## 1 Introduction  
Extreme forces exerted by ice against fixed offshore structures are a highly important design consideration and in some cases can exceed the 100-year wave force [1]. For sea ice, this force is generally limited by the force required to fail the ice sheets by bending, buckling, crushing or a combination of these. Continuous failure of ice against a structure, primarily in the form of crushing, can generate a condition of dynamic ice-structure interaction leading to severe vibration of the structure. This is known as ice-induced vibrations (IIV), and such events are widely discussed in the literature. The types of structures affected by IIV include lighthouses [2], channel markers [3], jacket structures [4] and even caisson-retained structures [5; 6]. During a nine-month monitoring period in the winter of 1985-86 using Molikpaq, a 90 m wide caisson retained structure operating in the Beaufort Sea, crushing was found to occur only 1% of the time [7; 8]. However, the highest levels of force were observed in this period, and a small portion of crushing produced simultaneous ice failure across the interaction area of the structure leading to ice-induced vibrations. Crushing is often characterized by the production and extrusion of fine-grained ice particles from the interaction surface and can occur in both ductile and brittle regimes. In the ductile regime, the extrusion process is often slow and continuous and is associated with extensive damage-enhanced creep, whereas in the brittle regime, the rate of extrusion is very rapid, and often is interrupted by sudden load drops due to fracture events. Indentation tests are an effective way to study the ice-crushing process, and many experimental programs on different scales have been carried out over the years, e.g., [9; 10; 11; 12; 13; 14; 15; 16; 17]. Depending on the types of tests, the experimental programs can be broadly classified into two categories: (1) edge indentation of ice sheet; (2) indentation of ice wall (vertical and conical shapes). Edge indentations are generally performed by pushing an indenter (usually flat) against an ice sheet in a test basin or in the field (landfast ice). The speed of the indenter, ice thickness, and width of the indenter are some of the common parameters that are varied during tests. The results of these tests have been reported by various authors [9; 10; 11; 12; 13; 14; 15; 16; 17] and a comprehensive review of the mechanism was provided by [15]. Through a series of 66 tests with varying interaction speed, indenter width, ice thickness, strain rate, and aspect ratio, ref. [12] found that crushing is the dominant mode of failure in the brittle range and is often accompanied by spalling, radial cracking, and circumferential cracking. Based on the results, he proposed a failure mode map as a function of strain rate and aspect ratio, highlighting the importance of these two parameters in the failure mode. Tests using a spherical indenter provide valuable insight into the ice-crushing process, and the behaviour of a single _lpyz_ can be studied in detail using such tests. Failure within the _lpyz_s is influenced by damage processes which typically include microcracking in zones of high shear and low confinement, as well as dynamic recrystallization and localized pressure melting in regions of high shear and high confinement [18; 19; 20]. Understanding how the _lpyz_s scale is important in modelling the correlation of pressures during non-simultaneous failure of ice against different sizes of structures. Pictures of the indented surface from medium-scale indentation tests at Hobson's Choice Island [21] showed evidence of an extensive white layer of crushed material with occasional 'blue' recrystallized zones [22]. The localized pressure melting and pressure softening within the layer results in a reduction in the load-bearing capacity leading to the extrusion of ice particles from beneath the contact zone.