Ice-slope Interaction: Transitions in Failure Mode

A two-dimensional hydrodynamic ice-slope interaction problem is formulated in this paper. The solution of this elastohydrodynamic problem will give the desired ice force. The main objective is to determine the influence that ice sheet velocity, slope angle, and ice-structure friction have on the ice force. A transition in failure mode is often observed to occur at a certain velocity (named the transition velocity) from predominantly bending to predominantly crushing. In this paper, the solution is provided for relatively slow interactions, to illustrate the validity of the approach. The treatment is non-dimensional so that different types of ice (model ice, freshwater ice and sea ice) can easily be related. INTRODUCTION The first objective of this paper is to formulate an approach which yields the ice force N̄ as the solution of the problem solved. Second, assuming the acceleration or velocity of the ice sheet is explicitly included in the problem statement, it should be possible to ascertain the functional dependencies of the failure strain, and breaking lengths, on the typical input parameters (characteristic length, `; flexural strength, σ f ; ice thickness, h; ice velocity, v; ice-structure friction, f ). For the sake of simplicity, the formulation and analysis are two-dimensional; for this Permanent Address: Department of Civil and Environmental Engineering Clarkson University, Potsdam, New York 136995710, U.S.A ([email protected]) reason, the influence of the structure width cannot be ascertained (Timco, 1984; Frederking and Timco, 1985). By solving one or two fully elastohydrodynamic problems, it is hoped that an effective approximate technique can be devised to include velocity-hydrodynamic effects that will thereby facilitate the accurate solution of the more complicated threedimensional problems. In this paper two closely related but necessarily idealized problems (see Figures 1a and 1b) are examined to gain some insight into the reasons for an observed transition in failure mode. A non-dimensional formulation is presented. For this reason, the analysis is applicable not just to model ice but also to freshwater (river and lake) ice as well as sea ice. ICE-SLOPE INTERACTIONS Haynes et al. (1983) conducted a total of 64 tests in the 33.5-m long, 9.15-m wide and 2.4-m deep refrigerated test basin at the U.S. Army Cold Regions Research and Engineering Laboratory (USACRREL). Using urea model ice, 22 ice sheets were pushed against a model sloping structure with varying slope angles. During 31 of these tests, the velocity of the ice sheet was increased at a constant rate from 0 to 10 cm/s over a period of 90 seconds. The horizontal force exerted by the ice on the structure was measured. A transition in the failure mode was observed to occur at a certain velocity (and named the transition velocity) from predominantly bending to predominantly crushing. For the given test duration studied (which involved 4.5-m of travel) this transition occurred for relatively high slope angles only. Figure 1. A semi-infinite ice cover impacting a sloping structure: fluid movement beneath the structure is (a) unrestricted and (b) restricted.