Ice fractures when subject to stress that exceeds the material failure strength. Previous studies have found that a von Mises failure criterion, which places a bound on the second invariant of the deviatoric stress tensor, is consistent with empirical data. Other studies have suggested that a scaling effect exists, such that larger sample specimens have a substantially lower failure strength, implying that estimating material strength from laboratory-scale experiments may be insufficient for glacier-scale modeling. In this paper, we analyze the stress conditions in crevasse onset regions to better understand the failure criterion and strength relevant for large-scale modeling. The local deviatoric stress is inferred using surface velocities and reanalysis temperatures, and crevasse onset regions are extracted from a remotely sensed crevasse density map. We project the stress state onto the failure plane spanned by Haigh–Westergaard coordinates, showing how failure depends on mode of stress. We find that existing crevasse data are consistent with a Schmidt–Ishlinsky failure criterion that places a bound on the absolute value of the maximal principal deviatoric stress, estimated to be

Understanding the mechanics of ice fracture is important for predicting the stability of ice sheets and glaciers, since fractures lead to crevassing, calving, and moulins

In classical failure theory, fractures form when an appropriate measure of the internal stress magnitude exceeds a critical value (material failure strength). Fracturing leads to a rapid elastic response with a redistribution of the internal stress, tending to concentrate near material defects and crack tips. Fracture propagation, and therefore ultimately the size of crevasses, is controlled by how the local stress field evolves in the presence of a crack. This kind of propagation has previously been modeled using linear elastic fracture mechanics that relies on material parameters such as the fracture toughness

There is, however, considerable discrepancy between failure strength estimates derived from lab experiments

Several failure criteria have been proposed in the literature.

In summary, there is a discrepancy between the failure strength inferred from laboratory and field observations, and multiple distinct failure criteria have been proposed. In this paper, we use a large dataset of Greenland crevasses to estimate a macro-scale failure criterion for naturally occurring glacier ice, relevant for large-scale modeling.

The spatial distribution of crevasses in Greenland from

Strain rates are derived from ice velocity measurements from the Greenland Ice Sheet Velocity Mosaic

We compare the calculated von Mises stress to BedMachine v5 ice thickness (

Average surface air temperatures from CARRA

Our aim is to relate crevassing to the local stress environment where crevasses initiate. Evidence suggests that most crevasses initiate at a depth of 15–30 m

Glen's flow law for solid ice relates the strain rate tensor to the deviatoric stress tensor (

The stress conditions where failure occurs can be represented by a three-dimensional threshold surface, spanned by the three principal stress components. For pressure-insensitive materials, the threshold surface must be reflection symmetric along the hydrostatic axis (

In the following, we will determine the failure criteria of ice by plotting principal deviatoric stresses in the

In this plane, the von Mises failure criterion appears as a circle with the radius

An alternative visualization (

Crevasses are transported with the flow, and thus not all crevasses are a product of the local stress conditions. As we are interested in the failure strength, we create a mask to select locations where crevasses have recently opened. These are defined as being located on the uphill edge of large-scale crevasse patches. We therefore apply a smoothed Sobel edge detection filter to a binary representation of the crevasse density map and select the upstream edge by requiring that the along-flow crevasse density gradient to increase. We further require the crevasse density to be smaller than 5 %. We label these as “crevassing onset” regions.

The high-elevation ice sheet interior has been excluded from the analysis using a manually traced polygon

Strain rates and stresses are calculated from long-term average ice velocities. This may not accurately reflect the conditions under which crevasses were formed since trends or seasonal variability in ice flow are unaccounted for

The spatial distribution of crevasses and the automatic detection of crevasse onset regions are shown in Fig.

The von Mises stress distribution over different subsets of the ice sheet. The counts per bin are all normalized to have the same peak height. Horizontal bars show the 5 %, 50 %, and 95 % percentiles of the distribution.

Empirical failure map showing a

Stresses are calculated assuming that ice temperatures, at the depth of crevasse initiation, can be approximated by surface air temperature as simulated by the CARRA regional reanalysis (Fig.

We find that crevasse onset regions are characterized by larger stresses than in crevasse fields in general (Fig.

We note that not every location where estimated stresses exceed the failure stress appear to be crevassed (Fig.

The empirical failure map in Fig.

In the Schmidt–Ishlinsky hypothesis, it is the largest principal deviatoric stress, rather than the magnitude of the second invariant, that defines the failure criterion:

Alternative criteria have also been proposed in the literature, such as the Coulomb criterion and the maximum strain energy dissipation criterion

In the maximum strain energy dissipation criterion

We find that ice thickness correlates positively with the von Mises stress (Fig.

The von Mises and Schmidt–Ishlinsky failure envelopes do not deviate strongly from each other, but, for a given stress magnitude, the failure criterion might be fulfilled in one case and not the other depending on the stress state: the von Mises criterion is indifferent to the stress state, whereas the Schmidt–Ishlinsky criterion favors failure by tension or compression for a given stress magnitude; that is, glacier ice appears stronger when subject to shear as opposed to tensile stresses (see Fig.

The choice of failure criterion may therefore impact where crevasses are formed in large-scale models. A popular approach is to model the evolution of the crevasse density field (or damage phase field) as a function of local conditions and couple it back into ice viscosity (e.g.,

The Schmidt–Ishlinsky criterion implies that the failure of ice depends not only on the second, but also the third invariant of the deviatoric stress,

We automatically identified crevasse onset regions from a dataset of Greenland crevasses (Fig.

This study is, to our knowledge, the first to propose a Schmidt–Ishlinsky failure criterion for glacier ice. More work is needed to validate this hypothesis using, e.g., forward modeling.

The failure strength of ice should largely be independent of location. We therefore plot the onset von Mises stress distribution by region

The calculated von Mises stress for opening crevasses varies substantially between different basins of the ice sheet. The counts per bin are all normalized to have the same peak height. Horizontal bars show the 5 %–50 %–95 % percentiles of the distribution.

Pair plot showing the relationships between various quantities extracted over regions where crevasses are opening. The variables plotted are the von Mises stress (

In this paper, we focus on the stress conditions that result in failure of glacier ice. We do not observe the stress state, but infer it from observed strain rates and our understanding of the mechanical properties of ice. In this section, we present the raw strain rate data. To investigate how the critical strain rate depends on the mode of deformation we define strain rate

Empirical failure map showing a

Crevasse density data are available from

AG conceived the study, performed computations, and wrote the first draft. AMS provided seasonal velocity amplitudes. All authors discussed the results and contributed to the final manuscript.

At least one of the (co-)authors is a member of the editorial board of

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Ice velocity maps were produced as part of the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) using Copernicus Sentinel-1 SAR images distributed by ESA and were provided by the Geological Survey of Denmark and Greenland (GEUS) at

This research has been supported by the Novo Nordisk Fond (grant no. NNF23OC0081251), the Villum Fond (grant nos. 16572 and 23261), and the Danmarks Frie Forskningsfond (grant no. 2032-00364B).

This paper was edited by Caroline Clason and reviewed by Douglas Benn and one anonymous referee.