The Dynamic Failure Behaviour of High-Pressure Zones during Medium-Scale Ice Indentation Tests

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The work presented here is valuable for estimating design loads for offshore structures operating in ice-prone regions, especially the ones susceptible to ice-induced vibrations. By exploring the effects of interaction speed, ice temperature, indenter size and structural compliance on failure behaviour, the work provides valuable insights into the dynamics of high-pressure zones (hpzs) during ice–structure interaction, which is essential for calculating dynamic ice load on offshore structures.

Abstract

Results from medium-scale ice-crushing dynamic tests are presented in this paper based on a series of indentation experiments on confined ice samples using spherical indenters to simulate high-pressure zones (hpzs) with areas on the order of 10³–10⁴ mm². The effects of ice temperature, interaction speed, indenter size and structural compliance on failure behaviour and associated structural dynamics have been studied. Observed failure behaviour consisted of a combination of continuous crushing extrusion and intermittent spalling, both of which were highly dependent on test conditions. Overall, the effects of the studied conditions on ice failure behaviour and associated interaction dynamics were found to be similar to the results reported from previous small-scale experiments, suggesting scale independence of the mechanisms that dominate ice failure behaviour. In general, warmer ice and smaller contact areas are associated with continuous extrusion with intermittent spalling, resulting in smoother peak pressures, while colder ice and larger contact areas tend to result in fracture-dominated behaviour with sharp peaks and substantial load drops. Ice temperature was also found to significantly influence interaction dynamics, with colder ice showing larger amplitude and longer duration dynamic activity, and higher peak pressures. Interaction speed was observed to primarily affect dynamic aspects of ice–structure interactions, with faster tests leading to higher failure frequencies. Similarly, structural compliance was found to mainly impact failure frequency, as well as the extent of load drops, with compliant structures tending to produce more significant load drops following failure. Overall, these experiments have helped enhance our understanding of compressive ice failure and contribute to improved models for dynamic ice–structure interactions.

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 hpz can be studied in detail using such tests. Failure within the hpzs 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 hpzs 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. However, such pressure release contributes to reversing the thermodynamic process associated with pressure melting and thus leads to partial recovery of the strength within the layer. This repeating pattern of pressure softening, and strength recovery (hardening) has been linked to the cyclic ice-loading behaviour during dynamic ice–structure interaction [22], which can induce frequency lock-in. Observations from the small-scale indentation tests on confined polycrystalline ice specimens showed cyclic loading up to a frequency of 250 Hz, and both indentation speed and structural compliance were found to have a direct relationship with failure frequency [23]. Short-lived sequences of “lock-in” behaviour have also been observed in recent small-scale indentation tests, and thin-section suggests that the depth range of the oscillating deformation cycles during vibration is contained within the crushed layer of ice [24]. This observation has important implications since it suggests that under such circumstances, the indenter is continuously in contact with damaged ice. Ice temperature was found to have a significant influence on the failure mode and the microstructure of the crushed layer in that work.

To understand how the observed behaviours can be translated to full-scale interaction, a larger-scale indentation program is presented in this paper. Confined samples of freshwater polycrystalline ice were used for the tests. The ice samples were confined to prevent spalling and allow pressure softening and extrusion observed during the continuous crushing process. The tests were performed in the Structures Laboratory of Memorial University and using spherical indenters with nominal contact area ranging from 20 cm²–180 cm². The effect of indentation speed, ice temperature, hpz area, and structural compliance on the cyclic nature of hpz failure behaviour has been studied in detail.

2. Experimental Setup

2.1. Structural Frame

Four steel-reinforced concrete pillars located at the Structures Laboratory of Memorial University were used as the core structural frame of the experimental setup. To increase the capacity of the overall system, a steel self-reacting frame with a capacity of 300,000 lb was built which encapsulated the concrete pillars through an upper and a lower support ring consisting of girders bolted together (Figure 1). Additional ring stiffeners were attached with the support rings in the direction of the loading and the upper and lower support rings were connected through four 152 mm × 152 mm box beams. Two 100 mm schedule 80 rails were bolted with the box beams on each side and guide bushes with Teflon sleeves were mounted on them to ensure smooth movement of the indentation system.

2.2. Indentation System

In this test series, an indenter is pushed using a hydraulic system against a single ice specimen mounted on concrete pillars. The hydraulic system for the slow indentation tests consists of an Enerpac GPEx5 series electric pump with a reservoir capacity of 40 litres and an Enerpac CLRG series double-acting high-tonnage cylinder. The maximum working pressure for the pump was 10,000 psi and the flow rate at maximum pressure was 2.0 L/min. The cylinder had a capacity of 500 tonnes with a maximum stroke of 30 cm and an effective area of 730.6 cm². The maximum speed with this hydraulic system was found to be 2.536 mm/s, which was used for all the slow speed indentation tests. For high-speed tests, a Hydraulic Power Unit (HPU) with a flow rate of 11 gal/min at 2500 psi was used with a 300-tonnes Enerpac CLRG series double-acting high-tonnage cylinder. The system resulted in a maximum ram speed of ≈16 mm/s, which was used for the high-speed tests.

The setup of the indentation system differed slightly depending on the compliance of the specific indenter configuration used in the tests. The complete indentation system and the instrumentations are shown in Figure 2. For compliant systems 1 and 2, the cylinder was used to push a 3.91 m W12 × 170 mild steel I-beam, which supported a parallel ‘compliant’ beam through two flex links made of SAE 4140 alloy steel. A 2.28 m long 8 × 21 mild steel I-beam was used as the ‘compliant’ beam for the compliant system 1 and an 8 × 67 mild steel I-beam of the same length was used for the compliant system 2. The flex links (flange dimensions 127 mm × 127 mm × 12.7 mm) were used to transfer the moment and permit rotation of the compliant beam. The maximum allowable load for the flex links was 444.82 kN with a maximum deflection of 0.04318 mm. The indenter was mounted at the centre of the beam with a base plate that housed the load cell. Three different sizes of indenters were used for the testing (shown in Figure 3). The specifications of the indenters are given in

Table 1. Indenter specifications.

Diameter (mm)	Radius of Curvature (mm)	Indenter Height (mm)	Nominal Surface Area (m2)
50	64	90	1.96 × 10−3
100	127	90	7.85 × 10−3
150	192	90	17.6 × 10−3

.

For compliant system 3, only the W12 × 170 mild steel I-beam was used, and the indenter was directly mounted on it. A 350 mm long schedule-100 6061 aluminium cylinder attached to two 305 mm × 305 mm × 10 mm aluminium flanges was used as a spacer between the hydraulic cylinder and the beam.

2.3. Indentation and Data Acquisition System

A number of different sensors were used to measure various parameters during the tests. An LPSW-100K Universal Tension & Compression Shear Web Load Cell with a maximum capacity of 445 kN was placed between the indenter and the base plate to measure the ice load. Three MHR 500 A.C. linear variable displacement transducers (LVDTs) were used to measure the structural deflection of the ‘compliant’ beams. One LVDT was positioned at the centre of the beam and the other two were placed 560 mm from the centre on each side. The LVDTs were bolted on an aluminium block and clamped to the W12 × 170 mild steel I-beam using C-clamps (Figure 4). These LVDTs had a stroke length of $\pm$12.7 mm, maximum non-linearity of <$\pm$0.25%, and an operating temperature range of −55 °C to 150 °C. A PCB piezoelectric accelerometer (model 352C33) was also used to measure the acceleration of the ‘compliant’ beam. The measurement range of the accelerometer was $\pm$50 g with a sensitivity of 100 mV/g. A series 330 LVDT was used to measure the distance travelled by the indenter in the ice sample which had a working range of $\pm$25.4 mm, maximum non-linearity of <$\pm$0.20%, and an operating temperature range of −20 °C to 80 °C. Resistance temperature detectors (RTDs) and a Mastercraft non-contact infrared digital thermometer were used to measure the temperature of the ice samples.

An HBM QuantumX MX840B (Hottinger Bruel & Kjaer Inc., Marlboro, MA, USA) universal measuring amplifier with 8 connectors was used as the data acquisition system. Using the HBM CATMAN software v.5.3 (https://www.hbm.com/en/2290/catman-data-acquisition-software/) easurements were recorded at a frequency of 4800 Hz. All the tests were recorded using GoPro cameras (GoPro, San Mateo, CA, USA).

2.4. Ice Sample Preparation

The cold room facilities at Memorial University and C-CORE were used throughout the project to prepare and store ice samples. Cylindrical ice holders with 1 m diameter and 50 cm height were used to prepare confined freshwater polycrystalline ice specimens used for all tests. The sample preparation took place in two stages. During the first stage, 30 cm of the ice holder was filled with commercially available ice cubes and water chilled at 0 °C. The mixture was stirred thoroughly to remove the air bubbles and was allowed to freeze at the target temperature for multiple days in the temperature-controlled cold room facility with a Styrofoam cover which insulated the sample from the top and allowed unidirectional ice growth. For the second stage, ice cubes were crushed using a Clawson Model HQ-C Ice Crusher, and the crushed ice was sieved using a 2–10 mm sieve (Figure 5). Once the bottom layer of the ice sample was frozen completely, the rest of the ice holder was filled with the sieved ice and chilled water. This allowed a consistent grain size ranging from 2–10 mm in all ice samples. The final height of the ice samples was approximately 45 cm. A sample ice specimen is shown in Figure 6.

3. Test Method

During the tests, the ice sample was transferred from the cold rooms to the laboratory using a forklift and was mounted on the concrete pillar with the help of a crane. The sample was bolted to the mounting plate and positioned accordingly to allow the indenter to make contact with the ice sample at the centre. All of the instrumentation was connected to the data acquisition system using VGA cables prior to installation to reduce the test time. To ensure that the ice sample and the indenter have the same temperature during testing, the indenter used for a particular test was also stored in the cold room with the sample. However, since the heat transfer of steel is faster than ice, in most cases, the indenter was found to have a slightly higher temperature than the ice surface at the time of testing. The non-contact infrared thermometer was used to measure the ice surface temperature just before the test and this temperature was recorded to be ice temperature for that particular test. The RTDs installed into the ice sample were used to confirm the recorded temperature. The hydraulic pump was operated using a remote control which resulted in a constant speed of the ram. The maximum allowed load was set to 70,000 lb and the maximum displacement of the indenter in the ice sample was set to 55 mm. The hydraulic ram was stopped when either of these two limits was reached.

The complete test matrix is presented in

Table 2. Test matrix.

Test ID	Indenter Diameter (cm)	Ice Temperature (°C)	Beam Stiffness (N/m)	Ram Speed (mm/s)
T1_5_16_C1_2.5	5	−16.5	C1 (2.67 × 107)	2.5
T1_5_19_C1_2.5	5	−19.5	C1 (2.67 × 107)	2.5
T1_5_7_C1_2.5	5	−7	C1 (2.67 × 107)	2.5
T1_5_4_C1_2.5	5	−4	C1 (2.67 × 107)	2.5
T1_5_15_C2_2.5	5	−15	C2 (9.61 × 107)	2.5
T1_5_3_C2_2.5	5	−3	C2 (9.61 × 107)	2.5
T1_5_7_C2_2.5	5	−7	C2 (9.61 × 107)	2.5
T1_5_16_C3_2.5	5	−16	C3 (4.64 × 108)	2.5
T1_5_7_C3_2.5	5	−7.5	C3 (4.64 × 108)	2.5
T1_5_3_C2_16	5	−3	C2 (9.61 × 107)	16
T1_5_9_C2_16	5	−9	C2 (9.61 × 107)	16
T1_10_18_C1_2.5	10	−18	C1 (2.67 × 107)	2.5
T1_10_1_C1_2.5	10	−1	C1 (2.67 × 107)	2.5
T1_10_7_C1_2.5	10	−7	C1 (2.67 × 107)	2.5
T1_10_17_C2_2.5	10	−17.5	C2 (9.61 × 107)	2.5
T1_10_6_C2_2.5	10	−6	C2 (9.61 × 107)	2.5
T1_10_2_C2_2.5	10	−2	C2 (9.61 × 107)	2.5
T1_10_15_C3_2.5	10	−15	C3 (4.64 × 108)	2.5
T1_10_6_C3_2.5	10	−6	C3 (4.64 × 108)	2.5
T1_10_5_C2_16	10	−5	C2 (9.61 × 107)	16
T1_10_11_C2_16	10	−11	C2 (9.61 × 107)	16
T1_15_18_C1_2.5	15	−18.5	C1 (2.67 × 107)	2.5
T1_15_6_C1_2.5	15	−6	C1 (2.67 × 107)	2.5
T1_15_6_C2_2.5	15	−6	C2 (9.61 × 107)	2.5
T1_15_8_C2_16	15	−8	C2 (9.61 × 107)	16

.

4. Results and Discussion

4.1. Observations during the Tests

Most of the tests showed some regular patterns which can be identified as the characteristics of the ice failure process during the indentation of the confined ice specimen. Figure 7 shows the force, displacement and acceleration obtained from test T1_10_17_C2_2.5. The ice force shows a periodic ‘sawtooth’ behaviour, which is observed during intermittent crushing. The first failure event usually generates a lower force due to lower initial confinement for spalls that ran to the free surface. Each load drop is associated with a transient vibration of the beam which damps out quickly. The synchronized displacement of the LVDT suggests that the beam was deflecting as a simply supported beam and its first mode was excited during the associated vibration.

At the beginning of each ascending part of the loading curve contact area increases as the load accumulates. The load keeps increasing until failure occurs even after the contact area reaches its local maximum value. The failure process was found to be associated with a competition between damage and fracture, the ratio of which is highly influenced by test parameters. Damage refers to the pulverization and extrusion of ice beneath the indenter whereas fracture refers to the propagation of cracks initiated at the contact zone which results in the removal of larger pieces of ice. By synchronizing the video with the obtained data, the effect of the interaction parameters on the ice failure process can be observed. For most of the tests, as the load increases, extrusion of pulverized ice and propagation of cracks occur simultaneously, suggesting the initialization of both damage and fracture processes. However, for warmer ice with a small indenter size and slow ram speed, the rate of pulverization and extrusion dominates over spalling crack propagation. The loading curve at this point shows a ‘smoothed-out’ peak usually followed by a dip. After that, the load might increase for a few moments eventually followed by a spall and sharp load drop (see Figure 8 (left)). On the other hand, for colder ice, especially with larger interaction areas, cracks develop very quickly and failure is associated with a sharp peak and large load drops (see Figure 8 (right)).

During each load drop, a large part of the contact area is usually removed and the indenter surges forward with the energy stored in the beam. Although the total force is less, due to the reduction in the contact area, the pressure in the contact zone becomes very high and the stored energy causes a rapid pulverization and extrusion process. The rapid extrusion process is often accompanied by pressure melting and dynamic recrystallization [22,25]. Eventually, due to the increase in the contact area and the release of strain energy stored in the beam, the process reaches a point where the load of the indenter can be borne by the ice, and a new cycle is initiated.

4.2. Effect of Temperature

For slow tests (≈2.5 mm/s ram speed), a significant difference in the failure behaviour can be observed for all indenter sizes and compliant systems when the ice temperature was above −3 °C. Figure 9 shows the comparison between tests T1_10_17_C2_2.5, T1_10_6_C2_2.5 and T1_10_2_C2_2.5. The indenter size, ram speed and structural compliance were kept constant for the three tests and the ice temperatures were varied. It is assumed that the nominal indenter area remains constant after the initial full envelopment and the nominal pressure was calculated by dividing the force recorded by the load cell by the indenter area. For the tests at −17.5 °C and −6 °C, the pressure–time plot shows a similar ‘sawtooth’ pattern described in the previous section although the peak failure pressure was significantly higher for colder ice for most of the peak pressures (Figure 9 (Left)). It should be noted that, in general, the peak failure pressure varied significantly within each test, and, therefore, not all peaks of the colder ice were higher than the warmer ice. However, the pressure associated with the first failure event was consistently found to have a significantly higher value for colder ice. Figure 9 (Right) shows the average failure frequency (i.e., the number of failure events over the interaction period) as a function of ice temperature. It is observed that when the failure is in the brittle domain, the frequency of the ‘sawtooth’ failure is not strongly influenced by ice temperature. However, for ‘warm’ ice, the failure frequency is significantly lower.

Figure 10 shows a closer look at the ice failure processes near the indentation area at the end of the tests and the effect of ice temperature on failure behaviour. For ice at −2 °C, the continuous extrusion of highly damaged ice which resulted in the continuous nonlinear pressure-time series can be clearly visible. For ‘colder’ ice, the failure surface looks very similar suggesting the similarity in the failure processes. However, for ice at −17.5 °C, the spall area was much larger compared to ice at −6 °C, which is consistent with the observed load drop in Figure 9.

For high-speed tests, the failure behaviour was slightly different for both the ‘warm’ ice and ‘cold’ ice. Figure 11 (Left) shows the nominal pressure and beam displacement at the centre vs. time for tests T1_5_3_C2_16 and T1_5_9_C2_16 where the ice temperatures were −3 °C and −9 °C, respectively. The pressure–time and displacement–time trace shows similar behaviour in this case with the failure being a mixture of both continuous extrusion and large load drops. The average failure frequency shows a similar trend to slow speed tests; the failure frequency is considerably high for colder ice (Figure 10 (Right)). The maximum pressure, load drops and maximum displacement were similar in nature; however, the acceleration data shows that the dynamics associated with the two cases were completely different (Figure 12). As shown in Figure 12, dynamic responses of the beam associated with ice failure were recorded in both cases. For the ice at −3 °C, the maximum value ranged only between −0.05 g to +0.05 g, whereas for −9 °C the value ranged between −20 g to +20 g. This has important implications for ice-induced vibration since the results suggest that for colder ice the failure process is sudden, and the rapid release of energy can significantly excite the structure. On the other hand, although the static deflection of the structure and the maximum load show a similar magnitude for warmer ice, the load drop involves a significant extrusion process which results in a more continuous, ‘slow’ release of energy; therefore, the process was unable to excite the structure as significantly. This observation is consistent with the results presented in the sensitivity study of ice-induced vibration models discussed by [26]. It is noted here that [27] reported from their analysis of field measurement data from Norströmsgrund lighthouse that ice-induced vibrations were observed to occur more frequently during warmer periods of time in the spring of the year. Further analysis is needed to relate the present work with such observations, since multiple hpzs act simultaneously during full-scale interactions, and further work is needed to better understand interactions between such hpzs over larger scales. Moreover, during the spring months in addition to being warmer, sea ice is at its thickest and is more mobile than during the winter. Since it is known that increases in thickness and drift speed are also expected to increase the likelihood of dynamic interactions, further work is needed to better understand the interplay between temperature, thickness, and drift speed in such observations.

4.3. Effect of Indentation Speed

The tests were performed at two different ram speeds: 2.5 mm/s and 16 mm/s. The effect of indentation speed can be seen in Figure 13 (Left) where the force was plotted against indentation depth for tests T1_10_6_C2_2.5 and T1_10_5_C2_16. Although the peak failure force was found to be on the same order of magnitude, a number of distinctions in the failure behaviour can be identified from the plot. For the slow tests, the force increases monotonically until the failure occurs with large pieces of ice being removed and the load dropping more than 90%. On the other hand, for fast tests, as the load increases it continues to produce local fractures with smaller ice pieces before a large load drop occurs and larger pieces of ice are removed. For higher rates, the existing flaws in the ice are subjected to a more rapidly increasing concentrated stress field (slower dissipative processes cannot relieve local intense stresses at a sufficiently fast rate, thus resulting in greater local stress accumulation), which results in a higher degree of local fracture. Also due to the release of stored energy upon rebound following local fracture events, the cumulative amount of energy stored in the beam is lower for fast tests, which in many cases, results in a lower load drop. This has important implications for the development of the damaged layer in the indentation contact zone. If a large amount of energy is stored in the beam during the loading period, the release of this energy upon failure can clear out most of the ice in the damaged layer through extrusion. However, if the energy is not sufficient, part of the damaged layer survives the rebound cycles and continues to grow triggered by the fracture event. Such behaviour can result in vibration within the damaged layer as has been observed in small-scale indentation tests [24]. The average failure frequency versus interaction speed is plotted in Figure 13 (Right). As expected, the average failure frequency was consistently found to be significantly higher for fast tests.

4.4. Effect of Indenter Size

The ‘pressure-area effect’ or ‘scale effect’ is a well-known concept in the ice research community and refers to the scale dependence of the material during failure [28,29]. The effect was observed in this test series as the indenter sizes were varied keeping the temperature, structural compliance and ram speed constant. Although the effect was observed in all combinations of test parameters, it was most pronounced with compliant system 1 during slow tests. Figure 14 (Left) shows the nominal pressure vs. time for tests T1_5_19_C1_2.5, T1_10_18_C1_2.5, T1_15_18_C1_2.5 and T1_15_18_C1_2.5, where the ram speed was 2.5 mm/s and structural compliance was C1 for all tests. The ice temperature varied between −16.5 °C to −19.5 °C and the result shows a clear scale effect for three indenter sizes. The maximum failure pressure for the 5 cm indenter was above 60 MPa whereas the maximum failure pressure for the 15 cm indenter was just above 10 MPa. The frequency of failure was also observed to be somewhat dependent on the indenter size (Figure 13 (Right)); however, such dependency was not found to be very strong.

4.5. Effect of Structural Compliance

In this test series, three levels of structural compliance were employed, corresponding to natural frequencies of 135 Hz, 145 Hz and 173 Hz for the C1, C2 and C3 systems. Nominal pressures are plotted against time in Figure 15 for tests T1_10_18_C1_2.5, T1_10_17_C2_2.5 and T1_10_15_C3_2.5 for an indenter size of 10 cm and a constant ram speed of 2.5 mm/s. Although there were minor variations in ice temperature between tests, the differences remained within $\pm$3 °C.

Assuming that compliance constitutes the primary distinction among these cases, it is notable that the variance in structural compliance does not exert a significant impact on peak failure pressure; however, it does notably influence the failure frequency. In the case of compliant system 1, only two major spalling occur, whereas for compliant system 3, seven failure events can be identified. A similar observation was made by [23] at a small scale where the failure frequency showed a linear relationship with structural compliance. The pressure drops following failure were more pronounced for C1 compared to the other two beams, attributed to the amount of stored energy in the beam at the point of failure. By comparing the events A, B and C for the three compliant systems with similar peak loads (Figure 15), the rebound of the indenter was found to be 0.98 mm for compliant system 1, 0.71 mm for complaint system 2 and 0.4 mm for compliant system 3. These results highlight the significant influence of the rebounding process on the extrusion of the damaged layer and associated vibrations within this layer, consistent with observations from small-scale experiments [24].

For the most compliant system, given the larger rebound distance that follows a failure event, it is expected that nearly all of the damaged ice would be extruded during the rebound process (e.g., very little of the damaged layer survives the extrusion phase of the oscillation cycle), resulting in the indenter being in contact with much more ‘intact’ ice at the beginning of the next cycle of loading. On the other hand, for the stiffest configuration, a lower rebound distance suggests that a more significant part of the damaged layer survives between subsequent ‘sawtooth’ cycles, highlighting that the ice contacting the indenter at the onset of each loading phase of an oscillation cycle is in a much more damaged state. This has important implications for modelling the behaviour of ice in the contact zone, since it implies that stiffer structures may be less likely to ‘reset’ the damage layer formation process during each subsequent load cycle, which may give rise to more periodic layer oscillation. By comparison, more compliant structures would extrude most of the damaged ice from the contact zone during each cycle, making such interactions more likely to take on a sawtooth character. Since the behaviour of the ice (e.g., damage rate, fracture behaviour, strain rate dependence and temperature effects) in turn govern the rate and depth of the damaged layer formation, this work further highlights the need for a coupled treatment of dynamics ice–structure interactions.

5. Concluding Remarks

This paper presents results from medium-scale ice-crushing dynamics tests which were used to simulate hpzs with areas in the order of 10³–10⁴ mm². The effect of ice temperature, interaction speed, indenter size and structural compliance on failure behaviour and associated structural dynamics have been studied and observed. The nature of the force–time curve was found to be highly correlated with observed failure behaviour which is influenced by competition between damage and fracture processes, in a manner similar to that described for small-scale tests. Several key findings emerged from these experiments:

Effect of Temperature: Ice temperature was observed to play a significant role in failure behaviour. Colder ice failure was dominated by fracture with sharp peaks and large load drops resulting in increased dynamic activity and higher peak pressures. In contrast, warmer ice tends to exhibit smoother peak pressure profiles due to the dominance of continuous extrusion with intermittent spalling.

Interaction Speed: Over the range of rates considered, the interaction speed did not have a significant effect on the magnitude of peak failure pressures. Rather, the interaction rate between ice and the structure was observed to primarily affect dynamic aspects of the interaction, with higher failure frequencies observed for faster tests. This highlights the importance of understanding the links between the drift speed and relative interaction rates for structures of different compliance levels in terms of their impact on dynamic aspects of ice-induced vibrations.

Indenter Size: The well-established “pressure-area” effect was observed, with larger indenters generating higher total force, but lower overall levels of pressure as compared to smaller indenters. This effect is more pronounced in colder ice and when interacting with more compliant structures as was also reported in prior analysis.

Structural Compliance: While peak pressures were found to be primarily influenced by ice-related processes, structural compliance was found to have a substantial impact on the failure frequency. It was observed that more compliant structures tend to extrude most of the damaged ice during each cycle, resulting in sawtooth-like interactions and the removal of much of the damaged ice beneath the indentation zone. This suggests that peak pressures are dominated by processes in the ice, while frequency is dominated by structural parameters and interaction conditions.

The consistency of the reported observations from this study with prior small-scale indentation tests [20,23,24,25] underscores the robustness of hpz failure mechanisms across the different scales. Since hpzs are a fundamental component of the compressive ice failure process, the observed consistency of their failure behaviour on multiple scales is highly beneficial in guiding the development of models of dynamic ice–structure interaction processes. For many of the existing ice-structure interaction models [30,31,32], one of the primary difficulties lies in linking the model parameters with fundamental ice mechanics; however, incorporating the hpz failure mechanisms can address this limitation. Recent models of non-simultaneous ice failure [33,34] have been extended to account for the dynamic coupling effects described, providing promising new approaches for modelling dynamic ice–structure interaction processes of interest for offshore structure design.