Devinder S. Sodhi

Vertical penetration of floating ice sheets

Abstract Existing failure criteria for the bearing capacity of floating ice sheets predict the load for the occurrence of the first radial crack or a circumferential crack, when the maximum stress obtained from an elastic analysis in the ice equals the tensile strength. From full-scale and small-scale tests, the ultimate load to cause complete penetration of a floating ice sheet is much higher than that to cause the first radial crack. This can be attributed to wedging action during deformation of a radially cracked ice sheet. We present three approaches taken to determine the ice penetration force: (1) plastic limit analysis, (2) small-scale experiments, and (3) full-scale measurements in the field. Small-scale experiments were conducted with freshwater ice in the basin at the laboratory to understand the wedging action during the vertical loading of floating ice sheets. Results of the following series of experiments are presented: (a) beams with fixed ends, (b) paired cantilever beams arranged free-end to free-end and loaded together, (c) beams with an apparatus inserted between the free ends of paired cantilever beams to measure the in-plane force during vertical loading, and (d) vertical downward loading of floating ice sheets with fixed and free boundaries. Analysis of the data from the beam tests reveals that the wedging action results in the development of wedging pressure in the top or bottom third of the ice thickness, and this results in a resisting moment that counters the deformation of a cracked ice sheet. An ice sheet attached to the basin wall inhibits the propagation of radial cracks because of the wedging action, whereas an ice sheet free at the edges from the surrounding ice sheet fails by the propagation of radial cracks all the way to the ice sheets free boundary. The difference between the two breakthrough loads of the free and the fixed ice sheets can be attributed to wedging action. The results of the beam tests are used in the results of plastic limit analysis to predict the breakthrough loads of floating ice sheets, which are in agreement with loads measured during full-scale and small-scale experiments.

Shore ice pile-up and ride-up: Field observations, models, theoretical analyses

Abstract A review of the literature on shore ice pile-up and ride-up in arctic and subarctic waters is presented, along with an account of recent observations made by the authors. Cross-sectional profiles of these features are presented from which models and theoretical analyses were made. The expressions derived give the force required to overcome gravitational potential and friction occurring during ice-piling and ride-up. It was estimated that the distributed force required during ice-piling or ride-up was of the order of 10 to 350 kPa (about 1.5 to 50 psi). Field observations revealed that shore ice pile-up or ride-up appears to occur within a period of less than 30 minutes, at any time of year but most often in the spring and fall. Pile-up seldom occurs more than 10 m inland from the sea but ride-up frequently extends 50 m or more inland, regardless of ice thickness. While steeply sloping shores do not favor ice ride-up, sea ice has mounted the steep, 9-m-high bluff at Barrow, Alaska, destroying structures and taking lives.

Crushing failure during ice–structure interaction

Abstract Small-scale indentation tests were conducted with compliant structures and freshwater ice sheets. Besides measuring forces and displacements, we installed grid-based tactile pressure sensors at the ice–structure interface to measure the pressure generated during an interaction. Similar to the results of earlier studies, the results of the present study with compliant structures show that there is ductile deformation of ice at low indentation speeds and continuous brittle crushing at high indentation speeds. During a typical cycle of the dynamic ice–structure interaction at intermediate speeds, the ice–structure interaction results in variable rates of indentation into the ice, and the tactile sensor data indicate that the ice deforms in a ductile manner at the low indentation rate (the loading phase), and fails in continuous brittle crushing at the high indentation rate (the ejection phase). Theoretical estimates of global force are given in terms of non-simultaneous local force per unit width during continuous brittle crushing. We find the effective pressure measured during small-scale indentation tests to be close to those measured on full-scale structures, when the indentation rate is high in both situations.

Nonsimultaneous crushing during edge indentation of freshwater ice sheets

Abstract Indentation tests were conducted by pushing segmented indentors into the edge of freshwater ice sheets at different velocities. Ice crushing forces were measured independently in each segment. Results of these tests indicate that there is simultaneous generation of forces on all segments during low-velocity indentation, whereas there is a nonsimultaneous force acting on the segments during high-velocity indentation. For brittle crushing of ice at a high indentation rate, the effective pressures measured during these tests are in the range of pressures measured in the field during the impact of ice floes against large structures. Under the assumption that the size of crushing zones becomes small with increasing indentation speed, a statistical model is used to determine the correlation between the forces measured in different segments in terms of a correlation length parameter. A comparison of the trends in the plots of experimental data with theoretical results shows that the correlation length parameter decreases as the reciprocal of the indentation velocity. Under the assumption of the similarity principle, according to replica modeling, an estimate of the correlation length parameter is empirically obtained in terms of ice thickness and indentation velocity.

High pressure zone formation during compressive ice failure

Abstract An understanding of the mechanics and physics of the formation of the high pressure zones that form during ice–structure interactions is sought. The influences of time, temperature and scale on the formation of these high pressure zones are explored in this paper. Line-like and localized high pressure contact zones are modeled via elastic-brittle hollow cylinder and hollow sphere idealizations, respectively. For both simultaneous and non-simultaneous contact, the critical lengths of stable cracking that may occur prior to flaking and flexural failure are strongly linked to the current level of specific pressure parameters for both line-like and localized high pressure zones. The stability aspects of the in-plane cracking, and the link between the maximum possible crack lengths and the relative magnitudes of the local and far-field pressures help explain the transitions observed within the realms of ductile, intermittent, and brittle crushing.

Ice - Structure Interaction During Indentation Tests

To study dynamic ice-structure interaction during crushing failure of ice, indentation tests were conducted by pushing a vertical, flat indentor into the edges of floating ice sheets. The indentor was supported on three load cells to measure interaction forces at the interface. The displacements of the carriage and the indentor were measured separately. The indentor displacement relative to the carriage and the indentor acceleration were also measured. These measurements provided comprehensive data on the dynamic ice-structure interaction during crushing failure of an ice sheet. Three basic modes of ice behavior were observed: creep deformation at low velocities, intermittent crushing at intermediate velocities, and continuous crushing at high velocities. Based on these measurements, a theoretical model is proposed which produces results similar to those of the experiments.

Characteristic frequency of force variations in continuous crushing of sheet ice against rigid cylindrical structures

Abstract The ice forces generated during continuous crushing of an ice sheet against a cylindrical vertical structure vary with time, according to the resistance offered by ice as it fails and clears from the path of the structure. Small-scale experiments were performed to measure the ice forces by pushing rigid cylindrical structures of different diameters at different velocities through an ice sheet. The dominant frequency of ice force variations, defined as the characteristic frequency, was determined from the frequency spectra of the force records. The characteristic frequency plot with respect to the velocity-to-thickness ratio reveals a linear relationship, which implies that the average length of the damage zone is proportional to the ice thickness. On the basis of the data presented here, the average length of the damage zone is about one-third of the ice thickness.

Determining the characteristic length of model ice sheets

Abstract For determining the characteristic length of a floating ice sheet, a vertical load is applied to the ice sheet either by placing dead weights in discrete increments or with a screw drive apparatus in series with a load cell, and the deflection of the ice sheet is monitored at the point of loading or near it. For a model ice sheet exhibiting creep behavior, the experimental results with the screw apparatus show that the slope of the load—deflection curve decreases as the load increases, and one is not able to choose a unique value of the slope for the computation of characteristic length. This is attributed to relaxation of stress in ice. For tests with sudden placement of dead weights, the elastic response of the ice sheet can be separated from the inelastic response. The latter method gives consistent results for the determination of the characteristic length. The effective modulus of elasticity may be calculated from the characteristic length, but the error in measuring the characteristic length and in assuming a value of Poissons ratio may result in a greater percentage of error in the modulus of elasticity. It is suggested that the characteristic length of a model ice sheet be scaled in ship resistance and other such tests as it describes the flexural behavior of the ice sheet.

An Ice-Structure Interaction Model

Publisher Summary This chapter presents a theoretical model to simulate ice–structure interaction during intermittent crushing. It is developed based on experimental results from indentation tests, which were conducted by pushing vertical, flat indentors into the edges of freshwater, floating ice sheets. An event during intermittent crushing comprises three phases: (1) a loading phase, (2) an extrusion phase, and (3) a separation phase. The chapter presents the differential equations and solutions during each phase of interaction along with conditions for termination of each phase. Besides simulating interaction during intermittent crushing, the model simulates the transition from intermittent to continuous crushing at high rates of indentation, as found during indentation tests. The chapter presents the results from the model to show the effect of various parameters on the velocity at which transition from intermittent to continuous crushing takes place and on the frequency of intermittent crushing.

Fracture toughness of columnar freshwater ice from large scale DCB tests

Abstract A series of 42 fracture toughness tests were performed on laboratory-grown S2 columnar freshwater ice at high homologous temperatures (−2 to 0° C). The floating double cantilever beam specimen used and the monitoring of the crack mouth opening displacement in addition to the applied load provided a means for obtaining an apparent fracture toughness, an effective elastic modulus, a lower-bound estimate of the crack speed, and a side-loaded flexural strength of the ice. An expression for the apparent fracture toughness as a function of the applied load, specimen geometry, and ice thickness was developed using a finite-element program. This allowed comparison with previously published values for the toughness of freshwater ice. The small range of scatter in apparent fracture toughness values as well as the ability to measure other mechanical properties of the ice indicates the usefulness of such tests.