Ice Failure Research Articles

Brittle failure of ice

This paper reviews the brittle failure of polycrystalline ice at temperatures (>0.8 T mp) and strain rates (∼10 −7–10 −1 s −1) of engineering interest. The discussion addresses ice as a material and emphasizes structure–property relationships. Tensile behavior is discussed in terms of the nucleation and propagation of cracks. Brittle compressive failure, a more complicated process, is addressed in terms of frictional crack sliding, wing cracking and a new mechanism termed comb cracking. The ductile-to-brittle transition under compression is modeled in terms of the competition between crack-tip creep and crack propagation. The paper closes with a discussion of leads in the Arctic sea ice cover and with evidence that failure mechanisms may be independent of scale. They may also operate in rock and other brittle materials.

High pressure zone formation during compressive ice failure

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.

Universal behaviour in compressive failure of brittle materials.

Brittle failure limits the compressive strength of rock and ice when rapidly loaded under low to moderate confinement. Higher confinement or slower loading results in ductile failure once the brittle-ductile transition is crossed. Brittle failure begins when primary cracks initiate and slide, creating wing cracks at their tips. Under little to no confinement, wing cracks extend and link together, splitting the material into slender columns which then fail. Under low to moderate confinement, wing crack growth is restricted and terminal failure is controlled by the localization of damage along a narrow band. Early investigations proposed that localization results from either the linkage of wing cracks or the buckling of microcolumns created between adjacent wing cracks. Observations of compressive failure in ice suggest a mechanism whereby localization initiates owing to the bending-induced failure of slender microcolumns created between sets of secondary cracks emanating from one side of a primary crack. Here we analyse this mechanism, and show that it leads to a closed-form, quantitative model that depends only on independently measurable mechanical parameters. Our model predictions for both the brittle compressive strength and the brittle-ductile transition are consistent with data from a variety of crystalline materials, offering quantitative evidence for universal processes in brittle failure and for the broad applicability of the model.

Scaling of Sea Ice Fracture—Part I: Vertical Penetration

Based on the premise that large-scale failure of sea ice is governed by fracture mechanics, recently validated by Dempsey’s in situ tests of fracture specimens of a record-breaking size, this two-part study applies fracture mechanics and asymptotic approach to obtain approximate explicit formulas for the size effect in two fundamental problems. In the present Part I, the load capacity of a floating ice plate subjected to vertical load is determined, and in Part II, which follows, the horizontal force exerted by an ice plate moving against a fixed structure is analyzed in a similar manner. The resulting formulas for vertical loading agree with previous sophisticated numerical fracture simulations as well with the limited field tests of vertical penetration that exist. The results contrast with the classical predictions of material strength or plasticity theories, which in general exhibit no size effect on the nominal strength of the structure.

First-year ridge interaction with the Molikpaq in the Beaufort Sea

This paper presents details of the failure behaviour and loads associated with the interaction of first-year ridges with the offshore structure Molikpaq. An analysis was made of ridge interactions during 2 years of deployment of the Molikpaq in the Canadian Beaufort Sea. The first-year ridge interactions were complex and characterized by a complicated sequence of ice failures that are largely dependent on the particulars of the ridge and the interaction event. Typical ridge failure modes included spine failures, failing behind the ridge, shearing, stopping and mixed modal. Typical load levels ranged from 30 to 100 MN for first-year ridges with sail heights up to 2.5 m. For these ridges, the ridge line load [ P LL in MN/m] was related to the ridge sail height [ H s in m] by P LL=0.36 H s+0.25.

On modeling the anisotropic failure and flow of flawed sea ice

The failure and flow of sea ice on scales small and large is characterized by the propagation of oriented leads and cracks. In this paper a theory for the dynamical treatment of anisotropic oriented flaws in sea ice is developed and used to examine the interaction of these oriented flaws under idealized stress forcing. The essential idea of the theory is to take one or more oriented weak leads imbedded in thick ice. A constitutive law for both the thin and thick ice is taken to be similar to laboratory observations, which are consistent with Mohr Coulomb‐like failure. Application of normal continuum mechanics boundary conditions leads to anisotropic flow and failure characteristics of this anisotropic composite under both near‐ and far‐field forcing. The local failure characteristics show that there is a preferred orientation for failure with the intersection between “leads” increasing as confinement increases. For spatially separated interacting flaws the theory predicts a preference for the weakening of flaws in a narrow range of angles of ∼10°–20° relative to the principal far‐field stress. Imbedding isolated flaws leads to simulated damage directions consistent with local failure characteristics. In the case where the ice is considered to have available flaws in all directions, fracture propagation is found to proceed by picking out oriented flaws alternating in direction along large‐scale damage strikes with individual flaw alignments of ∼20° relative to far‐field principal stresses. The mechanisms responsible for these results and how this anisotropic sea ice rheology might be implemented in current dynamic/thermodynamic sea ice models are discussed.

ICE PRESSURE DISTRBUTION IN ICE-STRUCTURE NIERFACE AND STRUCTURE STIFFNESS EFFECTS ONICE-STRUCTURE INTERACTTON

Field indentation tests using medium-scale model structures have been conducted since the winter of 1996. In the winter 1998 tests, two-dimensional pressure sensing panels were first installed on the face of the indentor. These panels clearly showed actual contact area, ice pressure distribution and movement of ice force location on the indentor surface during interaction. Ice flaking failure associated with a thin line-like contact area was observed from 3-D plots of pressure data in tests with an indentor velocity of 3.0mm/s. In the winter 1999 tests, a spring system (spring constant 15KN/mm) was first installed in the model structure to simulate a vibrating structure. These tests showed structure stiffness difference causes different manner of ice failure.

Research trends in ice mechanics

In sea ice geophysics, the formulation and implementation of a continuum anisotropic ice dynamics model is required in order to increase the spatial resolution of the Polar Ice Prediction System (PIPS) used by the National/Naval Ice Center to provide sea-ice analyses, forecasts, outlooks and ship-routing recommendations within the marginal ice zone of Arctic and Antarctic seas. Currently, too little is known about the formation of leads in the Arctic, a situation that should rapidly improve via automated ice-tracking SAR algorithms. Many questions remain concerning the influences of inhomogeneities (thermal cracks, ridges, thickness variability, and rubble) on wave propagation, constitutive behavior and overall ice strength at various scales. Floe scale ice models appear to offer the means to bridge the scales between geophysical and structural applications by being able to accurately model the mechanics of ridging, rafting and leading. At the scale of ice forces on structures and ships, a diverse range of creep-brittle failure modes awaits incorporation into ice force models. Knowledge concerning the multiaxial compressive failure of freshwater and saline ice is now available. The constitutive modeling of sea ice lags well behind that for freshwater ice. The important issues of scale effects and inhomogeneities on tensile strength at lab- to structural-scale are discussed, as are the links between various scales.

The brittle compressive failure of orthotropic ice under triaxial loading

Experiments on the brittle compressive failure of S2 fresh-water columnar ice loaded triaxially at −10°C at a strain rate of 6×10 −3/s have revealed three regimes of Coulombic-like behavior: 1 of lower across-column confinement where the along-column stress has no significant effect on the strength; 2 of higher across-column confinement where the along-column stress increases the strength; and 3 of predominantly along-column loading where the strength increases in proportion to the smaller of the two orthogonal across-column confining stresses. Within each regime the strength of the fresh-water ice is indistinguishable from that of porous salt-water ice (Gratz and Schulson, J. geophys. Res., 1997, 102, 5091) of otherwise similar microstructure, implying similar failure mechanisms. Both kinds of ice fail through macroscopic shear faulting which results from the linking up of cracks formed during the deformation. The principal difference between the two materials is that the deformation damage to the salt-water ice is restricted more to the vicinity of the faults, owing to the crack-stopping influence of pores incorporated during growth. Terminal failure is explained in terms of a new mechanism involving the bending of “splay cracks” under frictional sliding. “Splay cracks” are feather-like deformation features that emanate from one side of parent, sliding cracks. The idea is that slender microcolumns between the “splay cracks” are more likely to bend and break than are microcolumns between adjacent wing cracks because they do not have two fixed ends; instead, the end stemming from the sliding interface is free. A moment is then applied by frictional sliding. A first-order calculation shows that the stress required to break the columns and thus to initiate the fault is of the same order of magnitude as the terminal failure stress.

Disintegration of ice under fast compressive loading

During the interaction of ice with ships or other offshore structures, a compressive zone develops in the ice. This is the focus of the present work. An interpretation of field measurements shows that the compressive ice load is far from uniform; indeed, most of the load is transmitted through small areas of intense pressure characterized by a highly damaged layer. The processes leading to the formation of these zones include fractures, and in particular spalls near the edges of the zones, as well as a separate process of damage and microstructural change within the layer itself. In order to capture the essential points for deducing design requirements, we have formulated a probabilistic model of high-pressure zones. The mechanics of failure of ice in these zones is explored. Triaxial tests have been conducted. Mechanisms discussed include microcracking (shear banding), recrystallization and grain boundary melting. As pressures increase, the microcracking and recrystallization are suppressed and the strain rates decrease. At even higher pressures, the results show pressure softening with enhanced strain rates. Two state variables are used to model the ice deformation, corresponding to the hardening at lower pressures, and to the softening at higher pressures. Finite element analyses of the ice response incorporating these variables, corresponding to a medium scale indentation test have yielded promising results, showing the decline in load and the layer formation.

Medium-scale indentation tests on sea ice at various speeds

As part of a five-year program involving laboratory and field tests in Japan, we conducted medium-scale indentation tests on sea ice in the harbor of Lake Notoro, Hokkaido, by pushing a segmented indentor against the edge of a floating ice sheet. Measurements on each 10-cm-wide segment included forces in three directions and the moment about a horizontal line parallel to the indentor face. During the tests in 1998, we also installed four pressure-sensing panels on the face of the segmented indentor and measured interfacial pressure during indentation tests at three speeds. We present the results from the load cells and the pressure-sensing panels. We obtained data on the actual contact area and the magnitude of interfacial pressures from the pressure-sensing panels. We observed both a `line-like' contact during high-speed (3- and 30-mm s −1) indentation tests, and a gradually enlarging contact area attributable to creep deformation of the ice during low-speed (0.3-mm s −1) indentation tests. Using the results of a brittle flaking model from the literature, we estimate the apparent fracture toughness of the ice from the data on interfacial pressure and the width of the contact area. Taking creep and fracture properties into account, we present a theoretical model to estimate the speed at which the transition from ductile to brittle failure of ice takes place during ice-structure interaction.

Ductile compressive failure of columnar saline ice under triaxial loading

Experiments and analysis have shown that the ductile compressive yield stress (at −10°C at 4 × 10−5 s−1) of S2 saline ice, an orthotropic material whose crystallographic c axes are randomly oriented in the plane perpendicular to the long axis of the columnar grains [Michel, 1978], loaded triaxially both across and along the columnar‐shaped grains obeys Hill's [1950] criterion under low to intermediate levels of confinement. Correspondingly, the ratio of inelastic strains can be described by the attendant associated flow rule.

The architecture of an anisotropic elastic‐plastic sea ice mechanics constitutive law

The architecture for a new large‐scale anisotropic constitutive law intended for use in a sea ice dynamics model is presented here. This architecture accounts directly for refrozen lead systems in the pack ice strength (with an anisotropic failure surface) and in the ice thickness distribution (with an oriented thickness distribution). The lower limit (5 km) of the model resolution is controlled by the fracture spacing of old, thicker ice and the maximum lead width. The upper limit of the model resolution (100 km) is controlled by curvature in the lead directions and variations in the lead width. These, in turn, are controlled by the variations in internal ice stress due to driving forces (winds and currents), which set the time resolution. This architecture features abrupt changes in the failure surface and the associated flow rule that cannot be averaged over a time step. In addition, the principal stress normal to a new lead must be zero as it opens. This model has subscale simulations that allow for the inclusion of phenomena such as ridging, rafting, buckling, and fracture on the behavior of the ice. With this new ice constitutive law, it is possible to test directly the ice failure strength, plastic flow rule, and ice thickness distribution. The data most useful for this testing come from ice stress and position buoys together with synthetic aperture radar deformation data. Some data comparisons have already been made.

The role of discrete failures in local ice loads

A conceptual model of ice failure is proposed. The model describes ice failure as a nested hierarchy of discrete failure events. In this model, each failure event changes the geometry of the problem, and thus, sets one of the important initial conditions of the next failure event. The ice load, along with other results of the ice–structure interaction, depends on how the sequence of failure events progresses. It is argued that the best method of understanding ice loads is to treat ice failure as a process of discrete failure events. The literature on discrete failure events in ice is reviewed. The experimental background and specific solutions using discrete failure processes are described. Specific attention is given to those local failure processes that take place at an ice–structure interface. The mechanics of pulverisation, showing possible alternative discrete mechanisms are presented. Finally, an event tree for local ice failure is given.

Localized pressures during ice–structure interaction: relevance to design criteria

Crushing is a prevalent mode of ice failure during ice–structure interaction. This failure mode frequently occurs with vertical structures and over local areas on sloping structures. During ice crushing, the interaction zone is characterized by three distinct regions of pressure; critical zones, regions of background pressure, and areas of recently spalled ice. Critical zones may be defined as local regions of ice where intense pressures occur over short time periods. Critical zones influence significantly the crushing process. The parameters associated with critical zones are quantified by examining three types of field-scale interactions; medium-scale indentation tests, ship ramming trials of the Louis S. St. Laurent and CanMar Kigoriak, and an ice–structure interaction with the offshore structure Molikpaq. Critical zones occur regardless of the scale or type of interaction. Despite the highly random nature of critical zones, basic parameters such as zonal size, force, pressure, and spatial density are quantified. Critical zones are found to be approximately 0.10 m 2 in area and may exert forces ranging from 0.1–4 MN. Spatial densities of the critical zones, defined as the number of zones per unit meter, range from about 0.6 to 0.8 zones/m 2 and appear to be influenced by confining pressure and scale effects. Critical zones provide an explanation for the exhibited reduction in average pressure with increasing contact area. Two kinds of pressure–area relationships are presented; one in which the contact area increases over time, the other in which large, unconfined contact areas contain smaller, highly confined regions. The importance of aspect ratio in relation to the pressure–area trend is discussed. Reduction in contact area due to spalling and the orientation of the critical zones within an impacted area are examined with respect to the aspect ratio.

On the ice/structure interaction in medium scale field indentation tests (part 3)

Medium scale field indentation tests (MSFIT) in JOIA project had been conducted to evaluate the ice load on structure since 1996 winter, using natural sea ice in Lake Notoro. The key of the ice load evaluation is to understand the ice failure characteristics during indentation process.The effects of indentation velocity on ice failure were examined, using natural sea ice frozen in two ways. Also, ice failure process in detail is examined by the use of plane pressure sensor. This paper shows the test results in 1998 winter.

Eccentric impact of an ice feature: non-linear model

The eccentric impact of a floating ice feature interacting with a rigid wide structure has been studied using both numerical and analytical methods. The motion of an impacting body is assumed to be planar. It may be described by a dynamic system of three ordinary differential equations containing a non-linear reaction force in the right-hand side. The reaction force during the impact is governed by ice failure which has been characterized by a pressure-area curve. Current contact area is given as a non-linear function of the ice feature position using an approximation of the local shape of the impacting body in the vicinity of a contact point with either an elliptical cylinder or a three-axial ellipsoid. The resulting system of non-linear differential equations allows an approximate analytical solution for the maximum impact force and impact duration. The solution includes two consecutive steps. First, the maximum impact load is derived for the scenario when rotation of the impacting body about the vertical axis is not permitted. An energy balance equation is used at the first step. Subsequently, a decreasing factor resulting from rotation of the ice feature in the course of impact is evaluated using direct integration of the equation for the penetration depth. This analytical solution for non-linear ice failure load was compared with the solution for the earlier linear model of impact derived by the author (Matskevitch, 1997). The comparison has shown that inclusion of non-linearity of the reaction force leads to a decrease in the effect of impact eccentricity on the maximum ice load.

The influence of variable-thickness ice on the loads exerted on sloping structures

A test program has been carried out to investigate the influence of non-uniform ice thickness on the loads exerted by an ice sheet failing against both an upward-breaking and a downward-breaking sloping structure. Tests were performed with both level and non-uniform ice sheets in a model test basin. The comparison of the loads was used as a basis to determine the ‘effective’ thickness ( h eff) of the ice sheet where h eff = h μ + kh σ where h μ is the average ice thickness, h σ is the standard deviation of the ice thickness distribution, and k is a parameter that depends on structure slope and width and the mode of ice failure. For a wide, upward-breaking structure, k = 0.5 and 0.8 for slopes of 60° and 75°, respectively. For a wide downward-breaking structure, k= 1.4 and 1.6 for slopes of −60° and −75°, respectively. Based on these findings, analytical models for predicting ice forces on sloping structures have been modified to take into account the influence of non-uniform ice thickness.

The Brittle Failure of Ice under Compression

This paper reviews progress during the past decade in understanding the brittle compressive failure of ice. Evidence is presented for the frictional crack sliding-wing mechanism and for the role of localized fragmentation. The ductile-to-brittle transition is explained in terms of the suppression of crack growth and is modeled in terms of Ashby−Hallam wing crack mechanics and Riedel−Rice crack-tip creep. The brittle compressive strength is related to ice−ice friction. Modeling and experiment suggest that the transition strain rate of cracked ice scales as (crack size)-1.5 and that its brittle strength scales as (crack size)-0.5, at least for small specimens. Possible size effects are noted.

Eccentric impact of an ice feature: linearized model

Eccentric impacts of an ice feature against a floating or stationary offshore structure or ship are much more likely than a head-on collision. Both numerical models and analytical evaluations have demonstrated that eccentricity of impact leads to a significant decrease in the maximum ice load as compared to a head-on collision. This fact should have a great influence on the definition of the design ice load for structures subjected to impacts with moderately sized floating ice features. The present paper deals with a relatively simple model of ice-structure interaction which describes an ice feature motion in a horizontal plane (three-degrees-of-freedom model). The instant reaction force (i.e. ice failure load) is assumed to be directly proportional to indentation depth. In spite of simplicity of the model, analytical expressions for reduction in ice force due to eccentricity obtained seem to be valid for more general situations. It is shown that the relative reduction in the maximum reaction force due to impact eccentricity does not depend on the effective stiffness of contact. The influence of the frictional force on the maximum ice load has been considered as well. As it follows from the analysis of linearized model of interaction, the reduction coefficient does not change dramatically if frictional effects are taken into account. The general conclusions and results are readily illustrated by the example of interaction between homogeneous elliptical cylinder and rigid wall.