady bounded deflections exist only for speeds up to U * , with U * < c min . The weakly nonlinear results are validated by comparison with numerical results based on the full governing equations. The model is validated by comparison with experimental results in Antarctica (deep water) and in a lake in Japan (relatively shallow water). Finally, nonlinear effects are compared with dissipation effects. Our main conclusion is that nonlinear effects play a role in the response of a floating ice plate to a load moving at a speed slightly smaller than c min . In deep water, they are a possible explanation for the persistence of bounded ice deflections for load speeds up to c min . In shallow water, there seems to be an apparent contradiction, since bounded ice deflections have been observed for speeds up to c min while the theoretical results predict bounded ice deflection only for speeds up to U * < c min . But in practice the value of U * is so close to the value of c min that it is difficult to distinguish between these two values.

Numerical Simulations of Broken Ice Interaction with Structures

The interaction of moving broken ice with a structure is an important problem in ice mechanics. Ice-induced loads and pile-ups can result due to this type of interaction, for example, on a bridge pier during spring break-up or on a vessel stationkeeping in pack ice conditions. Numerical techniques can be developed and applied to investigate this type of problem. In this report, a numerical model of ice interaction with both slender and wide structures in varying ice conditions is presented. The model is based on a Particle-In-Cell (PIC) approach, combined with a viscous plastic ice rheology. The plastic yield follows a Mohr-Coulomb criterion. The Zhang-Hibler (1997) numerical scheme is used to solve the momentum equations. The model is used to examine the role of ice thickness, ice properties and velocity on the resulting forces on two different structures. The results show good agreement with the field measurements.

Numerical simulation of local ice loads in uniform and randomly varying ice conditions

Cold Regions Science and Technology, 2011

The ice loading process has a clear stochastic nature due to variations in the ice conditions and in the icebreaking processes of ships. The statistical characteristics of local ice loads are typically studied on the basis of field measurements. In this paper, a numerical method was applied to simulate a ship moving forward in either uniform or randomly varying ice conditions, where the thickness and strength properties of the ice encountered by the ship were assumed to be constant or randomly generated using the Monte Carlo method. The purpose of this simulation is to show the origin of the statistical variation in ice loading, which is difficult to identify in field measurements. To validate the numerical results, an icebreaking tanker, MT Uikku, was then modeled in a simulation program, the ice loading process was stochastically reproduced and the calculated amplitude values of the ice-induced frame loads were compared with the field measurements.